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  1. <?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-7029771534698050015</id><updated>2024-03-13T11:31:19.969-07:00</updated><category term="Biografías"/><category term="funciones"/><category term="ecuación diferencial"/><category term="integrales"/><category term="matemáticas"/><category term="topología"/><category term="limites"/><category term="noticias matemática"/><category term="trigonometría"/><category term="análisis"/><category term="completación de cuadrados"/><category term="factorización"/><category term="planos"/><category term="rectas"/><category term="Altura de un triángulo"/><category term="Examenes"/><category term="Parábola"/><category term="UNA"/><category term="derivada"/><category term="estrella de pitagoras"/><category term="factor cuadratico irreducible"/><category term="fracción parcial"/><category term="geometría"/><category term="logaritmos"/><category term="longitud de arco"/><category term="máximos y mínimos"/><category term="serie de potencias"/><category term="transformada de laplace"/><category term="álgebra"/><title type='text'>Matemáticas para Todos</title><subtitle type='html'>Blog de matemáticas, donde podrás encontrar la información necesaria para aclarar tus dudas.</subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default?redirect=false'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><link rel='next' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default?start-index=26&amp;max-results=25&amp;redirect=false'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>95</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-688517095663668822</id><published>2017-11-13T11:23:00.000-08:00</published><updated>2017-11-21T10:40:23.501-08:00</updated><title type='text'>Técnica para graficar funciones cuadráticas</title><content type='html'>&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  2. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;Para graficar una función cuadrática, que se representa por $f:\mathbb{R}\rightarrow\mathbb{R}$,
  3. definida mediante la curva $f\left(x\right)=ax^{2}+bx+c$, con $a\neq0$, debes conocer
  4. el vértice y los puntos de corte con el eje $x$ e $y$, otro aspecto importante es saber
  5. que la representación gráfica de una función cuadrática es una parábola que puede
  6. abrir hacia arriba o abajo dependiendo del signo del coeficiente a. Existen dos
  7. casos, si $a &amp;gt; 0$ entonces la parábola abre hacia arriba, si $a &amp;lt; 0$ entonces
  8. la parábola abre hacia abajo. Después te darás cuenta que hay funciones cuadráticas
  9. que cortan con el eje x y otras no. Cuando estas aprendiendo se hace un poco complicado
  10. pero luego de varios ejercicios verás que resulta hasta divertido.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  11. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  12. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  13. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  14. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;Ante todo examina la función, es decir observa si es de la forma $
  15. f\left(x\right)=ax^{2}+bx+c $, las funciones cuadráticas se te pueden presentar
  16. de la siguiente manera&amp;nbsp; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  17. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  18. &lt;br /&gt;&lt;/div&gt;
  19. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  20. &lt;br /&gt;&lt;/div&gt;
  21. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  22. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(x\right)=ax^{2}+bx+c$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  23. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  24. &lt;br /&gt;&lt;/div&gt;
  25. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  26. &lt;br /&gt;&lt;/div&gt;
  27. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  28. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(x\right)=ax^{2}$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  29. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  30. &lt;br /&gt;&lt;/div&gt;
  31. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  32. &lt;br /&gt;&lt;/div&gt;
  33. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  34. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(x\right)=ax^{2}+c$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  35. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  36. &lt;br /&gt;&lt;/div&gt;
  37. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  38. &lt;br /&gt;&lt;/div&gt;
  39. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  40. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(x\right)=ax^{2}+bx$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  41. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  42. &lt;br /&gt;&lt;/div&gt;
  43. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  44. &lt;br /&gt;&lt;/div&gt;
  45. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  46. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;Aquí examinaremos la forma $ f\left(x\right)=ax^{2}+bx+c $&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  47. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  48. &lt;br /&gt;&lt;/div&gt;
  49. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  50. &lt;/div&gt;
  51. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  52. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;Empecemos&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  53. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  54. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  55. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  56. &lt;span style=&quot;color: red;&quot;&gt;1.&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Calcula el punto de corte con el eje $y$, esto se logra haciendo $x=0$
  57. en la función dada, observemos;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  58. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  59. &lt;br /&gt;&lt;/div&gt;
  60. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  61. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(0\right)=a\left(0\right)^{2}+b\left(0\right)+c$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  62. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  63. &lt;br /&gt;&lt;/div&gt;
  64. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  65. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$f\left(0\right)=c$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  66. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  67. &lt;br /&gt;&lt;/div&gt;
  68. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  69. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;El punto de corte con el eje $y$ siempre será $p\left(0,c\right)$.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  70. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  71. &lt;br /&gt;&lt;/div&gt;
  72. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  73. &lt;span style=&quot;color: red;&quot;&gt;2.&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Calcula el vértice. Aplica la siguiente fórmula $$V\left(-\frac{b}{2a},\frac{4ac-b^{2}}{4a}\right)$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  74. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  75. &lt;br /&gt;&lt;/div&gt;
  76. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  77. &lt;span style=&quot;color: red;&quot;&gt;3.&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Obtener el discriminante $\Delta$. $$\Delta = b^{2}-4ac$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  78. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  79. &lt;br /&gt;&lt;/div&gt;
  80. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  81. &lt;/div&gt;
  82. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  83. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;Este paso es crucial, aquí se definen varios aspectos que te permitirán construir
  84. la gráfica correctamente, observemos:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  85. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  86. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  87. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  88. &lt;span style=&quot;color: blue;&quot;&gt;3.1&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Si $\Delta &amp;gt; 0$, entonces la gráfica tiene dos puntos de corte
  89. con el eje x, para obtener estos puntos de corte debes hacer $f\left(x\right)=0$,
  90. quedando la siguiente expresión $ax^{2}+bx+c=0$, los puntos de corte son los siguientes:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  91. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  92. &lt;br /&gt;&lt;/div&gt;
  93. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  94. &lt;span style=&quot;color: windowtext;&quot;&gt;$$p_{1}\left(x_1,0\right)$$&lt;/span&gt;&lt;/div&gt;
  95. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  96. &lt;span style=&quot;color: windowtext;&quot;&gt;y&lt;/span&gt;&lt;/div&gt;
  97. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  98. $$p_{2}\left(x_2,0\right)$$&lt;/div&gt;
  99. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  100. &lt;span style=&quot;color: windowtext;&quot;&gt;donde&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
  101. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  102. &lt;span style=&quot;color: windowtext;&quot;&gt;$$x_{1}=\frac{-b+\sqrt{\Delta}}{2a}$$&lt;/span&gt;&lt;/div&gt;
  103. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  104. &lt;span style=&quot;color: windowtext;&quot;&gt;y&lt;/span&gt;&lt;/div&gt;
  105. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  106. &lt;span style=&quot;color: windowtext;&quot;&gt;$$x_{2}=\frac{-b-\sqrt{\Delta}}{2a}$$&lt;/span&gt;&lt;/div&gt;
  107. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  108. &lt;br /&gt;&lt;/div&gt;
  109. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  110. &lt;br /&gt;&lt;/div&gt;
  111. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  112. &lt;/div&gt;
  113. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  114. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&amp;nbsp;Con estos cuatro puntos --cortes
  115. con el eje $x$ e $y$ y vertice-- es suficiente para construir la gráfica de la parábola
  116. en un plano cartesiano.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  117. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  118. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  119. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  120. &lt;span style=&quot;color: blue;&quot;&gt;3.2&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Si $\Delta = 0$, entonces la gráfica tiene un solo punto de corte
  121. con el eje x, es el siguiente:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  122. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  123. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&amp;nbsp; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  124. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  125. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;$$p_{1}\left(-\frac{b}{2a},0\right)$$&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  126. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  127. &lt;br /&gt;&lt;/div&gt;
  128. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  129. &lt;span lang=&quot;EN-US&quot; style=&quot;color: windowtext; mso-ansi-language: EN-US; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;En este caso debes
  130. construir una tabla de valores, con 5 valores es suficiente, estos valores no deben
  131. ser arbitrarios, deben estar condicionados a un valor central que será el valor
  132. que corresponde a la abscisa del vértice, o sea, el valor x del vértice&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  133. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  134. &lt;br /&gt;&lt;/div&gt;
  135. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  136. &lt;/div&gt;
  137. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  138. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&amp;nbsp;Ejemplo: Si el vértice es $V\left(\frac{3}{2},-4\right)$
  139. usted selecciona como valor central de la tabla a $x=\frac{3}{2}$, observa como
  140. quedaría la tabla de valores&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  141. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  142. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  143. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  144. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGS6v4eAu0iu4IeujrbjGNBsw4EMhQqBjkXSk6IomuTUEZXSfShUjUTtOaHjR3uOxCqkZ5yehNMgzRuHWnuxUghYqB6OcnPs4_iYR6yzoDNAevAWcrW0CUVO1VrokpFq4Gd3X-q1y74QQ/s1600/tabla.png&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;60&quot; data-original-width=&quot;241&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGS6v4eAu0iu4IeujrbjGNBsw4EMhQqBjkXSk6IomuTUEZXSfShUjUTtOaHjR3uOxCqkZ5yehNMgzRuHWnuxUghYqB6OcnPs4_iYR6yzoDNAevAWcrW0CUVO1VrokpFq4Gd3X-q1y74QQ/s1600/tabla.png&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  145. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  146. &lt;br /&gt;&lt;/div&gt;
  147. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  148. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;La idea es básica, debes seleccionar los enteros inmediatos a la derecha
  149. e izquierda del valor correspondiente al x del vertice. Si el vertice fuera&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;color: windowtext;&quot;&gt;$V\left(\frac{1}{2},-4\right)$, seleccionarías para la tabla -1, 0, 1/2,
  150. 1, 2.&lt;/span&gt;&lt;/div&gt;
  151. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  152. &lt;br /&gt;&lt;/div&gt;
  153. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  154. &lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt;De inmediato debes completar la tabla calculando los $f\left(x\right)$ correspondientes,
  155. posteriormente grafica estos valores junto al corte con el eje $y$ en un plano cartesiano
  156. y obtendrás la gráfica deseada.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  157. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  158. &lt;br /&gt;&lt;/div&gt;
  159. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  160. &lt;br /&gt;&lt;/div&gt;
  161. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; text-align: justify;&quot;&gt;
  162. &lt;/div&gt;
  163. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  164. &lt;span style=&quot;color: blue;&quot;&gt;3.3&lt;/span&gt;&lt;span style=&quot;color: windowtext; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: ES-VE;&quot;&gt; Si $\Delta &amp;lt; 0$,
  165. entonces la gráfica no tiene puntos de corte con el eje x, en este caso se debe
  166. construir la misma tabla de valores del paso anterior y graficar los valores de
  167. esta tabla junto al corte con el eje $y$.&lt;/span&gt;&lt;/div&gt;
  168. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  169. &lt;br /&gt;
  170. Próximamente estaré editando un ejemplo para que visualicen mejor la idea. Nos vemos.&lt;/div&gt;
  171. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/688517095663668822/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2017/11/tecnica-para-graficar-funciones.html#comment-form' title='1 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/688517095663668822'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/688517095663668822'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2017/11/tecnica-para-graficar-funciones.html' title='Técnica para graficar funciones cuadráticas'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGS6v4eAu0iu4IeujrbjGNBsw4EMhQqBjkXSk6IomuTUEZXSfShUjUTtOaHjR3uOxCqkZ5yehNMgzRuHWnuxUghYqB6OcnPs4_iYR6yzoDNAevAWcrW0CUVO1VrokpFq4Gd3X-q1y74QQ/s72-c/tabla.png" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-3352849044858299450</id><published>2017-11-10T06:58:00.000-08:00</published><updated>2017-11-10T11:33:00.404-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="factor cuadratico irreducible"/><title type='text'>Factor cuadrático irreducible</title><content type='html'>Es importante conocer cuando una expresión cuadrática es un factor irreducible, esto nos permite saber si esta expresión es factorizable o no. Por ejemplo,&lt;br /&gt;
  172. &lt;br /&gt;
  173. $s^{2}-2s+5$ ¿Será factorizable? La respuesta es no. Veremos de inmediato, obtenemos el discriminante delta&lt;br /&gt;
  174. &lt;br /&gt;
  175. $$\triangle=b^{2}-4ac$$&lt;br /&gt;
  176. &lt;br /&gt;
  177. A partir del valor de este discriminante, o sea, si&amp;nbsp; $\Delta &amp;gt; 0$, $\Delta &amp;lt; 0$ o $\Delta = 0$, podemos identificar si el factor es irreducible, en este caso es necesario que $\Delta$ sea negativo, es decir, $\Delta &amp;lt; 0$. Examinemos nuestro ejemplo:&lt;br /&gt;
  178. &lt;br /&gt;
  179. $$s^{2}-2s+5$$&lt;br /&gt;
  180. &lt;br /&gt;
  181. para este caso $a=1$, $b=-2$ y $c=5$, calculando el discriminante&lt;br /&gt;
  182. &lt;br /&gt;
  183. $$\Delta=\left(-2\right)^{2}-4*1*5$$&lt;br /&gt;
  184. $$\Delta=-16$$&lt;br /&gt;
  185. $$\Delta &amp;lt; 0$$&lt;br /&gt;
  186. &lt;br /&gt;
  187. Esto indica que el factor cuadrático es irreducible por lo tanto aseguramos que la expresión no es factorizable en términos elementales, para estos casos podemos aplicar la técnica de&amp;nbsp;&lt;span style=&quot;color: red;&quot;&gt;&lt;a href=&quot;https://linaresgsj.blogspot.com/2011/02/completacion-de-cuadrados.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;completación de cuadrados&lt;/span&gt;&lt;/a&gt;&amp;nbsp;&lt;/span&gt;para realizar cualquier otro cálculo.&lt;br /&gt;
  188. &lt;span style=&quot;color: red;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  189. &lt;span style=&quot;color: red;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  190. &lt;span style=&quot;color: red;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  191. &lt;span style=&quot;color: red;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/3352849044858299450/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2017/11/factor-cuadratico-irreducible.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3352849044858299450'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3352849044858299450'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2017/11/factor-cuadratico-irreducible.html' title='Factor cuadrático irreducible'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-3611236730052664264</id><published>2017-10-20T13:09:00.000-07:00</published><updated>2017-11-02T11:35:08.572-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="fracción parcial"/><category scheme="http://www.blogger.com/atom/ns#" term="transformada de laplace"/><title type='text'>Fracciones parciales aplicada a la transformada inversa de Laplace</title><content type='html'>El método de fracciones parciales es bien conocido, sin embargo, cuando se aplica a la transformada de Laplace y estamos en presencia de factores cuadráticos irreducibles cambia un poco, observemos:&lt;br /&gt;
  192. &lt;br /&gt;
  193. Supongamos que queremos calcular la siguiente expresión&lt;br /&gt;
  194. &lt;br /&gt;
  195. $$\mathcal{L}^{-1}\left\{ \frac{2s^{2}+10s}{\left(s^{2}-2s+5\right)\left(s+1\right)}\right\}&lt;br /&gt;
  196. &amp;nbsp;$$&lt;br /&gt;
  197. &lt;br /&gt;
  198. Como la expresión&amp;nbsp; $\left(s^{2}-2s+5\right)$ es un factor cuadrático irreducible, entonces el método clásico de descomposición en fracciones parciales quedaría&lt;br /&gt;
  199. &lt;br /&gt;
  200. $$\frac{2s^{2}+10s}{\left(s^{2}-2s+5\right)\left(s+1\right)}=\frac{As+B}{s^{2}-2s+5}+\frac{C}{s+1}&lt;br /&gt;
  201. &amp;nbsp;$$&lt;br /&gt;
  202. &lt;br /&gt;
  203. Ahora trataremos de calcular la inversa&lt;br /&gt;
  204. &lt;br /&gt;
  205. $$\mathcal{L}^{-1}\left\{ \frac{2s^{2}+10s}{\left(s^{2}-2s+5\right)\left(s+1\right)}\right\} =\mathcal{L}^{-1}\left\{ \frac{As+B}{s^{2}-2s+5}+\frac{C}{s+1}\right\}&lt;br /&gt;
  206. &amp;nbsp;$$&lt;br /&gt;
  207. &lt;br /&gt;
  208. $=\mathcal{L}^{-1}\left\{ \frac{As}{s^{2}-2s+5}+\frac{B}{s^{2}-2s+5}+\frac{C}{s+1}\right\}&lt;br /&gt;
  209. &amp;nbsp;$&lt;br /&gt;
  210. &lt;br /&gt;
  211. $=A\mathcal{L}^{-1}\left\{ \frac{s}{s^{2}-2s+5}\right\} +B\mathcal{L}^{-1}\left\{ \frac{1}{s^{2}-2s+5}\right\} +C\mathcal{L}^{-1}\left\{ \frac{1}{s+1}\right\}&lt;br /&gt;
  212. &amp;nbsp;$&lt;br /&gt;
  213. &lt;br /&gt;
  214. La primera y segunda transformada son un poco complicadas de desarrollar, se requiere de algunos artificios matemáticos, por esta razón&amp;nbsp; no considero que el método clásico de fracción parcial sea conveniente, en cambio, utilizaremos el siguiente:&lt;br /&gt;
  215. &lt;br /&gt;
  216. Este método consiste en la utilización de la &lt;a href=&quot;https://linaresgsj.blogspot.com/2011/02/completacion-de-cuadrados.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;completación de cuadrados&lt;/span&gt;&lt;/a&gt;&amp;nbsp;para nuestro caso el factor $\left(s^{2}-2s+5\right)$ queda $\left(s-1\right)^{2}+4$, ahora&lt;br /&gt;
  217. &lt;br /&gt;
  218. $$\mathcal{L}^{-1}\left\{ \frac{2s^{2}+10s}{\left[\left(s-1\right)^{2}+4\right]\left(s+1\right)}\right\} =\mathcal{L}^{-1}\left\{ \frac{A\left(s-1\right)+2B}{\left(s-1\right)^{2}+4}+\frac{C}{s+1}\right\}&lt;br /&gt;
  219. &amp;nbsp;$$&lt;br /&gt;
  220. Observación: el término que acompaña a $A$&amp;nbsp; y a $B$ es la raiz cuadrada de cada uno de los elementos del denominador.&lt;br /&gt;
  221. &lt;br /&gt;
  222. $=\mathcal{L}^{-1}\left\{ \frac{A\left(s-1\right)}{\left(s-1\right)^{2}+4}+\frac{2B}{\left(s-1\right)^{2}+4}+\frac{C}{s+1}\right\}&lt;br /&gt;
  223. &amp;nbsp;$&lt;br /&gt;
  224. &lt;br /&gt;
  225. $=\mathcal{L}^{-1}\left\{ \frac{A\left(s-1\right)}{\left(s-1\right)^{2}+4}\right\} +\mathcal{L}^{-1}\left\{ \frac{2B}{\left(s-1\right)^{2}+4}\right\} +\mathcal{L}^{-1}\left\{ \frac{C}{s+1}\right\}&lt;br /&gt;
  226. &amp;nbsp;$&lt;br /&gt;
  227. &lt;br /&gt;
  228. $=A\mathcal{L}^{-1}\left\{ \frac{\left(s-1\right)}{\left(s-1\right)^{2}+4}\right\} +B\mathcal{L}^{-1}\left\{ \frac{2}{\left(s-1\right)^{2}+4}\right\} +C\mathcal{L}^{-1}\left\{ \frac{1}{s+1}\right\}&lt;br /&gt;
  229. &amp;nbsp;$&lt;br /&gt;
  230. &lt;br /&gt;
  231. Ahora, estas transformadas son conocidas y pueden calcularse&lt;br /&gt;
  232. &lt;br /&gt;
  233. $=Ae^{t}cos\left(2t\right)+Be^{t}sen\left(2t\right)+Ce^{-t}&lt;br /&gt;
  234. &amp;nbsp;$.&lt;br /&gt;
  235. &lt;br /&gt;
  236. &lt;br /&gt;
  237. &lt;br /&gt;
  238. &lt;br /&gt;
  239. &lt;br /&gt;
  240. &lt;br /&gt;
  241. &lt;br /&gt;
  242. &lt;br /&gt;
  243. &lt;br /&gt;
  244. &lt;br /&gt;
  245. &lt;br /&gt;
  246. &lt;br /&gt;
  247. &lt;br /&gt;
  248. &lt;br /&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/3611236730052664264/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2017/10/fracciones-parciales-aplicada-la.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3611236730052664264'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3611236730052664264'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2017/10/fracciones-parciales-aplicada-la.html' title='Fracciones parciales aplicada a la transformada inversa de Laplace'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-2709050294849576506</id><published>2015-02-26T14:54:00.000-08:00</published><updated>2015-02-26T15:34:53.764-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="derivada"/><title type='text'>Derivada | Función Cociente</title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  249. En esta oportunidad resolveremos la derivada de una función cociente, quizá para muchos este ejemplo que daremos a continuación sea muy simple, pero usted debe de recordar que lo simple para unos puede ser muy complejo para otros, aquí mostramos la función cociente a resolver o muchas veces llamada función racional:&lt;/div&gt;
  250. &lt;br /&gt;
  251. &lt;b&gt;&lt;span style=&quot;font-size: large;&quot;&gt;$$y=\frac{2x}{1-x^{2}}$$&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  252. &lt;div style=&quot;text-align: justify;&quot;&gt;
  253. Imaginemos que tenemos que resolver la función anterior y que no nos han dicho que se trata de una función racional, entonces se detecta automáticamente que la expresión es una función racional ¿Por qué? ya que es la división de dos funciones polinomiales, ahora echaremos un vistazo a la tabla de derivadas, especificamente a la derivada de un cociente, esto es normal hacerlo debido que para aprendices y en ciertos casos expertos tienen que recurrir generalmente a una tabla de derivadas para facilitar el calculo&lt;/div&gt;
  254. &lt;div style=&quot;text-align: justify;&quot;&gt;
  255. &lt;br /&gt;&lt;/div&gt;
  256. &lt;div style=&quot;text-align: justify;&quot;&gt;
  257. $$Y=\frac{h(x)}{g(x)} \rightarrow Y&#39; =\frac{h&#39;(x)*g(x)-h(x)*g&#39;(x)}{[g(x)]^{2}}$$&lt;/div&gt;
  258. &lt;div style=&quot;text-align: justify;&quot;&gt;
  259. &lt;br /&gt;&lt;/div&gt;
  260. &lt;div style=&quot;text-align: justify;&quot;&gt;
  261. Esta fórmula será aplicada al ejercicio, tenemos:&lt;/div&gt;
  262. &lt;div style=&quot;text-align: justify;&quot;&gt;
  263. &lt;br /&gt;&lt;/div&gt;
  264. &lt;b&gt;&lt;span style=&quot;font-size: large;&quot;&gt;$y&#39; = \frac{(2x)&#39;(1-x^{2})-2x(1-x^{2})&#39;}{(1-x^{2})^{2}}$&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  265. &lt;b&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  266. ahora vamos a resolver las derivadas que quedaron pendientes, o sea, aquella que tienen el apóstrofo&lt;br /&gt;
  267. &lt;br /&gt;
  268. &lt;span style=&quot;font-size: large;&quot;&gt;$y&#39;=\frac{2(1-x^{2})-2x(-2x)}{(1-x^{2})^{2}}$&lt;/span&gt;&lt;br /&gt;
  269. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  270. Resolviendo operaciones algebraicas&lt;br /&gt;
  271. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  272. &lt;span style=&quot;font-size: large;&quot;&gt;$y&#39;=\frac{2-2x^{2}+4x^{2}}{(1-x^{2})^{2}}$&lt;/span&gt;&lt;br /&gt;
  273. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  274. &lt;span style=&quot;font-size: large;&quot;&gt;$y&#39;=\frac{2+2x^{2}}{(1-x^{2})^{2}}$&lt;/span&gt;&lt;br /&gt;
  275. &lt;br /&gt;
  276. Y este resultado final es la derivada de la función.&lt;br /&gt;
  277. &lt;br /&gt;
  278. &lt;b&gt;Entradas Interesantes&lt;/b&gt;&lt;br /&gt;
  279. &lt;span style=&quot;background-color: yellow;&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/tabla-de-derivadas.html&quot; target=&quot;_blank&quot;&gt;Tabla de derivadas&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
  280. &lt;a href=&quot;http://linaresgsj.blogspot.com/2011/02/completacion-de-cuadrados.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;background-color: yellow; color: black;&quot;&gt;Completacion de Cuadrados&lt;/span&gt;&lt;/a&gt;&lt;br /&gt;
  281. &lt;a href=&quot;http://linaresgsj.blogspot.com/p/blog-page_11.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;background-color: yellow; color: black;&quot;&gt;Gana Dinero&lt;/span&gt;&lt;/a&gt;&lt;br /&gt;
  282. &lt;b&gt;&lt;br /&gt;&lt;/b&gt;
  283. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/2709050294849576506/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/derivada-funcion-cociente.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2709050294849576506'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2709050294849576506'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/derivada-funcion-cociente.html' title='Derivada | Función Cociente'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-5205676819542439447</id><published>2015-02-16T11:22:00.000-08:00</published><updated>2015-02-17T14:05:21.800-08:00</updated><title type='text'>Intercambios | Referidos Directos </title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  284. Hola amig@s aquí os traigo otra forma de adquirir referidos directos para sus PTC&#39;s. Como siempre os digo, este sitio fue creado para aquellas personas que no poseen un blog o pagina web donde puedan hacer publicidad a sus banner o enlaces Ptc. En esta oportunidad les cuento que la mayoría de las personas al iniciarse en el mundo de las PTC&#39;s solo poseen una cuenta en la PTC de su preferencia, bien sea porque un amigo los instruyó o ellos mismos se aventuraron a este mundo. Al pasar el tiempo y tener éxito en sus cuentas ellos comienzan a entender como se maneja estos sistema y muchas veces poseen 2, 3 o mas cuentas en otras PTC. Todos sabemos lo importante y a veces complicado de conseguir &lt;b&gt;REFERIDOS DIRECTOS &lt;/b&gt;mas aun cuando poseemos varias cuentas ya que debes conseguir referidos para todas las cuentas. Te recomiendo que si eres de esas personas que vas a empezar a tener varias cuentas aun no lo hagas, seria bueno empezar aunque sea con un referido directo, Aquí te traigo mi Método:&lt;/div&gt;
  285. &lt;div style=&quot;text-align: justify;&quot;&gt;
  286. &lt;br /&gt;&lt;/div&gt;
  287. &lt;div style=&quot;text-align: justify;&quot;&gt;
  288. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 1: Rellena el Formulario que está al Final, E&lt;/span&gt;&lt;/b&gt;&lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;n el &quot;asunto&quot; coloca la&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  289. &lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;PTC para &amp;nbsp;la cual usted desea hacer el cambio&lt;/span&gt;&lt;/b&gt;&lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp;y en el cuadro grande&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  290. &lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;coloca el Codigo HTML&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;de tu banner.&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  291. &lt;div style=&quot;text-align: justify;&quot;&gt;
  292. &lt;b style=&quot;background-color: white;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;span style=&quot;line-height: 20.533332824707px;&quot;&gt;PASO 2:&amp;nbsp;Envía&amp;nbsp;en Formulario.&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  293. &lt;div style=&quot;text-align: justify;&quot;&gt;
  294. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 3: Espera que publique tu Banner en mi Blog --&lt;a href=&quot;http://linaresgsj.blogspot.com/p/intercambios-ptc-publicados.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Ver Aquí&lt;/span&gt;&lt;/a&gt;-- este proceso&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  295. &lt;div style=&quot;text-align: justify;&quot;&gt;
  296. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; puede durar 24 horas y está regido por orden de llegada.&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  297. &lt;div style=&quot;text-align: justify;&quot;&gt;
  298. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 4: Una vez que veas tu banner Publicado comparte el enlace donde&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  299. &lt;div style=&quot;text-align: justify;&quot;&gt;
  300. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; aparece tu Banner en tus redes sociales.&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  301. &lt;div style=&quot;text-align: justify;&quot;&gt;
  302. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 5: Listo&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  303. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  304. &lt;span style=&quot;background-color: white;&quot;&gt;&lt;span style=&quot;font-family: Times, Times New Roman, serif;&quot;&gt;&lt;span style=&quot;line-height: 20.533332824707px;&quot;&gt;Nota: Una vez que veas tu banner publicado en mi blog empieza a publicar el enlace donde aparece tu banner en redes sociales de tu preferencia,&amp;nbsp;tendrás unos días&amp;nbsp;ante que lo retire, si en esos&amp;nbsp;días&amp;nbsp;no has&amp;nbsp;logrado tu intercambio, puedes solicitarme que coloque tu banner de nuevo, con este&amp;nbsp;método&amp;nbsp;vas a llegar a miles y tal vez millones de&amp;nbsp;posibles REFERIDOS DIRECTOS ya que los otros usuarios&amp;nbsp;harán&amp;nbsp;lo mismo.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  305. &lt;div style=&quot;text-align: justify;&quot;&gt;
  306. &lt;b&gt;&lt;br /&gt;&lt;/b&gt;
  307. &lt;span style=&quot;font-size: large;&quot;&gt;
  308. &lt;b&gt;REFERIDOS DIRECTOS&lt;/b&gt;&lt;/span&gt;&lt;br /&gt;
  309. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
  310. &lt;iframe allowtransparency=&quot;true&quot; frameborder=&quot;0&quot; src=&quot;http://www.suformulario.com/formulario.php?id=OTI0OQ%3D%3D&quot; style=&quot;background-color: transparent; border-width: 0px; height: 500px; width: 500px;&quot;&gt;
  311. &lt;/iframe&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/5205676819542439447/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/intercambios-referidos-directos.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5205676819542439447'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5205676819542439447'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/intercambios-referidos-directos.html' title='Intercambios | Referidos Directos '/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-211842187558975963</id><published>2015-02-15T14:43:00.002-08:00</published><updated>2015-02-18T10:38:43.326-08:00</updated><title type='text'>Referidos Directos</title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  312. Hola amigos, de todas las comunidades PTC&#39;s --sin excepción-- Este sitio fue creado para ayudar aquellas personas que no tienen la posibilidad de tener un blog o sitio web a su disposición para hacer publicidad a sus banner, herramienta que brinda toda PTC a sus usuarios. Utilizar este sitio es muy fácil ya os mostrare. Aquí les muestro una forma de obtener REFERIDOS DIRECTOS, cosa que como sabemos es un poco complicado ya que pocas personas están dispuesto a registrarse en sitios que solo pagan centavos de dolares o centavos de otra moneda, estas personas no lo hacen por desconocimiento de estrategias y por mala información. Ellos desconocen el manejo de una PTC y como muchas personas --lamentablemente-- &amp;nbsp;juzgan sin saber o en otras palabras juzgan a ciegas.&lt;br /&gt;
  313. &lt;br /&gt;
  314. &lt;b&gt;&lt;span style=&quot;background-color: white; text-align: start;&quot;&gt;&lt;span style=&quot;color: #444444; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 15px; line-height: 20px;&quot;&gt;Este Método basa su funcionamiento en el sistema de la duplicación, en este caso duplicación de banner para cualquier Ptc, me&amp;nbsp;envías&amp;nbsp;tu banner, YO lo publico de numero 1&amp;nbsp;en la lista del blog&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;--&lt;a href=&quot;http://linaresgsj.blogspot.com/p/ptcs-publicadas.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Ver Aquí&lt;/span&gt;&lt;/a&gt;-- TU&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 20.533332824707px; text-align: start;&quot;&gt;&lt;span style=&quot;color: #444444; font-size: 15px; line-height: 20px;&quot;&gt;&amp;nbsp;promueves el enlace donde aparece tu banner, en sitios web, foros, youtube, facebook y en poco tiempo tu banner se habrá duplicado automáticamente muchas veces ya que otras personas estaran haciendo lo mismo.&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&lt;/b&gt;&lt;/div&gt;
  315. &lt;div style=&quot;text-align: justify;&quot;&gt;
  316. &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;/div&gt;
  317. &lt;div style=&quot;text-align: justify;&quot;&gt;
  318. Lo mas interesante de este método que voy a mostraros es que es TOTALMENTE GRATIS, no pagaras ni un centavo para anunciar tu PTC, solamente debes promover el link donde aparece tu banner en redes sociales y esto va en beneficio a la obtención de tus REFERIDOS DIRECTOS.&lt;br /&gt;
  319. &lt;br /&gt;
  320. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 1: Rellena el Formulario que está al Final, E&lt;/span&gt;&lt;/b&gt;&lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;n el cuadro azul grande&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  321. &lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; debajo de &quot;pagina web&quot; coloca el Codigo HTML de tu banner.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  322. &lt;b style=&quot;background-color: white;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;span style=&quot;line-height: 20.533332824707px;&quot;&gt;PASO 2:&amp;nbsp;Envía&amp;nbsp;en Formulario.&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  323. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 3: Espera que publique tu Banner en mi Blog --&lt;a href=&quot;http://linaresgsj.blogspot.com/p/ptcs-publicadas.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Ver Aquí&lt;/span&gt;&lt;/a&gt;-- este proceso&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  324. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; puede durar 24 horas y está regido por orden de llegada.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  325. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 4: Una vez que veas tu banner Publicado comparte el enlace donde&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  326. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; aparece tu Banner en tus redes sociales.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  327. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 5: Listo&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  328. &lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;Nota: Una vez que veas tu banner publicado en mi blog empieza a publicar el enlace donde aparece tu banner en redes sociales de tu preferencia,&amp;nbsp;tendrás 1 días&amp;nbsp;ante que lo retire, con este&amp;nbsp;método&amp;nbsp;vas a llegar a miles y tal vez millones de&amp;nbsp;posibles REFERIDOS DIRECTOS ya que los otros usuarios&amp;nbsp;harán&amp;nbsp;lo mismo.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  329. &lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  330. &lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  331. &lt;br /&gt;
  332. &lt;div&gt;
  333. &lt;/div&gt;
  334. &lt;/div&gt;
  335. &lt;b&gt;REFERIDOS DIRECTOS&lt;/b&gt;
  336. &lt;iframe allowtransparency=&quot;true&quot; frameborder=&quot;0&quot; src=&quot;http://www.suformulario.com/formulario.php?id=OTIyMA%3D%3D&quot; style=&quot;background-color: transparent; border-width: 0px; height: 500px; width: 500px;&quot;&gt;
  337. &lt;/iframe&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/211842187558975963/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/referidos-directos_15.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/211842187558975963'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/211842187558975963'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/referidos-directos_15.html' title='Referidos Directos'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-3964801826159086682</id><published>2015-02-15T12:44:00.000-08:00</published><updated>2015-02-17T14:12:04.070-08:00</updated><title type='text'>Anuncia tu banner PTC Gratis</title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  338. Hola amigos, de todas las comunidades PTC&#39;s --sin excepción-- Este sitio fue creado para ayudar aquellas personas que no tienen la posibilidad de tener un blog o sitio web a su disposición para hacer publicidad a sus banner, herramienta que brinda toda PTC a sus usuarios. Utilizar este sitio es muy fácil ya os mostrare. Aquí les muestro una forma de obtener REFERIDOS DIRECTOS, cosa que como sabemos es un poco complicado ya que pocas personas están dispuesto a registrarse en sitios que solo pagan centavos de dolares o centavos de otra moneda, estas personas no lo hacen por desconocimiento de estrategias y por mala información. Ellos desconocen el manejo de una PTC y como muchas personas --lamentablemente-- &amp;nbsp;juzgan sin saber o en otras palabras juzgan a ciegas.&lt;br /&gt;
  339. &lt;br /&gt;
  340. &lt;b&gt;&lt;span style=&quot;background-color: white; text-align: start;&quot;&gt;&lt;span style=&quot;color: #444444; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 15px; line-height: 20px;&quot;&gt;Este Método basa su funcionamiento en el sistema de la duplicación, en este caso duplicación de banner para cualquier Ptc, me&amp;nbsp;envías&amp;nbsp;tu banner, YO lo publico de numero 1&amp;nbsp;en la lista del blog&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;--&lt;a href=&quot;http://linaresgsj.blogspot.com/p/ptcs-publicadas.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Ver Aquí&lt;/span&gt;&lt;/a&gt;-- TU&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 20.533332824707px; text-align: start;&quot;&gt;&lt;span style=&quot;color: #444444;&quot;&gt;&lt;span style=&quot;font-size: 15px; line-height: 20px;&quot;&gt;&amp;nbsp;promueves el enlace donde aparece tu banner, en sitios web, foros, youtube, facebook y en poco tiempo tu banner se habrá duplicado automáticamente muchas veces ya que otras personas&amp;nbsp;estarán&amp;nbsp;haciendo lo mismo.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; &amp;nbsp;&lt;/b&gt;&lt;br /&gt;
  341. &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/div&gt;
  342. &lt;div style=&quot;text-align: justify;&quot;&gt;
  343. Lo mas interesante de este método que te estoy mostrando es que es TOTALMENTE GRATIS, no pagaras ni un centavo para anunciar tu PTC, solamente debes promover el enlace donde aparece tu banner, eso va en beneficio a la obtención de tus REFERIDOS DIRECTOS.&lt;/div&gt;
  344. &lt;div style=&quot;text-align: justify;&quot;&gt;
  345. &lt;br /&gt;
  346. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 1: Rellena el Formulario que está al Final, E&lt;/span&gt;&lt;/b&gt;&lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;n el cuadro azul grande&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  347. &lt;b style=&quot;background-color: white; line-height: 20.533332824707px;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; debajo de &quot;pagina web&quot; coloca el Codigo HTML de tu banner.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  348. &lt;b style=&quot;background-color: white;&quot;&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;span style=&quot;line-height: 20.533332824707px;&quot;&gt;PASO 2:&amp;nbsp;Envía&amp;nbsp;en Formulario.&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  349. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 3: Espera que publique tu Banner en mi Blog --&lt;a href=&quot;http://linaresgsj.blogspot.com/p/ptcs-publicadas.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Ver Aquí&lt;/span&gt;&lt;/a&gt;-- este proceso&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  350. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; puede durar 24 horas y está regido por orden de llegada.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  351. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 4: Una vez que veas tu banner Publicado comparte el enlace donde&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  352. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; aparece tu Banner en tus redes sociales.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  353. &lt;b&gt;&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;PASO 5: Listo&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  354. &lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;Nota: Una vez que veas tu banner publicado en mi blog empieza a publicar el enlace donde aparece tu banner en redes sociales de tu preferencia,&amp;nbsp;tendrás 1 días&amp;nbsp;ante que lo retire, con este&amp;nbsp;método&amp;nbsp;vas a llegar a miles y tal vez millones de&amp;nbsp;posibles REFERIDOS DIRECTOS ya que los otros usuarios&amp;nbsp;harán&amp;nbsp;lo mismo.&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
  355. &lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  356. &lt;b&gt;&lt;span style=&quot;font-size: x-small;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;
  357. &lt;br /&gt;
  358. &lt;div&gt;
  359. &lt;/div&gt;
  360. &lt;/div&gt;
  361. &lt;b&gt;REFERIDOS DIRECTOS&lt;/b&gt;
  362. &lt;iframe allowtransparency=&quot;true&quot; frameborder=&quot;0&quot; src=&quot;http://www.suformulario.com/formulario.php?id=OTIyMA%3D%3D&quot; style=&quot;background-color: transparent; border-width: 0px; height: 500px; width: 500px;&quot;&gt;
  363. &lt;/iframe&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/3964801826159086682/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/anuncia-tu-ptc-gratis-referidos-directos.html#comment-form' title='1 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3964801826159086682'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3964801826159086682'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2015/02/anuncia-tu-ptc-gratis-referidos-directos.html' title='Anuncia tu banner PTC Gratis'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-100047916591346871</id><published>2014-12-09T21:51:00.003-08:00</published><updated>2014-12-09T21:55:27.972-08:00</updated><title type='text'>Tipos de Variables</title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  364. Según su naturaleza, las variables pueden ser &lt;span style=&quot;color: red;&quot;&gt;cuantitativas&lt;/span&gt; y &lt;span style=&quot;color: red;&quot;&gt;cualitativas&lt;/span&gt;:&lt;/div&gt;
  365. &lt;div style=&quot;text-align: justify;&quot;&gt;
  366. &lt;br /&gt;&lt;/div&gt;
  367. &lt;div style=&quot;text-align: justify;&quot;&gt;
  368. &lt;span style=&quot;color: red;&quot;&gt;Cuantitativas:&lt;/span&gt; son aquellas que se expresan en valores o datos numéricos.&lt;/div&gt;
  369. &lt;div style=&quot;text-align: justify;&quot;&gt;
  370. &lt;br /&gt;&lt;/div&gt;
  371. &lt;div style=&quot;text-align: justify;&quot;&gt;
  372. Ejemplos: Cantidad de habitantes en una región, notas o calificaciones estudiantiles, número de personas que pertenecen a un partido político, tiempo empleado en un trabajo.&lt;/div&gt;
  373. &lt;div style=&quot;text-align: justify;&quot;&gt;
  374. &lt;br /&gt;&lt;/div&gt;
  375. &lt;div style=&quot;text-align: justify;&quot;&gt;
  376. Así mismo,las variables cuantitativas se clasifican en discretas y continuas.&lt;/div&gt;
  377. &lt;div style=&quot;text-align: justify;&quot;&gt;
  378. &lt;br /&gt;&lt;/div&gt;
  379. &lt;div style=&quot;text-align: justify;&quot;&gt;
  380. Discretas: son las que asumen valores o cifras enteras.&lt;/div&gt;
  381. &lt;div style=&quot;text-align: justify;&quot;&gt;
  382. &lt;br /&gt;&lt;/div&gt;
  383. &lt;div style=&quot;text-align: justify;&quot;&gt;
  384. Ejemplos: cantidad de estudiantes en una aula de clases -pueden ser 39,40 ó 41, pero nunca 40,7 estudiantes-; otro ejemplo es la cantidad de libros que pueden ser consultados, ya que nunca podrá revisar 25,3 libros, pero si podrá consultar 25 ó 26.&lt;/div&gt;
  385. &lt;div style=&quot;text-align: justify;&quot;&gt;
  386. &lt;br /&gt;&lt;/div&gt;
  387. &lt;div style=&quot;text-align: justify;&quot;&gt;
  388. Continuas: son aquellas que adoptan números fraccionados o decimales. Ejemplos: la temperatura ambiental puede alcanzar 32,4 °C. Un objeto puede medir 58,6 cm de alto.&lt;/div&gt;
  389. &lt;div style=&quot;text-align: justify;&quot;&gt;
  390. &lt;br /&gt;&lt;/div&gt;
  391. &lt;div style=&quot;text-align: justify;&quot;&gt;
  392. &lt;span style=&quot;color: red;&quot;&gt;Cualitativas&lt;/span&gt; : también llamadas categóricas, son características o atributos que se expresan de forma verbal -no numérica-, es decir, mediante palabras. Éstas pueden ser:&lt;/div&gt;
  393. &lt;div style=&quot;text-align: justify;&quot;&gt;
  394. &lt;br /&gt;&lt;/div&gt;
  395. &lt;div style=&quot;text-align: justify;&quot;&gt;
  396. Dicotómicas: se presentan en sólo dos clases o categorías. Ejemplos: género: masculino o femenino; tipos de escuelas: públicas o privadas; procedencia de un producto: nacional o importado; tipos de vehículos: automático o sincrónico.&lt;/div&gt;
  397. &lt;div style=&quot;text-align: justify;&quot;&gt;
  398. &lt;br /&gt;&lt;/div&gt;
  399. &lt;div style=&quot;text-align: justify;&quot;&gt;
  400. Policotómicas: se manifiestan en más de dos categorías. Ejemplos: marcas de computadoras, colores de tintas, tipos de empresas, clases sociales.&lt;/div&gt;
  401. &lt;div style=&quot;text-align: justify;&quot;&gt;
  402. &lt;br /&gt;&lt;/div&gt;
  403. &lt;div style=&quot;text-align: justify;&quot;&gt;
  404. fuente: Fidias Arias. El proyecto de Investigación. 6ta ed. Editorial Episteme.&lt;/div&gt;
  405. &lt;br /&gt;
  406. &lt;br /&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/100047916591346871/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/12/tipos-de-variables.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/100047916591346871'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/100047916591346871'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/12/tipos-de-variables.html' title='Tipos de Variables'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-6642907933084329903</id><published>2014-07-14T13:54:00.002-07:00</published><updated>2014-07-14T14:02:12.872-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="análisis"/><category scheme="http://www.blogger.com/atom/ns#" term="topología"/><title type='text'>Conjuntos Compactos en $\mathbb{R}$</title><content type='html'>&lt;div style=&quot;text-align: justify;&quot;&gt;
  407. Se dice que un conjunto de $F$ de $\mathbb{R}$ es Compacto si toda cubierta abierta de  $F$ tiene una subcubierta finita.&lt;/div&gt;
  408. &lt;div style=&quot;text-align: justify;&quot;&gt;
  409. &lt;br /&gt;&lt;/div&gt;
  410. &lt;div style=&quot;text-align: justify;&quot;&gt;
  411. Examinando la definición de conjuntos compacto surgen dos inquietudes:&lt;/div&gt;
  412. &lt;div style=&quot;text-align: justify;&quot;&gt;
  413. &lt;br /&gt;&lt;/div&gt;
  414. &lt;div style=&quot;text-align: justify;&quot;&gt;
  415. &lt;a href=&quot;http://linaresgsj.blogspot.com/2014/07/cubierta-abierta-y-subcubierta-finita.html&quot; target=&quot;_blank&quot;&gt;¿Qué es una cubierta abierta?&lt;/a&gt;&lt;/div&gt;
  416. &lt;div style=&quot;text-align: justify;&quot;&gt;
  417. &lt;a href=&quot;http://linaresgsj.blogspot.com/2014/07/cubierta-abierta-y-subcubierta-finita.html&quot; target=&quot;_blank&quot;&gt;¿Qué es una subcubierta finita?&lt;/a&gt;&lt;/div&gt;
  418. &lt;div style=&quot;text-align: justify;&quot;&gt;
  419. &lt;br /&gt;&lt;/div&gt;
  420. &lt;div style=&quot;text-align: justify;&quot;&gt;
  421. Una vez aclarado estas definiciones podemos retomar el camino de conjuntos compacto, estableciendo lo siguiente; Un conjunto $F$ es compacto si, siempre que esté contenido en la unión de una colección $\varphi = \left \{ G_{\alpha } \right \}$de conjuntos abiertos en $\mathbb{R}$, entonces está contenido en la unión de algún numero finito de conjuntos en $\varphi$.&lt;/div&gt;
  422. &lt;div style=&quot;text-align: justify;&quot;&gt;
  423. &lt;br /&gt;&lt;/div&gt;
  424. &lt;div style=&quot;text-align: justify;&quot;&gt;
  425. Dos cosas hay que advertir, si usted desea demostrar que un conjunto es compacto, se debe examinar una colección cualesquiera de conjuntos abiertos cuya unión contenga a $F$, y probar que $F$ está contenido en la unión de algún número finito de conjuntos de la colección dada. &lt;/div&gt;
  426. &lt;div style=&quot;text-align: justify;&quot;&gt;
  427. &lt;br /&gt;&lt;/div&gt;
  428. &lt;div style=&quot;text-align: justify;&quot;&gt;
  429. &lt;b&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Arial, sans-serif; font-size: 18pt; line-height: 115%;&quot;&gt;Si
  430. consideras que este artículo ha aclarado tus dudas, te invitamos a dejar un
  431. comentario. Gracias.&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  432. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/6642907933084329903/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/07/conjuntos-compactos-en-mathbbr.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/6642907933084329903'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/6642907933084329903'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/07/conjuntos-compactos-en-mathbbr.html' title='Conjuntos Compactos en $\mathbb{R}$'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-4870811409505682178</id><published>2014-07-03T14:19:00.000-07:00</published><updated>2014-07-14T13:54:30.501-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="topología"/><title type='text'>Cubierta Abierta y subcubierta finita en $\mathbb{R}$</title><content type='html'>&lt;!--[if gte mso 9]&gt;&lt;xml&gt;
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  562.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Quote&quot;/&gt;
  563.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  564.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 1&quot;/&gt;
  565.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  566.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 1&quot;/&gt;
  567.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  568.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 1&quot;/&gt;
  569.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  570.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 1&quot;/&gt;
  571.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  572.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 1&quot;/&gt;
  573.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  574.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 1&quot;/&gt;
  575.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  576.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 1&quot;/&gt;
  577.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  578.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 1&quot;/&gt;
  579.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  580.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 2&quot;/&gt;
  581.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  582.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 2&quot;/&gt;
  583.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  584.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 2&quot;/&gt;
  585.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  586.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 2&quot;/&gt;
  587.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  588.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 2&quot;/&gt;
  589.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  590.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 2&quot;/&gt;
  591.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  592.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 2&quot;/&gt;
  593.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  594.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 2&quot;/&gt;
  595.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  596.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 2&quot;/&gt;
  597.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  598.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 2&quot;/&gt;
  599.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  600.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 2&quot;/&gt;
  601.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  602.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 2&quot;/&gt;
  603.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  604.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 2&quot;/&gt;
  605.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  606.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 2&quot;/&gt;
  607.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  608.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 3&quot;/&gt;
  609.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  610.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 3&quot;/&gt;
  611.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  612.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 3&quot;/&gt;
  613.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  614.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 3&quot;/&gt;
  615.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  616.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 3&quot;/&gt;
  617.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  618.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 3&quot;/&gt;
  619.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  620.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 3&quot;/&gt;
  621.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  622.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 3&quot;/&gt;
  623.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  624.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 3&quot;/&gt;
  625.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  626.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 3&quot;/&gt;
  627.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  628.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 3&quot;/&gt;
  629.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  630.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 3&quot;/&gt;
  631.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  632.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 3&quot;/&gt;
  633.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  634.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 3&quot;/&gt;
  635.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  636.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 4&quot;/&gt;
  637.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  638.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 4&quot;/&gt;
  639.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  640.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 4&quot;/&gt;
  641.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  642.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 4&quot;/&gt;
  643.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  644.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 4&quot;/&gt;
  645.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  646.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 4&quot;/&gt;
  647.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  648.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 4&quot;/&gt;
  649.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  650.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 4&quot;/&gt;
  651.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  652.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 4&quot;/&gt;
  653.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  654.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 4&quot;/&gt;
  655.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  656.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 4&quot;/&gt;
  657.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  658.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 4&quot;/&gt;
  659.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  660.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 4&quot;/&gt;
  661.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  662.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 4&quot;/&gt;
  663.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  664.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 5&quot;/&gt;
  665.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  666.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 5&quot;/&gt;
  667.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  668.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 5&quot;/&gt;
  669.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  670.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 5&quot;/&gt;
  671.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  672.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 5&quot;/&gt;
  673.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  674.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 5&quot;/&gt;
  675.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  676.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 5&quot;/&gt;
  677.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  678.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 5&quot;/&gt;
  679.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  680.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 5&quot;/&gt;
  681.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  682.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 5&quot;/&gt;
  683.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  684.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 5&quot;/&gt;
  685.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  686.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 5&quot;/&gt;
  687.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  688.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 5&quot;/&gt;
  689.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  690.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 5&quot;/&gt;
  691.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  692.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 6&quot;/&gt;
  693.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  694.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 6&quot;/&gt;
  695.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  696.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 6&quot;/&gt;
  697.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  698.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 6&quot;/&gt;
  699.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  700.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 6&quot;/&gt;
  701.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  702.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 6&quot;/&gt;
  703.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  704.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 6&quot;/&gt;
  705.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  706.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 6&quot;/&gt;
  707.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  708.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 6&quot;/&gt;
  709.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  710.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 6&quot;/&gt;
  711.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  712.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 6&quot;/&gt;
  713.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  714.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 6&quot;/&gt;
  715.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  716.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 6&quot;/&gt;
  717.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  718.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 6&quot;/&gt;
  719.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;19&quot; SemiHidden=&quot;false&quot;
  720.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Emphasis&quot;/&gt;
  721.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;21&quot; SemiHidden=&quot;false&quot;
  722.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Emphasis&quot;/&gt;
  723.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;31&quot; SemiHidden=&quot;false&quot;
  724.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Reference&quot;/&gt;
  725.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;32&quot; SemiHidden=&quot;false&quot;
  726.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Reference&quot;/&gt;
  727.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;33&quot; SemiHidden=&quot;false&quot;
  728.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Book Title&quot;/&gt;
  729.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;37&quot; Name=&quot;Bibliography&quot;/&gt;
  730.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; QFormat=&quot;true&quot; Name=&quot;TOC Heading&quot;/&gt;
  731. &lt;/w:LatentStyles&gt;
  732. &lt;/xml&gt;&lt;![endif]--&gt;&lt;!--[if gte mso 10]&gt;
  733. &lt;style&gt;
  734. /* Style Definitions */
  735. table.MsoNormalTable
  736. {mso-style-name:&quot;Tabla normal&quot;;
  737. mso-tstyle-rowband-size:0;
  738. mso-tstyle-colband-size:0;
  739. mso-style-noshow:yes;
  740. mso-style-priority:99;
  741. mso-style-qformat:yes;
  742. mso-style-parent:&quot;&quot;;
  743. mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
  744. mso-para-margin-top:0cm;
  745. mso-para-margin-right:0cm;
  746. mso-para-margin-bottom:10.0pt;
  747. mso-para-margin-left:0cm;
  748. line-height:115%;
  749. mso-pagination:widow-orphan;
  750. font-size:11.0pt;
  751. font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
  752. mso-ascii-font-family:Calibri;
  753. mso-ascii-theme-font:minor-latin;
  754. mso-fareast-font-family:&quot;Times New Roman&quot;;
  755. mso-fareast-theme-font:minor-fareast;
  756. mso-hansi-font-family:Calibri;
  757. mso-hansi-theme-font:minor-latin;}
  758. &lt;/style&gt;
  759. &lt;![endif]--&gt;
  760.  
  761. &lt;br /&gt;
  762. &lt;div class=&quot;MsoNormal&quot;&gt;
  763. &lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  764. &lt;w:WordDocument&gt;
  765.  &lt;w:View&gt;Normal&lt;/w:View&gt;
  766.  &lt;w:Zoom&gt;0&lt;/w:Zoom&gt;
  767.  &lt;w:TrackMoves/&gt;
  768.  &lt;w:TrackFormatting/&gt;
  769.  &lt;w:HyphenationZone&gt;21&lt;/w:HyphenationZone&gt;
  770.  &lt;w:PunctuationKerning/&gt;
  771.  &lt;w:ValidateAgainstSchemas/&gt;
  772.  &lt;w:SaveIfXMLInvalid&gt;false&lt;/w:SaveIfXMLInvalid&gt;
  773.  &lt;w:IgnoreMixedContent&gt;false&lt;/w:IgnoreMixedContent&gt;
  774.  &lt;w:AlwaysShowPlaceholderText&gt;false&lt;/w:AlwaysShowPlaceholderText&gt;
  775.  &lt;w:DoNotPromoteQF/&gt;
  776.  &lt;w:LidThemeOther&gt;ES&lt;/w:LidThemeOther&gt;
  777.  &lt;w:LidThemeAsian&gt;X-NONE&lt;/w:LidThemeAsian&gt;
  778.  &lt;w:LidThemeComplexScript&gt;X-NONE&lt;/w:LidThemeComplexScript&gt;
  779.  &lt;w:Compatibility&gt;
  780.   &lt;w:BreakWrappedTables/&gt;
  781.   &lt;w:SnapToGridInCell/&gt;
  782.   &lt;w:WrapTextWithPunct/&gt;
  783.   &lt;w:UseAsianBreakRules/&gt;
  784.   &lt;w:DontGrowAutofit/&gt;
  785.   &lt;w:SplitPgBreakAndParaMark/&gt;
  786.   &lt;w:DontVertAlignCellWithSp/&gt;
  787.   &lt;w:DontBreakConstrainedForcedTables/&gt;
  788.   &lt;w:DontVertAlignInTxbx/&gt;
  789.   &lt;w:Word11KerningPairs/&gt;
  790.   &lt;w:CachedColBalance/&gt;
  791.  &lt;/w:Compatibility&gt;
  792.  &lt;w:BrowserLevel&gt;MicrosoftInternetExplorer4&lt;/w:BrowserLevel&gt;
  793.  &lt;m:mathPr&gt;
  794.   &lt;m:mathFont m:val=&quot;Cambria Math&quot;/&gt;
  795.   &lt;m:brkBin m:val=&quot;before&quot;/&gt;
  796.   &lt;m:brkBinSub m:val=&quot;--&quot;/&gt;
  797.   &lt;m:smallFrac m:val=&quot;off&quot;/&gt;
  798.   &lt;m:dispDef/&gt;
  799.   &lt;m:lMargin m:val=&quot;0&quot;/&gt;
  800.   &lt;m:rMargin m:val=&quot;0&quot;/&gt;
  801.   &lt;m:defJc m:val=&quot;centerGroup&quot;/&gt;
  802.   &lt;m:wrapIndent m:val=&quot;1440&quot;/&gt;
  803.   &lt;m:intLim m:val=&quot;subSup&quot;/&gt;
  804.   &lt;m:naryLim m:val=&quot;undOvr&quot;/&gt;
  805.  &lt;/m:mathPr&gt;&lt;/w:WordDocument&gt;
  806. &lt;/xml&gt;&lt;![endif]--&gt;&lt;/div&gt;
  807. &lt;br /&gt;
  808. &lt;div class=&quot;MsoNormal&quot;&gt;
  809. &lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  810. &lt;w:LatentStyles DefLockedState=&quot;false&quot; DefUnhideWhenUsed=&quot;true&quot;
  811.  DefSemiHidden=&quot;true&quot; DefQFormat=&quot;false&quot; DefPriority=&quot;99&quot;
  812.  LatentStyleCount=&quot;267&quot;&gt;
  813.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;0&quot; SemiHidden=&quot;false&quot;
  814.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Normal&quot;/&gt;
  815.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; SemiHidden=&quot;false&quot;
  816.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;heading 1&quot;/&gt;
  817.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 2&quot;/&gt;
  818.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 3&quot;/&gt;
  819.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 4&quot;/&gt;
  820.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 5&quot;/&gt;
  821.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 6&quot;/&gt;
  822.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 7&quot;/&gt;
  823.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 8&quot;/&gt;
  824.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 9&quot;/&gt;
  825.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 1&quot;/&gt;
  826.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 2&quot;/&gt;
  827.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 3&quot;/&gt;
  828.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 4&quot;/&gt;
  829.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 5&quot;/&gt;
  830.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 6&quot;/&gt;
  831.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 7&quot;/&gt;
  832.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 8&quot;/&gt;
  833.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 9&quot;/&gt;
  834.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;35&quot; QFormat=&quot;true&quot; Name=&quot;caption&quot;/&gt;
  835.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;10&quot; SemiHidden=&quot;false&quot;
  836.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Title&quot;/&gt;
  837.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; Name=&quot;Default Paragraph Font&quot;/&gt;
  838.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;11&quot; SemiHidden=&quot;false&quot;
  839.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtitle&quot;/&gt;
  840.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;22&quot; SemiHidden=&quot;false&quot;
  841.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Strong&quot;/&gt;
  842.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;20&quot; SemiHidden=&quot;false&quot;
  843.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Emphasis&quot;/&gt;
  844.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;59&quot; SemiHidden=&quot;false&quot;
  845.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Table Grid&quot;/&gt;
  846.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Placeholder Text&quot;/&gt;
  847.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; SemiHidden=&quot;false&quot;
  848.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;No Spacing&quot;/&gt;
  849.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  850.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading&quot;/&gt;
  851.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  852.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List&quot;/&gt;
  853.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  854.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid&quot;/&gt;
  855.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  856.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1&quot;/&gt;
  857.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  858.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2&quot;/&gt;
  859.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  860.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1&quot;/&gt;
  861.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  862.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2&quot;/&gt;
  863.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  864.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1&quot;/&gt;
  865.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  866.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2&quot;/&gt;
  867.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  868.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3&quot;/&gt;
  869.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  870.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List&quot;/&gt;
  871.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  872.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading&quot;/&gt;
  873.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  874.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List&quot;/&gt;
  875.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  876.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid&quot;/&gt;
  877.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  878.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 1&quot;/&gt;
  879.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  880.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 1&quot;/&gt;
  881.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  882.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 1&quot;/&gt;
  883.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  884.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 1&quot;/&gt;
  885.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  886.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 1&quot;/&gt;
  887.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  888.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 1&quot;/&gt;
  889.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Revision&quot;/&gt;
  890.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;34&quot; SemiHidden=&quot;false&quot;
  891.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;List Paragraph&quot;/&gt;
  892.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;29&quot; SemiHidden=&quot;false&quot;
  893.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Quote&quot;/&gt;
  894.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;30&quot; SemiHidden=&quot;false&quot;
  895.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Quote&quot;/&gt;
  896.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  897.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 1&quot;/&gt;
  898.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  899.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 1&quot;/&gt;
  900.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  901.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 1&quot;/&gt;
  902.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  903.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 1&quot;/&gt;
  904.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  905.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 1&quot;/&gt;
  906.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  907.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 1&quot;/&gt;
  908.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  909.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 1&quot;/&gt;
  910.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  911.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 1&quot;/&gt;
  912.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  913.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 2&quot;/&gt;
  914.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  915.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 2&quot;/&gt;
  916.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  917.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 2&quot;/&gt;
  918.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  919.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 2&quot;/&gt;
  920.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  921.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 2&quot;/&gt;
  922.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  923.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 2&quot;/&gt;
  924.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  925.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 2&quot;/&gt;
  926.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  927.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 2&quot;/&gt;
  928.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  929.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 2&quot;/&gt;
  930.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  931.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 2&quot;/&gt;
  932.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  933.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 2&quot;/&gt;
  934.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  935.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 2&quot;/&gt;
  936.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  937.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 2&quot;/&gt;
  938.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  939.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 2&quot;/&gt;
  940.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  941.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 3&quot;/&gt;
  942.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  943.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 3&quot;/&gt;
  944.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  945.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 3&quot;/&gt;
  946.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  947.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 3&quot;/&gt;
  948.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  949.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 3&quot;/&gt;
  950.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  951.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 3&quot;/&gt;
  952.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  953.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 3&quot;/&gt;
  954.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  955.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 3&quot;/&gt;
  956.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  957.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 3&quot;/&gt;
  958.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  959.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 3&quot;/&gt;
  960.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  961.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 3&quot;/&gt;
  962.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  963.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 3&quot;/&gt;
  964.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  965.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 3&quot;/&gt;
  966.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  967.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 3&quot;/&gt;
  968.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  969.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 4&quot;/&gt;
  970.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  971.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 4&quot;/&gt;
  972.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  973.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 4&quot;/&gt;
  974.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  975.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 4&quot;/&gt;
  976.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  977.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 4&quot;/&gt;
  978.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  979.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 4&quot;/&gt;
  980.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  981.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 4&quot;/&gt;
  982.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  983.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 4&quot;/&gt;
  984.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  985.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 4&quot;/&gt;
  986.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  987.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 4&quot;/&gt;
  988.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  989.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 4&quot;/&gt;
  990.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  991.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 4&quot;/&gt;
  992.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  993.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 4&quot;/&gt;
  994.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  995.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 4&quot;/&gt;
  996.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  997.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 5&quot;/&gt;
  998.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  999.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 5&quot;/&gt;
  1000.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1001.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 5&quot;/&gt;
  1002.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1003.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 5&quot;/&gt;
  1004.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1005.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 5&quot;/&gt;
  1006.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1007.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 5&quot;/&gt;
  1008.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1009.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 5&quot;/&gt;
  1010.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1011.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 5&quot;/&gt;
  1012.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1013.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 5&quot;/&gt;
  1014.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1015.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 5&quot;/&gt;
  1016.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1017.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 5&quot;/&gt;
  1018.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1019.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 5&quot;/&gt;
  1020.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1021.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 5&quot;/&gt;
  1022.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1023.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 5&quot;/&gt;
  1024.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1025.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 6&quot;/&gt;
  1026.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1027.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 6&quot;/&gt;
  1028.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1029.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 6&quot;/&gt;
  1030.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1031.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 6&quot;/&gt;
  1032.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1033.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 6&quot;/&gt;
  1034.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1035.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 6&quot;/&gt;
  1036.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1037.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 6&quot;/&gt;
  1038.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1039.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 6&quot;/&gt;
  1040.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1041.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 6&quot;/&gt;
  1042.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1043.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 6&quot;/&gt;
  1044.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1045.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 6&quot;/&gt;
  1046.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1047.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 6&quot;/&gt;
  1048.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1049.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 6&quot;/&gt;
  1050.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1051.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 6&quot;/&gt;
  1052.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;19&quot; SemiHidden=&quot;false&quot;
  1053.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Emphasis&quot;/&gt;
  1054.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;21&quot; SemiHidden=&quot;false&quot;
  1055.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Emphasis&quot;/&gt;
  1056.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;31&quot; SemiHidden=&quot;false&quot;
  1057.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Reference&quot;/&gt;
  1058.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;32&quot; SemiHidden=&quot;false&quot;
  1059.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Reference&quot;/&gt;
  1060.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;33&quot; SemiHidden=&quot;false&quot;
  1061.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Book Title&quot;/&gt;
  1062.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;37&quot; Name=&quot;Bibliography&quot;/&gt;
  1063.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; QFormat=&quot;true&quot; Name=&quot;TOC Heading&quot;/&gt;
  1064. &lt;/w:LatentStyles&gt;
  1065. &lt;/xml&gt;&lt;![endif]--&gt;&lt;!--[if gte mso 10]&gt;
  1066. &lt;style&gt;
  1067. /* Style Definitions */
  1068. table.MsoNormalTable
  1069. {mso-style-name:&quot;Tabla normal&quot;;
  1070. mso-tstyle-rowband-size:0;
  1071. mso-tstyle-colband-size:0;
  1072. mso-style-noshow:yes;
  1073. mso-style-priority:99;
  1074. mso-style-qformat:yes;
  1075. mso-style-parent:&quot;&quot;;
  1076. mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
  1077. mso-para-margin-top:0cm;
  1078. mso-para-margin-right:0cm;
  1079. mso-para-margin-bottom:10.0pt;
  1080. mso-para-margin-left:0cm;
  1081. line-height:115%;
  1082. mso-pagination:widow-orphan;
  1083. font-size:11.0pt;
  1084. font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
  1085. mso-ascii-font-family:Calibri;
  1086. mso-ascii-theme-font:minor-latin;
  1087. mso-fareast-font-family:&quot;Times New Roman&quot;;
  1088. mso-fareast-theme-font:minor-fareast;
  1089. mso-hansi-font-family:Calibri;
  1090. mso-hansi-theme-font:minor-latin;}
  1091. &lt;/style&gt;
  1092. &lt;![endif]--&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  1093. &lt;w:WordDocument&gt;
  1094.  &lt;w:View&gt;Normal&lt;/w:View&gt;
  1095.  &lt;w:Zoom&gt;0&lt;/w:Zoom&gt;
  1096.  &lt;w:TrackMoves/&gt;
  1097.  &lt;w:TrackFormatting/&gt;
  1098.  &lt;w:HyphenationZone&gt;21&lt;/w:HyphenationZone&gt;
  1099.  &lt;w:PunctuationKerning/&gt;
  1100.  &lt;w:ValidateAgainstSchemas/&gt;
  1101.  &lt;w:SaveIfXMLInvalid&gt;false&lt;/w:SaveIfXMLInvalid&gt;
  1102.  &lt;w:IgnoreMixedContent&gt;false&lt;/w:IgnoreMixedContent&gt;
  1103.  &lt;w:AlwaysShowPlaceholderText&gt;false&lt;/w:AlwaysShowPlaceholderText&gt;
  1104.  &lt;w:DoNotPromoteQF/&gt;
  1105.  &lt;w:LidThemeOther&gt;ES&lt;/w:LidThemeOther&gt;
  1106.  &lt;w:LidThemeAsian&gt;X-NONE&lt;/w:LidThemeAsian&gt;
  1107.  &lt;w:LidThemeComplexScript&gt;X-NONE&lt;/w:LidThemeComplexScript&gt;
  1108.  &lt;w:Compatibility&gt;
  1109.   &lt;w:BreakWrappedTables/&gt;
  1110.   &lt;w:SnapToGridInCell/&gt;
  1111.   &lt;w:WrapTextWithPunct/&gt;
  1112.   &lt;w:UseAsianBreakRules/&gt;
  1113.   &lt;w:DontGrowAutofit/&gt;
  1114.   &lt;w:SplitPgBreakAndParaMark/&gt;
  1115.   &lt;w:DontVertAlignCellWithSp/&gt;
  1116.   &lt;w:DontBreakConstrainedForcedTables/&gt;
  1117.   &lt;w:DontVertAlignInTxbx/&gt;
  1118.   &lt;w:Word11KerningPairs/&gt;
  1119.   &lt;w:CachedColBalance/&gt;
  1120.  &lt;/w:Compatibility&gt;
  1121.  &lt;w:BrowserLevel&gt;MicrosoftInternetExplorer4&lt;/w:BrowserLevel&gt;
  1122.  &lt;m:mathPr&gt;
  1123.   &lt;m:mathFont m:val=&quot;Cambria Math&quot;/&gt;
  1124.   &lt;m:brkBin m:val=&quot;before&quot;/&gt;
  1125.   &lt;m:brkBinSub m:val=&quot;--&quot;/&gt;
  1126.   &lt;m:smallFrac m:val=&quot;off&quot;/&gt;
  1127.   &lt;m:dispDef/&gt;
  1128.   &lt;m:lMargin m:val=&quot;0&quot;/&gt;
  1129.   &lt;m:rMargin m:val=&quot;0&quot;/&gt;
  1130.   &lt;m:defJc m:val=&quot;centerGroup&quot;/&gt;
  1131.   &lt;m:wrapIndent m:val=&quot;1440&quot;/&gt;
  1132.   &lt;m:intLim m:val=&quot;subSup&quot;/&gt;
  1133.   &lt;m:naryLim m:val=&quot;undOvr&quot;/&gt;
  1134.  &lt;/m:mathPr&gt;&lt;/w:WordDocument&gt;
  1135. &lt;/xml&gt;&lt;![endif]--&gt;&lt;/div&gt;
  1136. &lt;div class=&quot;MsoNormal&quot;&gt;
  1137. &lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  1138. &lt;w:LatentStyles DefLockedState=&quot;false&quot; DefUnhideWhenUsed=&quot;true&quot;
  1139.  DefSemiHidden=&quot;true&quot; DefQFormat=&quot;false&quot; DefPriority=&quot;99&quot;
  1140.  LatentStyleCount=&quot;267&quot;&gt;
  1141.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;0&quot; SemiHidden=&quot;false&quot;
  1142.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Normal&quot;/&gt;
  1143.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; SemiHidden=&quot;false&quot;
  1144.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;heading 1&quot;/&gt;
  1145.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 2&quot;/&gt;
  1146.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 3&quot;/&gt;
  1147.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 4&quot;/&gt;
  1148.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 5&quot;/&gt;
  1149.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 6&quot;/&gt;
  1150.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 7&quot;/&gt;
  1151.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 8&quot;/&gt;
  1152.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 9&quot;/&gt;
  1153.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 1&quot;/&gt;
  1154.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 2&quot;/&gt;
  1155.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 3&quot;/&gt;
  1156.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 4&quot;/&gt;
  1157.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 5&quot;/&gt;
  1158.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 6&quot;/&gt;
  1159.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 7&quot;/&gt;
  1160.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 8&quot;/&gt;
  1161.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 9&quot;/&gt;
  1162.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;35&quot; QFormat=&quot;true&quot; Name=&quot;caption&quot;/&gt;
  1163.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;10&quot; SemiHidden=&quot;false&quot;
  1164.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Title&quot;/&gt;
  1165.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; Name=&quot;Default Paragraph Font&quot;/&gt;
  1166.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;11&quot; SemiHidden=&quot;false&quot;
  1167.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtitle&quot;/&gt;
  1168.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;22&quot; SemiHidden=&quot;false&quot;
  1169.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Strong&quot;/&gt;
  1170.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;20&quot; SemiHidden=&quot;false&quot;
  1171.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Emphasis&quot;/&gt;
  1172.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;59&quot; SemiHidden=&quot;false&quot;
  1173.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Table Grid&quot;/&gt;
  1174.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Placeholder Text&quot;/&gt;
  1175.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; SemiHidden=&quot;false&quot;
  1176.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;No Spacing&quot;/&gt;
  1177.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1178.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading&quot;/&gt;
  1179.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1180.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List&quot;/&gt;
  1181.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1182.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid&quot;/&gt;
  1183.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1184.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1&quot;/&gt;
  1185.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1186.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2&quot;/&gt;
  1187.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1188.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1&quot;/&gt;
  1189.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1190.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2&quot;/&gt;
  1191.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1192.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1&quot;/&gt;
  1193.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1194.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2&quot;/&gt;
  1195.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1196.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3&quot;/&gt;
  1197.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1198.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List&quot;/&gt;
  1199.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1200.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading&quot;/&gt;
  1201.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1202.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List&quot;/&gt;
  1203.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1204.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid&quot;/&gt;
  1205.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1206.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 1&quot;/&gt;
  1207.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1208.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 1&quot;/&gt;
  1209.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1210.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 1&quot;/&gt;
  1211.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1212.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 1&quot;/&gt;
  1213.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1214.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 1&quot;/&gt;
  1215.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1216.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 1&quot;/&gt;
  1217.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Revision&quot;/&gt;
  1218.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;34&quot; SemiHidden=&quot;false&quot;
  1219.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;List Paragraph&quot;/&gt;
  1220.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;29&quot; SemiHidden=&quot;false&quot;
  1221.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Quote&quot;/&gt;
  1222.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;30&quot; SemiHidden=&quot;false&quot;
  1223.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Quote&quot;/&gt;
  1224.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1225.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 1&quot;/&gt;
  1226.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1227.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 1&quot;/&gt;
  1228.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1229.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 1&quot;/&gt;
  1230.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1231.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 1&quot;/&gt;
  1232.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1233.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 1&quot;/&gt;
  1234.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1235.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 1&quot;/&gt;
  1236.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1237.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 1&quot;/&gt;
  1238.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1239.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 1&quot;/&gt;
  1240.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1241.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 2&quot;/&gt;
  1242.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1243.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 2&quot;/&gt;
  1244.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1245.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 2&quot;/&gt;
  1246.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1247.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 2&quot;/&gt;
  1248.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1249.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 2&quot;/&gt;
  1250.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1251.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 2&quot;/&gt;
  1252.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1253.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 2&quot;/&gt;
  1254.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1255.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 2&quot;/&gt;
  1256.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1257.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 2&quot;/&gt;
  1258.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1259.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 2&quot;/&gt;
  1260.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1261.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 2&quot;/&gt;
  1262.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1263.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 2&quot;/&gt;
  1264.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1265.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 2&quot;/&gt;
  1266.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1267.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 2&quot;/&gt;
  1268.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1269.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 3&quot;/&gt;
  1270.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1271.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 3&quot;/&gt;
  1272.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1273.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 3&quot;/&gt;
  1274.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1275.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 3&quot;/&gt;
  1276.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1277.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 3&quot;/&gt;
  1278.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1279.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 3&quot;/&gt;
  1280.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1281.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 3&quot;/&gt;
  1282.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1283.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 3&quot;/&gt;
  1284.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1285.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 3&quot;/&gt;
  1286.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1287.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 3&quot;/&gt;
  1288.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1289.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 3&quot;/&gt;
  1290.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1291.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 3&quot;/&gt;
  1292.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1293.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 3&quot;/&gt;
  1294.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1295.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 3&quot;/&gt;
  1296.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1297.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 4&quot;/&gt;
  1298.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1299.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 4&quot;/&gt;
  1300.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1301.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 4&quot;/&gt;
  1302.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1303.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 4&quot;/&gt;
  1304.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1305.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 4&quot;/&gt;
  1306.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1307.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 4&quot;/&gt;
  1308.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1309.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 4&quot;/&gt;
  1310.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1311.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 4&quot;/&gt;
  1312.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1313.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 4&quot;/&gt;
  1314.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1315.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 4&quot;/&gt;
  1316.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1317.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 4&quot;/&gt;
  1318.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1319.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 4&quot;/&gt;
  1320.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1321.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 4&quot;/&gt;
  1322.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1323.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 4&quot;/&gt;
  1324.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1325.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 5&quot;/&gt;
  1326.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1327.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 5&quot;/&gt;
  1328.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1329.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 5&quot;/&gt;
  1330.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1331.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 5&quot;/&gt;
  1332.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1333.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 5&quot;/&gt;
  1334.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1335.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 5&quot;/&gt;
  1336.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1337.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 5&quot;/&gt;
  1338.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1339.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 5&quot;/&gt;
  1340.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1341.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 5&quot;/&gt;
  1342.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1343.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 5&quot;/&gt;
  1344.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1345.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 5&quot;/&gt;
  1346.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1347.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 5&quot;/&gt;
  1348.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1349.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 5&quot;/&gt;
  1350.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1351.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 5&quot;/&gt;
  1352.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1353.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 6&quot;/&gt;
  1354.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1355.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 6&quot;/&gt;
  1356.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1357.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 6&quot;/&gt;
  1358.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1359.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 6&quot;/&gt;
  1360.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1361.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 6&quot;/&gt;
  1362.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1363.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 6&quot;/&gt;
  1364.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1365.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 6&quot;/&gt;
  1366.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1367.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 6&quot;/&gt;
  1368.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1369.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 6&quot;/&gt;
  1370.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1371.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 6&quot;/&gt;
  1372.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1373.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 6&quot;/&gt;
  1374.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1375.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 6&quot;/&gt;
  1376.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1377.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 6&quot;/&gt;
  1378.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1379.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 6&quot;/&gt;
  1380.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;19&quot; SemiHidden=&quot;false&quot;
  1381.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Emphasis&quot;/&gt;
  1382.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;21&quot; SemiHidden=&quot;false&quot;
  1383.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Emphasis&quot;/&gt;
  1384.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;31&quot; SemiHidden=&quot;false&quot;
  1385.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtle Reference&quot;/&gt;
  1386.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;32&quot; SemiHidden=&quot;false&quot;
  1387.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Reference&quot;/&gt;
  1388.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;33&quot; SemiHidden=&quot;false&quot;
  1389.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Book Title&quot;/&gt;
  1390.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;37&quot; Name=&quot;Bibliography&quot;/&gt;
  1391.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; QFormat=&quot;true&quot; Name=&quot;TOC Heading&quot;/&gt;
  1392. &lt;/w:LatentStyles&gt;
  1393. &lt;/xml&gt;&lt;![endif]--&gt;&lt;!--[if gte mso 10]&gt;
  1394. &lt;style&gt;
  1395. /* Style Definitions */
  1396. table.MsoNormalTable
  1397. {mso-style-name:&quot;Tabla normal&quot;;
  1398. mso-tstyle-rowband-size:0;
  1399. mso-tstyle-colband-size:0;
  1400. mso-style-noshow:yes;
  1401. mso-style-priority:99;
  1402. mso-style-qformat:yes;
  1403. mso-style-parent:&quot;&quot;;
  1404. mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
  1405. mso-para-margin-top:0cm;
  1406. mso-para-margin-right:0cm;
  1407. mso-para-margin-bottom:10.0pt;
  1408. mso-para-margin-left:0cm;
  1409. line-height:115%;
  1410. mso-pagination:widow-orphan;
  1411. font-size:11.0pt;
  1412. font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
  1413. mso-ascii-font-family:Calibri;
  1414. mso-ascii-theme-font:minor-latin;
  1415. mso-fareast-font-family:&quot;Times New Roman&quot;;
  1416. mso-fareast-theme-font:minor-fareast;
  1417. mso-hansi-font-family:Calibri;
  1418. mso-hansi-theme-font:minor-latin;}
  1419. &lt;/style&gt;
  1420. &lt;![endif]--&gt;
  1421.  
  1422. &lt;/div&gt;
  1423. &lt;div class=&quot;MsoNormal&quot;&gt;
  1424. Sea $A$ un conjunto de $\mathbb{R}$. Una cubierta abierta de
  1425. $A$ es una colección $\varphi = \left \{ G_{\alpha } \right \}$ de conjuntos
  1426. abiertos en $\mathbb{R}$ cuya unión contiene a $A$; es decir,&lt;/div&gt;
  1427. &lt;div class=&quot;MsoNormal&quot;&gt;
  1428. &lt;br /&gt;&lt;/div&gt;
  1429. &lt;div class=&quot;MsoNormal&quot;&gt;
  1430. $$A \subseteq \bigcup_{\alpha }^{^{}}G_{\alpha }$$&lt;/div&gt;
  1431. &lt;div class=&quot;MsoNormal&quot;&gt;
  1432. &lt;br /&gt;&lt;/div&gt;
  1433. &lt;div class=&quot;MsoNormal&quot;&gt;
  1434. Si $ {\varphi }&#39;$ es una subcolección de conjuntos de $\varphi$
  1435. tal que la unión de los conjuntos de $ {\varphi }&#39;$ también contiene a $A$,
  1436. entonces a $ {\varphi }&#39;$ se le llama subcubierta de $\varphi$. Si $ {\varphi
  1437. }&#39;$ consta de un número finito de conjuntos, entonces a $ {\varphi }&#39;$ se le
  1438. llama subcubierta finita de $\varphi$.&lt;/div&gt;
  1439. &lt;div class=&quot;MsoNormal&quot;&gt;
  1440. &lt;br /&gt;&lt;/div&gt;
  1441. &lt;div class=&quot;MsoNormal&quot;&gt;
  1442. EJEMPLO &lt;/div&gt;
  1443. &lt;div class=&quot;MsoNormal&quot;&gt;
  1444. &lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  1445. &lt;w:WordDocument&gt;
  1446.  &lt;w:View&gt;Normal&lt;/w:View&gt;
  1447.  &lt;w:Zoom&gt;0&lt;/w:Zoom&gt;
  1448.  &lt;w:TrackMoves/&gt;
  1449.  &lt;w:TrackFormatting/&gt;
  1450.  &lt;w:HyphenationZone&gt;21&lt;/w:HyphenationZone&gt;
  1451.  &lt;w:PunctuationKerning/&gt;
  1452.  &lt;w:ValidateAgainstSchemas/&gt;
  1453.  &lt;w:SaveIfXMLInvalid&gt;false&lt;/w:SaveIfXMLInvalid&gt;
  1454.  &lt;w:IgnoreMixedContent&gt;false&lt;/w:IgnoreMixedContent&gt;
  1455.  &lt;w:AlwaysShowPlaceholderText&gt;false&lt;/w:AlwaysShowPlaceholderText&gt;
  1456.  &lt;w:DoNotPromoteQF/&gt;
  1457.  &lt;w:LidThemeOther&gt;ES&lt;/w:LidThemeOther&gt;
  1458.  &lt;w:LidThemeAsian&gt;X-NONE&lt;/w:LidThemeAsian&gt;
  1459.  &lt;w:LidThemeComplexScript&gt;X-NONE&lt;/w:LidThemeComplexScript&gt;
  1460.  &lt;w:Compatibility&gt;
  1461.   &lt;w:BreakWrappedTables/&gt;
  1462.   &lt;w:SnapToGridInCell/&gt;
  1463.   &lt;w:WrapTextWithPunct/&gt;
  1464.   &lt;w:UseAsianBreakRules/&gt;
  1465.   &lt;w:DontGrowAutofit/&gt;
  1466.   &lt;w:SplitPgBreakAndParaMark/&gt;
  1467.   &lt;w:DontVertAlignCellWithSp/&gt;
  1468.   &lt;w:DontBreakConstrainedForcedTables/&gt;
  1469.   &lt;w:DontVertAlignInTxbx/&gt;
  1470.   &lt;w:Word11KerningPairs/&gt;
  1471.   &lt;w:CachedColBalance/&gt;
  1472.  &lt;/w:Compatibility&gt;
  1473.  &lt;w:BrowserLevel&gt;MicrosoftInternetExplorer4&lt;/w:BrowserLevel&gt;
  1474.  &lt;m:mathPr&gt;
  1475.   &lt;m:mathFont m:val=&quot;Cambria Math&quot;/&gt;
  1476.   &lt;m:brkBin m:val=&quot;before&quot;/&gt;
  1477.   &lt;m:brkBinSub m:val=&quot;--&quot;/&gt;
  1478.   &lt;m:smallFrac m:val=&quot;off&quot;/&gt;
  1479.   &lt;m:dispDef/&gt;
  1480.   &lt;m:lMargin m:val=&quot;0&quot;/&gt;
  1481.   &lt;m:rMargin m:val=&quot;0&quot;/&gt;
  1482.   &lt;m:defJc m:val=&quot;centerGroup&quot;/&gt;
  1483.   &lt;m:wrapIndent m:val=&quot;1440&quot;/&gt;
  1484.   &lt;m:intLim m:val=&quot;subSup&quot;/&gt;
  1485.   &lt;m:naryLim m:val=&quot;undOvr&quot;/&gt;
  1486.  &lt;/m:mathPr&gt;&lt;/w:WordDocument&gt;
  1487. &lt;/xml&gt;&lt;![endif]--&gt;&lt;/div&gt;
  1488. &lt;br /&gt;
  1489. &lt;div class=&quot;MsoNormal&quot;&gt;
  1490. &lt;!--[if gte mso 9]&gt;&lt;xml&gt;
  1491. &lt;w:LatentStyles DefLockedState=&quot;false&quot; DefUnhideWhenUsed=&quot;true&quot;
  1492.  DefSemiHidden=&quot;true&quot; DefQFormat=&quot;false&quot; DefPriority=&quot;99&quot;
  1493.  LatentStyleCount=&quot;267&quot;&gt;
  1494.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;0&quot; SemiHidden=&quot;false&quot;
  1495.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Normal&quot;/&gt;
  1496.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; SemiHidden=&quot;false&quot;
  1497.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;heading 1&quot;/&gt;
  1498.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 2&quot;/&gt;
  1499.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 3&quot;/&gt;
  1500.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 4&quot;/&gt;
  1501.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 5&quot;/&gt;
  1502.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 6&quot;/&gt;
  1503.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 7&quot;/&gt;
  1504.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 8&quot;/&gt;
  1505.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;9&quot; QFormat=&quot;true&quot; Name=&quot;heading 9&quot;/&gt;
  1506.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 1&quot;/&gt;
  1507.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 2&quot;/&gt;
  1508.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 3&quot;/&gt;
  1509.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 4&quot;/&gt;
  1510.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 5&quot;/&gt;
  1511.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 6&quot;/&gt;
  1512.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 7&quot;/&gt;
  1513.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 8&quot;/&gt;
  1514.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;39&quot; Name=&quot;toc 9&quot;/&gt;
  1515.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;35&quot; QFormat=&quot;true&quot; Name=&quot;caption&quot;/&gt;
  1516.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;10&quot; SemiHidden=&quot;false&quot;
  1517.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Title&quot;/&gt;
  1518.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; Name=&quot;Default Paragraph Font&quot;/&gt;
  1519.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;11&quot; SemiHidden=&quot;false&quot;
  1520.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Subtitle&quot;/&gt;
  1521.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;22&quot; SemiHidden=&quot;false&quot;
  1522.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Strong&quot;/&gt;
  1523.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;20&quot; SemiHidden=&quot;false&quot;
  1524.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Emphasis&quot;/&gt;
  1525.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;59&quot; SemiHidden=&quot;false&quot;
  1526.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Table Grid&quot;/&gt;
  1527.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Placeholder Text&quot;/&gt;
  1528.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;1&quot; SemiHidden=&quot;false&quot;
  1529.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;No Spacing&quot;/&gt;
  1530.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1531.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading&quot;/&gt;
  1532.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1533.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List&quot;/&gt;
  1534.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1535.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid&quot;/&gt;
  1536.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1537.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1&quot;/&gt;
  1538.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1539.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2&quot;/&gt;
  1540.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1541.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1&quot;/&gt;
  1542.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1543.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2&quot;/&gt;
  1544.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1545.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1&quot;/&gt;
  1546.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1547.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2&quot;/&gt;
  1548.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1549.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3&quot;/&gt;
  1550.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1551.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List&quot;/&gt;
  1552.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1553.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading&quot;/&gt;
  1554.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1555.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List&quot;/&gt;
  1556.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1557.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid&quot;/&gt;
  1558.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1559.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 1&quot;/&gt;
  1560.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1561.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 1&quot;/&gt;
  1562.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1563.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 1&quot;/&gt;
  1564.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1565.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 1&quot;/&gt;
  1566.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1567.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 1&quot;/&gt;
  1568.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1569.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 1&quot;/&gt;
  1570.  &lt;w:LsdException Locked=&quot;false&quot; UnhideWhenUsed=&quot;false&quot; Name=&quot;Revision&quot;/&gt;
  1571.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;34&quot; SemiHidden=&quot;false&quot;
  1572.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;List Paragraph&quot;/&gt;
  1573.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;29&quot; SemiHidden=&quot;false&quot;
  1574.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Quote&quot;/&gt;
  1575.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;30&quot; SemiHidden=&quot;false&quot;
  1576.   UnhideWhenUsed=&quot;false&quot; QFormat=&quot;true&quot; Name=&quot;Intense Quote&quot;/&gt;
  1577.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1578.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 1&quot;/&gt;
  1579.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1580.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 1&quot;/&gt;
  1581.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1582.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 1&quot;/&gt;
  1583.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1584.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 1&quot;/&gt;
  1585.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1586.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 1&quot;/&gt;
  1587.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1588.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 1&quot;/&gt;
  1589.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1590.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 1&quot;/&gt;
  1591.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1592.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 1&quot;/&gt;
  1593.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1594.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 2&quot;/&gt;
  1595.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1596.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 2&quot;/&gt;
  1597.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1598.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 2&quot;/&gt;
  1599.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1600.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 2&quot;/&gt;
  1601.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1602.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 2&quot;/&gt;
  1603.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1604.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 2&quot;/&gt;
  1605.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1606.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 2&quot;/&gt;
  1607.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1608.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 2&quot;/&gt;
  1609.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1610.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 2&quot;/&gt;
  1611.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1612.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 2&quot;/&gt;
  1613.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1614.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 2&quot;/&gt;
  1615.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1616.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 2&quot;/&gt;
  1617.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1618.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 2&quot;/&gt;
  1619.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1620.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 2&quot;/&gt;
  1621.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1622.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 3&quot;/&gt;
  1623.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1624.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 3&quot;/&gt;
  1625.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1626.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 3&quot;/&gt;
  1627.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1628.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 3&quot;/&gt;
  1629.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1630.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 3&quot;/&gt;
  1631.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1632.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 3&quot;/&gt;
  1633.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1634.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 3&quot;/&gt;
  1635.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1636.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 3&quot;/&gt;
  1637.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1638.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 3&quot;/&gt;
  1639.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1640.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 3&quot;/&gt;
  1641.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1642.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 3&quot;/&gt;
  1643.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1644.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 3&quot;/&gt;
  1645.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1646.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 3&quot;/&gt;
  1647.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1648.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 3&quot;/&gt;
  1649.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1650.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 4&quot;/&gt;
  1651.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1652.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 4&quot;/&gt;
  1653.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1654.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 4&quot;/&gt;
  1655.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1656.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 4&quot;/&gt;
  1657.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1658.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 4&quot;/&gt;
  1659.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1660.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 4&quot;/&gt;
  1661.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1662.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 4&quot;/&gt;
  1663.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1664.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 4&quot;/&gt;
  1665.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1666.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 4&quot;/&gt;
  1667.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1668.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 4&quot;/&gt;
  1669.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1670.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 4&quot;/&gt;
  1671.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1672.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 4&quot;/&gt;
  1673.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1674.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 4&quot;/&gt;
  1675.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1676.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 4&quot;/&gt;
  1677.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1678.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 5&quot;/&gt;
  1679.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1680.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 5&quot;/&gt;
  1681.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1682.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 5&quot;/&gt;
  1683.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
  1684.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 1 Accent 5&quot;/&gt;
  1685.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;64&quot; SemiHidden=&quot;false&quot;
  1686.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Shading 2 Accent 5&quot;/&gt;
  1687.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;65&quot; SemiHidden=&quot;false&quot;
  1688.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 1 Accent 5&quot;/&gt;
  1689.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;66&quot; SemiHidden=&quot;false&quot;
  1690.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium List 2 Accent 5&quot;/&gt;
  1691.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;67&quot; SemiHidden=&quot;false&quot;
  1692.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 1 Accent 5&quot;/&gt;
  1693.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;68&quot; SemiHidden=&quot;false&quot;
  1694.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 2 Accent 5&quot;/&gt;
  1695.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;69&quot; SemiHidden=&quot;false&quot;
  1696.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Medium Grid 3 Accent 5&quot;/&gt;
  1697.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;70&quot; SemiHidden=&quot;false&quot;
  1698.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Dark List Accent 5&quot;/&gt;
  1699.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;71&quot; SemiHidden=&quot;false&quot;
  1700.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Shading Accent 5&quot;/&gt;
  1701.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;72&quot; SemiHidden=&quot;false&quot;
  1702.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful List Accent 5&quot;/&gt;
  1703.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;73&quot; SemiHidden=&quot;false&quot;
  1704.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Colorful Grid Accent 5&quot;/&gt;
  1705.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;60&quot; SemiHidden=&quot;false&quot;
  1706.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Shading Accent 6&quot;/&gt;
  1707.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;61&quot; SemiHidden=&quot;false&quot;
  1708.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light List Accent 6&quot;/&gt;
  1709.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;62&quot; SemiHidden=&quot;false&quot;
  1710.   UnhideWhenUsed=&quot;false&quot; Name=&quot;Light Grid Accent 6&quot;/&gt;
  1711.  &lt;w:LsdException Locked=&quot;false&quot; Priority=&quot;63&quot; SemiHidden=&quot;false&quot;
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  1798. consideras que este artículo ha aclarado tus dudas, te invitamos a dejar un
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  1854. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/4870811409505682178/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/07/cubierta-abierta-y-subcubierta-finita.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/4870811409505682178'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/4870811409505682178'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/07/cubierta-abierta-y-subcubierta-finita.html' title='Cubierta Abierta y subcubierta finita en $\mathbb{R}$'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-2763001610100479686</id><published>2014-01-24T17:09:00.001-08:00</published><updated>2017-11-14T04:59:05.345-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="análisis"/><category scheme="http://www.blogger.com/atom/ns#" term="topología"/><title type='text'>Espacio Métrico Completo</title><content type='html'>Definición. &lt;br /&gt;
  1855. Se dice que un espacio metrico $\left(S,d\right)$ es completo si toda sucesión de Cauchy en $S$ converge a un punto de $S$.&lt;br /&gt;
  1856. &lt;br /&gt;
  1857. Ejemplo. El espacio métrico $\left(\mathbb{Q},d\right)$ de los números racionales con el métrico definido por la función del valor absoluto NO es completo. &lt;br /&gt;
  1858. &lt;br /&gt;
  1859. Solución: Si $\left(X_{n}\right)$ es una sucesión de números racionales que converge a un número irracional, digamos a $\sqrt{2}$, entonces es una sucesión de Cauchy en $\mathbb{Q}$, pero no converge a un punto de $\mathbb{Q}$. Por lo tanto, $\left(\mathbb{Q},d\right)$ NO es un espacio métrico completo.&lt;br /&gt;
  1860. &lt;br /&gt;
  1861. Invitamos al lector a construir una sucesión de números racionales que sea convergente a un número no racional.&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/2763001610100479686/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/espacio-metrico-completo.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2763001610100479686'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2763001610100479686'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/espacio-metrico-completo.html' title='Espacio Métrico Completo'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-8346983153958476889</id><published>2014-01-24T07:14:00.001-08:00</published><updated>2014-01-24T07:14:50.452-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="trigonometría"/><title type='text'>Ecuaciones Trigonométricas</title><content type='html'>&lt;p&gt;Son aquellas en las cuales la inc&amp;#243;gnita aparece como &amp;#225;ngulo de funciones trigonom&amp;#233;tricas. &lt;/p&gt;
  1862. &lt;p&gt;No existe m&amp;#233;todo general para resolver una ecuaci&amp;#243;n trigonom&amp;#233;trica. Generalmente se transforma toda la ecuaci&amp;#243;n de manera que quede expresada en una sola funci&amp;#243;n trigonom&amp;#233;trica y entonces se resuelve como una ecuaci&amp;#243;n algebraica cualquiera. La &amp;#250;nica diferencia es que la inc&amp;#243;gnita es una funci&amp;#243;n trigonom&amp;#233;tica, en vez de ser X, Y o Z. &lt;/p&gt;
  1863. &lt;p&gt;Como a veces hay que elevar al cuadrado o multiplicar por un factor, se introducen soluciones extra&amp;#241;as. Por &amp;#233;sto, hay que comprobar las obtenidas en la ecuaci&amp;#243;n dada. Por ejemplo, si estamos resolviendo una ecuaci&amp;#243;n, cuya inc&amp;#243;gnita sea sen(a) y obtenemos para ella los valores -1 y 2, tenemos que despreciar el valor 2, porque el seno de un &amp;#225;ngulo no puede valer m&amp;#225;s de 1.&lt;/p&gt;
  1864. &lt;p&gt;Resulta la ecuaci&amp;#243;n algebraicamente, queda por resolver la parte trigonom&amp;#233;trica; es decir, conociendo el valor de la funci&amp;#243;n trigonom&amp;#233;trica de un &amp;#225;ngulo determinar cu&amp;#225;l es ese &amp;#225;ngulo. Recordemos que las funciones trigononetricas repiten sus valores en los cuadrantes, siendo positivas en dos de ellos y negativas en los otros dos, es decir, que hay dos &amp;#225;ngulos para los cuales una funci&amp;#243;n trigonom&amp;#233;trica tiene el mismo valor y signo. &lt;/p&gt;
  1865. &lt;p&gt;Adem&amp;#225;s, como las funciones trigonom&amp;#233;tricas de &amp;#225;ngulos que se diferencian en un n&amp;#250;mero exacto de vueltas, son iguales, ser&amp;#225; necesario a&amp;#241;adir a las soluciones obtenidas, un m&amp;#250;ltiplo cualquiera de 360&amp;#176;, es decir, n*360&amp;#176;. &lt;/p&gt;
  1866. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/8346983153958476889/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/ecuaciones-trigonometricas_8231.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/8346983153958476889'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/8346983153958476889'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/ecuaciones-trigonometricas_8231.html' title='Ecuaciones Trigonométricas'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-5385305625861118290</id><published>2014-01-21T16:55:00.001-08:00</published><updated>2014-01-21T16:55:26.169-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="topología"/><title type='text'>¿Que es la topologia?</title><content type='html'>&lt;p&gt;La topolog&amp;#237;a es una versi&amp;#243;n de la geometr&amp;#237;a, Euler dec&amp;#237;a q ademas de la geometr&amp;#237;a que trabajaba sobre cantidades habia otra que no se veia afectada por las cantidades y por ello cuando se manipulaba con la geometr&amp;#237;a normal no admit&amp;#237;a soluci&amp;#243;n, aquellas propiedades de las figuras que permanecen invariantes, cuando son plegadas, dilatadas, contraidas o deformadas, el estudio de estas propiedades no tenia sentido en la geometr&amp;#237;a anterior del siglo XVIII, por lo que plantearon una nueva versi&amp;#243;n, la topolog&amp;#237;a. Formalmente dir&amp;#237;amos que la topolog&amp;#237;a es la rama de las matem&amp;#225;ticas dedicadas al estudio de aquellas propiedades de los cuerpos geom&amp;#233;tricos que permanecen inalteradas por transformaciones continuas, con la topolog&amp;#237;a la geometr&amp;#237;a no se fija en las cantidades si no en las cualidades, asi la topolog&amp;#237;a considera los mismos objetos que el geometra pero de un modo distinto, no se fija en las distancias o los &amp;#225;ngulos y no ve diferencia entre c&amp;#237;rculo y elipse, una bola o un cubo, Henrry Poincare el gran creador de esta rama, escribir&amp;#237;a a principios del siglo XX, las proporciones de las figuras pueden ser alteradas pero sus elementos no pueden ser trastocados y deben conservar su posicion relativa, en otras palabras las propiedades cuantitativas no son importantes si no que se deben respetar las propiedades cualitativas, es decir, aquellas de las que se ocupa el analisis en situ, como Poincare denominaba a la topolog&amp;#237;a que provenia de la geometr&amp;#237;a de la&amp;#160; posici&amp;#243;n que utilizaba Euler. &lt;/p&gt;
  1867. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/5385305625861118290/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/que-es-la-topologia.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5385305625861118290'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5385305625861118290'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2014/01/que-es-la-topologia.html' title='¿Que es la topologia?'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-5481592061334773591</id><published>2013-05-16T12:09:00.003-07:00</published><updated>2013-05-16T12:23:26.597-07:00</updated><title type='text'>Cursos UNA, resolución de exámenes y realización de trabajos y tareas asignadas </title><content type='html'>&lt;div style=&quot;font-family: Times,&amp;quot;Times New Roman&amp;quot;,serif; text-align: justify;&quot;&gt;
  1868. &lt;span style=&quot;font-size: x-large;&quot;&gt;Hola amigos UNA, en vista de la demanda y de las llamadas que he recibido he decidido publicar esta entrada para darle una salida a aquellas personas que por una u otra razón se le hace imposible o complicado cumplir con las tareas encomendadas, solo deben comunicarse con tiempo a este numero &lt;b&gt;04148302137&lt;/b&gt; y preguntar por saul linares. saludos y éxitos, un abrazo.&lt;/span&gt;&lt;/div&gt;
  1869. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/5481592061334773591/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2013/05/cursos-una-resolucion-de-examenes-y.html#comment-form' title='9 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5481592061334773591'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5481592061334773591'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2013/05/cursos-una-resolucion-de-examenes-y.html' title='Cursos UNA, resolución de exámenes y realización de trabajos y tareas asignadas '/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>9</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-7849257848452125144</id><published>2013-01-16T10:16:00.002-08:00</published><updated>2013-01-16T10:17:54.307-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Examenes"/><category scheme="http://www.blogger.com/atom/ns#" term="UNA"/><title type='text'>Exámenes de la Universidad Nacional Abierta </title><content type='html'>Hola, esta entrada esta dirigida principalmente a los estudiantes de la&lt;b&gt; UNIVERSIDAD NACIONAL ABIERTA (UNA)&lt;/b&gt; Venezuela, aquí podran encontrar suficiente informacion de examenes de periodos anteriones.... estos examenes pertenecen al área de Licenciatura en Matemáticas, Educación matemática e&amp;nbsp; Ingeniería Industrial y Sistemas, cabe destacar que los únicos examenes de las ingenierias son las contenidas en los cursos de Matemáticas I, II, III, IV, V. &lt;br /&gt;
  1870. &lt;br /&gt;
  1871. A los amigos seguidodes del Blog en otros paises le hago saber que la información es muy interesante y didáctica si quieren verla y obtenerla solo deben descargarla..... vayan al siguiente link&lt;br /&gt;
  1872. &lt;br /&gt;
  1873. &lt;br /&gt;
  1874. &lt;span style=&quot;font-size: x-large;&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/p/blog-page_8559.html&quot; target=&quot;_blank&quot;&gt;Examenes&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
  1875. &lt;br /&gt;
  1876. &lt;br /&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/7849257848452125144/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2013/01/examenes-de-la-universidad-nacional.html#comment-form' title='12 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/7849257848452125144'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/7849257848452125144'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2013/01/examenes-de-la-universidad-nacional.html' title='Exámenes de la Universidad Nacional Abierta '/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>12</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-1284841624834114132</id><published>2012-11-23T17:12:00.000-08:00</published><updated>2012-11-23T17:12:20.057-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="planos"/><category scheme="http://www.blogger.com/atom/ns#" term="rectas"/><title type='text'>Distancia de un punto a una recta en el espacio</title><content type='html'>&lt;br /&gt;
  1877. &lt;div class=&quot;MsoNormal&quot;&gt;
  1878. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Hallar la distancia de punto P(-1,2,3) a la recta &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1879. &lt;div class=&quot;MsoNormal&quot;&gt;
  1880. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1881. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  1882. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpfHD9bJer6fN_IJgiMqvW3GTSGfHu3nfM3iSKw6tIm8fhX-uNBYD3fCZVtDIboJPUnQRe9sntlm-jLd1RMhNpQJ88ws7Wn4Qta9DlM5k2Aw_h-w4BVzndex_UGYEdTGDO7ryNDfCTLSM/s1600/recta1.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpfHD9bJer6fN_IJgiMqvW3GTSGfHu3nfM3iSKw6tIm8fhX-uNBYD3fCZVtDIboJPUnQRe9sntlm-jLd1RMhNpQJ88ws7Wn4Qta9DlM5k2Aw_h-w4BVzndex_UGYEdTGDO7ryNDfCTLSM/s1600/recta1.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  1883. &lt;br /&gt;
  1884. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  1885. &lt;br /&gt;&lt;/div&gt;
  1886. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1887. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Hace un tiempo me enfrente
  1888. a este problema, (no específicamente a este pero uno muy parecido), el cual lo
  1889. hice como lo explica la mayoría de los textos de cálculo, lo hice por
  1890. proyecciones. Después de un tiempo revisando un libro de geometría analítica sentí
  1891. curiosidad como daban solución este tipo de problemas y adopte esta forma: &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1892. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1893. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1894. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1895. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Solución&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1896. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1897. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1898. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1899. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  1900. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Es obvio que la distancia que pide el
  1901. problema es la distancia mínima.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1902. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1903. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1904. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1905. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  1906. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Se forma un plano que pase por el punto
  1907. dado y que sea perpendicular a la recta dada.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1908. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1909. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1910. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1911. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  1912. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Por supuesto si la recta es
  1913. perpendicular al plano el vector normal del plano es igual al vector director
  1914. de la recta.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1915. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  1916. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1917. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1918. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;La ecuación del plano
  1919. es:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1920. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1921. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1922. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1923. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;A(x-x&lt;sub&gt;0&lt;/sub&gt;)+B(y-y&lt;sub&gt;0&lt;/sub&gt;)+C(z-z&lt;sub&gt;0&lt;/sub&gt;)
  1924. = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1925. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1926. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1927. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1928. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;N
  1929. &lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;=
  1930. (A,B,C) vector normal del plano.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1931. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1932. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1933. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1934. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;a
  1935. = &lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;(6,
  1936. -2, 3) vector director de la recta&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
  1937. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1938. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1939. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1940. Entonces por lo expuesto
  1941. anteriormente el vector normal del plano es&lt;/div&gt;
  1942. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1943. &lt;br /&gt;&lt;/div&gt;
  1944. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1945. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;N
  1946. &lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;=
  1947. (6, -2, 3)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1948. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1949. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1950. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1951. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;El plano pasa por el
  1952. punto P(-1,2,3), y al sustituir en la ecuación del plano queda:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1953. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1954. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1955. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1956. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;6(x+1)-2(y-2)+3(z-3) =
  1957. 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1958. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1959. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1960. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1961. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;6x+6-2y+4+3z-9 = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1962. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1963. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1964. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1965. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;6x-2y+3z+1 = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1966. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1967. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1968. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1969. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Encontramos el plano
  1970. buscado, ahora viene la parte donde nos preguntamos ¿para qué encontramos ese
  1971. plano?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1972. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1973. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1974. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1975. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1976. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1977. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Esa pregunta es
  1978. sencilla de contestar, ese plano fue encontrado nada más y nada menos para
  1979. buscar la intersección de la recta y ese plano, osea, debemos encontrar el punto
  1980. de intersección para después buscar la distancia entre ese punto y el punto
  1981. dado, y esa será la distancia mínima porque es obvio que entre esos dos puntos
  1982. se forma una perpendicular a la recta.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1983. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1984. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1985. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1986. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1987. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1988. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Para encontrar ese
  1989. punto de intersección debemos expresar la recta simétrica dad en paramétrica,
  1990. esto se logra así:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  1991. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1992. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  1993. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  1994. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWHMWufSRcm1PmRZsENgwXXubfvLbfT7abQ8VKMME5D0EEJHMmX-RMFvHXX_5NceMdx9YKgtwo96aqIh73dqvyRrFfdc2Zz_ZeGMTSmmwMTiTjFlgTi5Q_9ote11TTkXy2sEmF7S6QGxA/s1600/recta32.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWHMWufSRcm1PmRZsENgwXXubfvLbfT7abQ8VKMME5D0EEJHMmX-RMFvHXX_5NceMdx9YKgtwo96aqIh73dqvyRrFfdc2Zz_ZeGMTSmmwMTiTjFlgTi5Q_9ote11TTkXy2sEmF7S6QGxA/s1600/recta32.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  1995. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1996. &lt;/div&gt;
  1997. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  1998. &lt;br /&gt;&lt;/div&gt;
  1999. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2000. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Luego&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2001. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2002. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2003. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2004. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;X = 6t + 7, Y = -2t – 3,
  2005. Z = 3t&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2006. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2007. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2008. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2009. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Ahora sustituimos en el
  2010. plano encontrado, 6x-2y+3z+1 = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2011. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2012. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2013. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2014. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;6(6t + 7)-2(-2t – 3)+3(3t)+1
  2015. = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2016. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2017. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2018. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2019. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;36t + 42 + 4t +6 +9t +1
  2020. = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2021. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2022. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2023. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2024. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;49t +49 = 0&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2025. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2026. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2027. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2028. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;t = -1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2029. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2030. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2031. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2032. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Con este valor de t =
  2033. -1, sustituimos y encontramos X, Y, Z (el punto de intersección)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2034. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2035. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2036. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2037. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;X = 6(-1) + 7, Y = -2(-1)
  2038. – 3, Z = 3(-1)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2039. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2040. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2041. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2042. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;X = 1, Y = -1, Z = -3&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2043. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2044. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2045. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2046. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;P&lt;sub&gt;1&lt;/sub&gt;(1,-1,-3)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2047. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2048. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2049. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2050. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;Ahora hayamos la
  2051. distancia entre P(-1,2,3) y P&lt;sub&gt;1&lt;/sub&gt;(1,-1,-3)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2052. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2053. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2054. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2055. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVQMs-vGQwh8MgGvDKCxN2P3135U5BsGohnLwd9SMzYTu5bEoR4sQiBi5VgCpwUL9QXuq4_W1v80IoEuT0J-XWF4cySQsEEnGOZt27YpBCsNmZPQ5Q7oqaui8SWdy5ZqgaVRQeMIaNQro/s1600/recta3.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; height=&quot;172&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVQMs-vGQwh8MgGvDKCxN2P3135U5BsGohnLwd9SMzYTu5bEoR4sQiBi5VgCpwUL9QXuq4_W1v80IoEuT0J-XWF4cySQsEEnGOZt27YpBCsNmZPQ5Q7oqaui8SWdy5ZqgaVRQeMIaNQro/s320/recta3.bmp&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2056. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2057. &lt;br /&gt;&lt;/div&gt;
  2058. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2059. &lt;br /&gt;&lt;/div&gt;
  2060. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2061. &lt;br /&gt;&lt;/div&gt;
  2062. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2063. &lt;br /&gt;&lt;/div&gt;
  2064. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2065. &lt;br /&gt;&lt;/div&gt;
  2066. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2067. &lt;br /&gt;&lt;/div&gt;
  2068. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2069. &lt;br /&gt;&lt;/div&gt;
  2070. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2071. &lt;br /&gt;&lt;/div&gt;
  2072. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2073. &lt;br /&gt;&lt;/div&gt;
  2074. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2075. &lt;br /&gt;&lt;/div&gt;
  2076. &lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: justify;&quot;&gt;
  2077. &lt;br /&gt;&lt;/div&gt;
  2078. &lt;div class=&quot;MsoNormal&quot;&gt;
  2079. &lt;br /&gt;&lt;/div&gt;
  2080. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/1284841624834114132/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/11/distancia-de-un-punto-una-recta-en-el.html#comment-form' title='4 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/1284841624834114132'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/1284841624834114132'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/11/distancia-de-un-punto-una-recta-en-el.html' title='Distancia de un punto a una recta en el espacio'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpfHD9bJer6fN_IJgiMqvW3GTSGfHu3nfM3iSKw6tIm8fhX-uNBYD3fCZVtDIboJPUnQRe9sntlm-jLd1RMhNpQJ88ws7Wn4Qta9DlM5k2Aw_h-w4BVzndex_UGYEdTGDO7ryNDfCTLSM/s72-c/recta1.bmp" height="72" width="72"/><thr:total>4</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-439151304128469022</id><published>2012-09-26T10:39:00.000-07:00</published><updated>2017-10-24T11:31:40.636-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="matemáticas"/><title type='text'>El ajedrez y las Matemáticas</title><content type='html'>&lt;br /&gt;
  2081. &lt;div class=&quot;MsoNormal&quot;&gt;
  2082. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , serif; font-size: 12pt; line-height: 150%; text-align: justify;&quot;&gt;Es increíble el gran número de personas
  2083. que asocian el ajedrez con las matemáticas, he tenido la oportunidad, en muchas
  2084. ocasiones, de asistir a torneos de ajedrez y especialmente observar partidas en
  2085. las categorías infantiles, siempre una sorpresa me aguarda, en cada ocasión me
  2086. encuentro con niños que destacan, hago referencias a categorías infantiles
  2087. porque en las categoría mayores no se percibe lo que voy a expresar en líneas posteriores,
  2088. tal vez no se perciba por el simple hecho que el curso de la vida ya está
  2089. definido a la edad adulta.&lt;/span&gt;&lt;/div&gt;
  2090. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2091. &lt;br /&gt;&lt;/div&gt;
  2092. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2093. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Cada vez que uno de estos pequeños se
  2094. corona campeón del torneo se nota emoción y felicidad en ellos, esto es normal,
  2095. es un aspecto tan natural de la vida emocionarse y alegrase por el éxito obtenido,
  2096. el éxito en cualquier aspecto de la vida ayuda a las personas a aumentar su
  2097. autoestima y en el caso especifico de los pequeños ayuda a fortalecer su carácter
  2098. y los prepara para el mundo que están por enfrentar a lo largo de su existencia.
  2099. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2100. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2101. &lt;br /&gt;&lt;/div&gt;
  2102. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2103. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;La emoción de los padres no se hace
  2104. esperar, sus hijos los llenan de orgullo, y por supuesto, prestar atención a
  2105. nuestros hijos es un aspecto fundamental que como padres debemos conocer,
  2106. aunque nuestro hijo no sea el campeón del torneo igual uno debe sentirse orgulloso de él, solo por el hecho de intentar obtener el triunfo.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2107. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2108. &lt;br /&gt;&lt;/div&gt;
  2109. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2110. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Al finalizar estos torneos, siempre los
  2111. padres están dispuestos a tomarse unos minutos para conversar sobre sus hijos, en
  2112. ese momento cuando me brindan la oportunidad o simplemente por el aspecto
  2113. sociable que caracteriza a los seres humanos, intervengo en las conversaciones,
  2114. tal vez me crean o no, pero es curioso escuchar las siguientes afirmaciones: “tu
  2115. hijo sabe jugar al ajedrez muy bien, debe ser bueno en matemáticas”, otros
  2116. dicen, “debe ser un niño que no tiene complicaciones con matemáticas”, cada vez
  2117. que escucho este tipo de comentarios solo sonrió.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2118. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2119. &lt;br /&gt;&lt;/div&gt;
  2120. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2121. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;El proceso inverso suele escucharse,
  2122. pero en poca proporción, es decir, niños aplicados en matemáticas son inscritos
  2123. en cursos vacacionales de ajedrez con la idea que será un buen ajedrecista por
  2124. el solo hecho de dominar matemáticas, este paradigma despertó mi curiosidad e
  2125. investigue sobre los campeones mundiales de ajedrez, observemos:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2126. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2127. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2128. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2129. &lt;br /&gt;&lt;/div&gt;
  2130. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2131. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;Campeones
  2132. del mundo no oficiales&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2133. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2134. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2135. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2136. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Ruy_L%C3%B3pez_de_Segura&quot; title=&quot;Ruy López de Segura&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Ruy López de Segura&lt;/span&gt;&lt;/a&gt;, ~1560,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Espa%C3%B1a&quot; title=&quot;España&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;España&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2137. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2138. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Paolo_Boi&quot; title=&quot;Paolo Boi&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Paolo Boi&lt;/span&gt;&lt;/a&gt;&amp;nbsp;y&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Leonardo_da_Cutri&quot; title=&quot;Leonardo da Cutri&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Leonardo da
  2139. Cutri&lt;/span&gt;&lt;/a&gt;, ~1575,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Italia&quot; title=&quot;Italia&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Italia&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2140. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2141. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Alessandro_Salvio&quot; title=&quot;Alessandro Salvio&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Alessandro
  2142. Salvio&lt;/span&gt;&lt;/a&gt;, ~1600, Italia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2143. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2144. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Gioacchino_Greco&quot; title=&quot;Gioacchino Greco&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Gioacchino
  2145. Greco&lt;/span&gt;&lt;/a&gt;, ~1620, Italia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2146. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2147. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Kermur_Sire_de_L%C3%A9gal&quot; title=&quot;Kermur Sire de Légal&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Legall de Kermeur&lt;/span&gt;&lt;/a&gt;, ~1730–1747,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Francia&quot; title=&quot;Francia&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Francia&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2148. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2149. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Philidor&quot; title=&quot;Philidor&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Philidor&lt;/span&gt;&lt;/a&gt;,
  2150. ~1747–1795, Francia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2151. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2152. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Alexandre_Deschapelles&quot; title=&quot;Alexandre Deschapelles&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Alexandre Deschapelles&lt;/span&gt;&lt;/a&gt;, ~1800–1820,
  2153. Francia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2154. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2155. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Louis_de_la_Bourdonnais&quot; title=&quot;Louis de la Bourdonnais&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Louis de la Bourdonnais&lt;/span&gt;&lt;/a&gt;, ~1820–1840,
  2156. Francia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2157. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2158. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Howard_Staunton&quot; title=&quot;Howard Staunton&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Howard
  2159. Staunton&lt;/span&gt;&lt;/a&gt;, 1843–1851,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Inglaterra&quot; title=&quot;Inglaterra&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Inglaterra&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2160. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2161. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Adolf_Anderssen&quot; title=&quot;Adolf Anderssen&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Adolf
  2162. Anderssen&lt;/span&gt;&lt;/a&gt;, 1851–1858,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Alemania&quot; title=&quot;Alemania&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Alemania&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2163. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2164. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Paul_Morphy&quot; title=&quot;Paul Morphy&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Paul Morphy&lt;/span&gt;&lt;/a&gt;,
  2165. 1858–1859,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Estados_Unidos&quot; title=&quot;Estados Unidos&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Estados Unidos&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2166. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2167. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Adolf_Anderssen&quot; title=&quot;Adolf Anderssen&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Adolf
  2168. Anderssen&lt;/span&gt;&lt;/a&gt;, 1859–1866, Alemania&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2169. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2170. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2171. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l3 level1 lfo1; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2172. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2173. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2174. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;Campeones
  2175. del mundo oficiales&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2176. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2177. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2178. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2179. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Wilhelm_Steinitz&quot; title=&quot;Wilhelm Steinitz&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Wilhelm
  2180. Steinitz&lt;/span&gt;&lt;/a&gt;, 1886–1894, Austria/EE. UU.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2181. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2182. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Emanuel_Lasker&quot; title=&quot;Emanuel Lasker&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Emanuel
  2183. Lasker&lt;/span&gt;&lt;/a&gt;, 1894–1921, Alemania&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2184. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2185. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Jos%C3%A9_Ra%C3%BAl_Capablanca&quot; title=&quot;José Raúl Capablanca&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;José Raúl Capablanca&lt;/span&gt;&lt;/a&gt;, 1921–1927,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Cuba&quot; title=&quot;Cuba&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Cuba&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2186. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2187. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Alexander_Alekhine&quot; title=&quot;Alexander Alekhine&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Alexander Alekhine&lt;/span&gt;&lt;/a&gt;, 1927–1935,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Rusia&quot; title=&quot;Rusia&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Rusia&lt;/span&gt;&lt;/a&gt;/Francia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2188. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2189. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Max_Euwe&quot; title=&quot;Max Euwe&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Max Euwe&lt;/span&gt;&lt;/a&gt;,
  2190. 1935–1937,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Pa%C3%ADses_Bajos&quot; title=&quot;Países Bajos&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Países Bajos&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2191. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2192. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Alexander_Alekhine&quot; title=&quot;Alexander Alekhine&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Alexander Alekhine&lt;/span&gt;&lt;/a&gt;, 1937–1946,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Francia&quot; title=&quot;Francia&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Francia&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2193. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2194. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Mija%C3%ADl_Botv%C3%ADnnik&quot; title=&quot;Mijaíl Botvínnik&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Mijaíl Botvínnik&lt;/span&gt;&lt;/a&gt;, 1948–1957,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Uni%C3%B3n_Sovi%C3%A9tica&quot; title=&quot;Unión Soviética&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Unión Soviética&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2195. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2196. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Vasili_Smyslov&quot; title=&quot;Vasili Smyslov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Vasili
  2197. Smyslov&lt;/span&gt;&lt;/a&gt;, 1957–1958, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2198. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2199. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Mija%C3%ADl_Botv%C3%ADnnik&quot; title=&quot;Mijaíl Botvínnik&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Mijaíl Botvínnik&lt;/span&gt;&lt;/a&gt;, 1958–1960, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2200. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2201. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Mija%C3%ADl_Tal&quot; title=&quot;Mijaíl Tal&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Mijaíl Tal&lt;/span&gt;&lt;/a&gt;,
  2202. 1960–1961, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2203. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2204. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Mija%C3%ADl_Botv%C3%ADnnik&quot; title=&quot;Mijaíl Botvínnik&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Mijaíl Botvínnik&lt;/span&gt;&lt;/a&gt;, 1961–1963, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2205. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2206. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Tigran_Petrosian&quot; title=&quot;Tigran Petrosian&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Tigran
  2207. Petrosian&lt;/span&gt;&lt;/a&gt;, 1963–1969, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2208. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2209. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Boris_Spassky&quot; title=&quot;Boris Spassky&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Boris Spassky&lt;/span&gt;&lt;/a&gt;,
  2210. 1969–1972, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2211. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2212. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Robert_James_Fischer&quot; title=&quot;Robert James Fischer&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Robert James Fischer&lt;/span&gt;&lt;/a&gt;, 1972–1975, EE. UU.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2213. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2214. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Anatoli_K%C3%A1rpov&quot; title=&quot;Anatoli Kárpov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Anatoli
  2215. Kárpov&lt;/span&gt;&lt;/a&gt;, 1975–1985, Unión Soviética&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2216. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l1 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2217. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Gari_Kasp%C3%A1rov&quot; title=&quot;Gari Kaspárov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Gari Kaspárov&lt;/span&gt;&lt;/a&gt;,
  2218. 1985–1993, Unión Soviética/Rusia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2219. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2220. &lt;br /&gt;&lt;/div&gt;
  2221. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2222. &lt;br /&gt;&lt;/div&gt;
  2223. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2224. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;Campeones
  2225. del mundo &quot;clásicos&quot;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2226. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2227. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2228. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2229. &lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10pt; line-height: 14.4pt; text-indent: -18pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , serif; font-size: 12pt; line-height: 14.4pt; text-indent: -18pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Gari_Kasp%C3%A1rov&quot; title=&quot;Gari Kaspárov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Gari Kaspárov&lt;/span&gt;&lt;/a&gt;,
  2230. 1993–2000, Rusia&lt;/span&gt;&lt;/div&gt;
  2231. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l4 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2232. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Vlad%C3%ADmir_Kr%C3%A1mnik&quot; title=&quot;Vladímir Krámnik&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Vladímir Krámnik&lt;/span&gt;&lt;/a&gt;, 2000–2006, Rusia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2233. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l4 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2234. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2235. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2236. &lt;br /&gt;&lt;/div&gt;
  2237. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2238. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;Campeones
  2239. del mundo de la FIDE desde 1993&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2240. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2241. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2242. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2243. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Anatoli_K%C3%A1rpov&quot; title=&quot;Anatoli Kárpov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Anatoli
  2244. Kárpov&lt;/span&gt;&lt;/a&gt;, 1993–1999, Rusia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2245. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2246. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Aleksandr_J%C3%A1lifman&quot; title=&quot;Aleksandr Jálifman&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Aleksandr Jálifman&lt;/span&gt;&lt;/a&gt;, 1999–2000, Rusia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2247. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2248. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Viswanathan_Anand&quot; title=&quot;Viswanathan Anand&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Viswanathan
  2249. Anand&lt;/span&gt;&lt;/a&gt;, 2000–2002, India&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2250. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2251. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Rusl%C3%A1n_Ponomariov&quot; title=&quot;Ruslán Ponomariov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Ruslán Ponomariov&lt;/span&gt;&lt;/a&gt;, 2002–2004,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Ucrania&quot; title=&quot;Ucrania&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Ucrania&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2252. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2253. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Rustam_Kasimdzhanov&quot; title=&quot;Rustam Kasimdzhanov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Rustam Kasimdzhanov&lt;/span&gt;&lt;/a&gt;, 2004–2005,&amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Uzbekist%C3%A1n&quot; title=&quot;Uzbekistán&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Uzbekistán&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2254. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2255. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Veselin_Topalov&quot; title=&quot;Veselin Topalov&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Veselin
  2256. Topalov&lt;/span&gt;&lt;/a&gt;, 2005–2006,&amp;nbsp;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Bulgaria&quot; title=&quot;Bulgaria&quot;&gt;Bulgaria&lt;/a&gt;&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2257. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2258. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2259. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l2 level1 lfo4; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2260. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2261. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2262. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;Campeones
  2263. del mundo unificados&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2264. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-margin-top-alt: auto;&quot;&gt;
  2265. &lt;b&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 14.0pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
  2266. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l0 level1 lfo5; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2267. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Vlad%C3%ADmir_Kr%C3%A1mnik&quot; title=&quot;Vladímir Krámnik&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Vladímir Krámnik&lt;/span&gt;&lt;/a&gt;, 2006-2007 , Rusia&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2268. &lt;div class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 14.4pt; margin-bottom: 1.2pt; margin-left: 19.2pt; mso-list: l0 level1 lfo5; mso-margin-top-alt: auto; tab-stops: list 36.0pt; text-indent: -18.0pt;&quot;&gt;
  2269. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;wingdings&amp;quot;; font-size: 10.0pt;&quot;&gt;§&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;a href=&quot;http://es.wikipedia.org/wiki/Viswanathan_Anand&quot; title=&quot;Viswanathan Anand&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Viswanathan
  2270. Anand&lt;/span&gt;&lt;/a&gt;, 2007– , India ( actual campeón del mundo)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2271. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2272. &lt;br /&gt;&lt;/div&gt;
  2273. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2274. &lt;br /&gt;&lt;/div&gt;
  2275. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2276. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;¿Qué te dice esa lista? Si conoces de
  2277. ajedrez te dice mucho, si no conoces de ajedrez te dice poco o nada, en mi investigación
  2278. busque la biografía de cada uno de estos campeones, parece increíble pero la
  2279. gran variedad de oficios a los que se dedicaban o se dedican estos campeones de
  2280. ajedrez es de considerar, la gran mayoría son ajedrecista de profesión, otros
  2281. nunca terminaron sus carreras universitarias, un gran porcentaje son
  2282. escritores, otros políticos, psicólogos, es como tratar de buscar un patrón o
  2283. secuencia a los números primos, hasta la actualidad imposible.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2284. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2285. &lt;br /&gt;&lt;/div&gt;
  2286. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2287. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Es curioso observar que solo dos (2) campeones
  2288. mundiales de ajedrez han sido matemáticos de profesión, ellos son &amp;nbsp;&lt;a href=&quot;http://es.wikipedia.org/wiki/Emanuel_Lasker&quot; title=&quot;Emanuel Lasker&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;EMANUEL
  2289. LASKER&lt;/span&gt;&lt;/a&gt;&amp;nbsp; --&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot;, serif; font-size: 16px;&quot;&gt;27 años con el titulo--&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12pt; line-height: 150%;&quot;&gt;&amp;nbsp;y &lt;a href=&quot;http://es.wikipedia.org/wiki/Max_Euwe&quot; title=&quot;Max Euwe&quot;&gt;&lt;span style=&quot;text-decoration-line: none;&quot;&gt;MAX EUWE&lt;/span&gt;&lt;/a&gt;&amp;nbsp;--&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , serif; font-size: 12pt;&quot;&gt;2 años con el titulo--&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , serif; font-size: 12pt;&quot;&gt;, es cierto que LASKER es el campeón del mundo de ajedrez
  2290. que más tiempo ha retenido el titulo, durante 27 años consecutivos, pero esto
  2291. no indica que haya sido por las matemáticas, la historia atribuye a su éxito en
  2292. ajedrez a los aspectos psicológicos del juego, sin embargo, EUWE, quien obtuvo
  2293. un doctorado en matemáticas solo retuvo el título 2 años.&lt;/span&gt;&lt;/div&gt;
  2294. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2295. &lt;br /&gt;
  2296. &lt;br /&gt;
  2297. &lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white; background-position: initial initial; background-repeat: initial initial; line-height: 150%; margin-bottom: 0.0001pt;&quot;&gt;
  2298. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Para finalizar, vuelvo
  2299. y repito, tratar de buscar alguna dependencia entre matemáticas y ajedrez es
  2300. como buscar una fórmula o&amp;nbsp;relación&amp;nbsp;de recurrencia que genere los
  2301. números primos, tal vez no sea imposible, pero vaya que es difícil, a mi juicio,
  2302. estas características no son dependientes, una no implica la otra o viceversa,
  2303. son mitos creados tal vez por el desconocimiento de una o ambas actividades.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2304. &lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white; background-position: initial initial; background-repeat: initial initial; line-height: 150%; margin-bottom: 0.0001pt;&quot;&gt;
  2305. &lt;br /&gt;&lt;/div&gt;
  2306. &lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white; background-position: initial initial; background-repeat: initial initial; line-height: 150%; margin-bottom: 0.0001pt;&quot;&gt;
  2307. &lt;span style=&quot;font-family: &amp;quot;times new roman&amp;quot; , &amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Saul linares&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2308. &lt;/div&gt;
  2309. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/439151304128469022/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/el-ajedrez-y-las-matematicas.html#comment-form' title='4 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/439151304128469022'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/439151304128469022'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/el-ajedrez-y-las-matematicas.html' title='El ajedrez y las Matemáticas'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>4</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-5492484464027680051</id><published>2012-09-25T09:14:00.000-07:00</published><updated>2012-09-25T09:14:56.584-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Biografías"/><title type='text'>Niels Henrik Abel</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2310. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheAMg4Kuy1tQkehQU6RyoShyqu_tFClvAQd9UcHbjoDukzpvJNM0kFcxUN-mxiWcIgDuBU6HRdXWcKCf-XJl00MV_piMMRYkMxZEezc93oV-LTqEt5ijWMfQla2PhapTeWZ9zO-1VlRZc/s1600/abel.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: right; float: right; margin-bottom: 1em; margin-left: 1em;&quot;&gt;&lt;img border=&quot;0&quot; height=&quot;320&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheAMg4Kuy1tQkehQU6RyoShyqu_tFClvAQd9UcHbjoDukzpvJNM0kFcxUN-mxiWcIgDuBU6HRdXWcKCf-XJl00MV_piMMRYkMxZEezc93oV-LTqEt5ijWMfQla2PhapTeWZ9zO-1VlRZc/s320/abel.bmp&quot; width=&quot;313&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2311. &lt;br /&gt;
  2312. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2313. &lt;/div&gt;
  2314. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: 0.0001pt;&quot;&gt;
  2315. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Niels Henrik Abel&lt;span style=&quot;text-align: start;&quot;&gt; (&lt;/span&gt;&lt;a href=&quot;http://es.wikipedia.org/w/index.php?title=Find%C3%B6&amp;amp;action=edit&amp;amp;redlink=1&quot; style=&quot;text-align: start;&quot; title=&quot;Findö (aún no redactado)&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Findö&lt;/span&gt;&lt;/a&gt;&lt;span style=&quot;text-align: start;&quot;&gt;, &lt;a href=&quot;http://es.wikipedia.org/wiki/Noruega&quot; title=&quot;Noruega&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Noruega&lt;/span&gt;&lt;/a&gt;, &lt;a href=&quot;http://es.wikipedia.org/wiki/5_de_agosto&quot; title=&quot;5 de agosto&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;5 de agosto&lt;/span&gt;&lt;/a&gt; de &lt;a href=&quot;http://es.wikipedia.org/wiki/1802&quot; title=&quot;1802&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;1802&lt;/span&gt;&lt;/a&gt; - &lt;a href=&quot;http://es.wikipedia.org/w/index.php?title=Froland&amp;amp;action=edit&amp;amp;redlink=1&quot; title=&quot;Froland (aún no redactado)&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Froland&lt;/span&gt;&lt;/a&gt;, &lt;a href=&quot;http://es.wikipedia.org/wiki/Noruega&quot; title=&quot;Noruega&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;Noruega&lt;/span&gt;&lt;/a&gt;, &lt;a href=&quot;http://es.wikipedia.org/wiki/6_de_abril&quot; title=&quot;6 de abril&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;6 de abril&lt;/span&gt;&lt;/a&gt;de &lt;a href=&quot;http://es.wikipedia.org/wiki/1829&quot; title=&quot;1829&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;1829&lt;/span&gt;&lt;/a&gt;) fue un &lt;a href=&quot;http://es.wikipedia.org/wiki/Matem%C3%A1tico&quot; title=&quot;Matemático&quot;&gt;&lt;span style=&quot;color: windowtext; text-decoration: none; text-underline: none;&quot;&gt;matemático&lt;/span&gt;&lt;/a&gt; noruego.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2316. &lt;br /&gt;
  2317.  
  2318.  
  2319. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2320. &lt;br /&gt;&lt;/div&gt;
  2321. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2322. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Hijo
  2323. de un pastor protestante, creció en un ambiente familiar de mucha pobreza a
  2324. causa de las tendencias alcohólicas de su padre. Fue enviado a estudiar junto a
  2325. su hermano a una Escuela de Oslo; su precocidad para las matemáticas fueron valoradas
  2326. por sus profesores, especialmente Holm Boe, quien tras la muerte de su
  2327. progenitor, le ayudo en el financiamiento de sus estudios universitarios. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2328. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2329. &lt;br /&gt;&lt;/div&gt;
  2330. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2331. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Tras
  2332. ganarse junto a JACOBI el gran premio de las matemáticas del Instituto de
  2333. Francia por el brillante y novedoso tema sobre la teoría de las funciones
  2334. elípticas, en viaje a Berlín, publica en el Diario Creelles, medio escrito
  2335. especializado en tema matemático, la demostración de la imposibilidad de la
  2336. resolución de los ecuaciones de quinto grado usando raíces. Fue considerado el
  2337. mejor algebrista del siglo XIX. Los aportes de Abel son fundamentales para el
  2338. desarrollo de un método general para la construcción de funciones periódicas reciprocas
  2339. de las integrales elípticas.Sus obras fueron publicadas por el Gobierno Sueco en
  2340. 1.839, por el interés de su ilustre profesor M. Holmboe, en la Universidad Cristiana
  2341. (hoy Oslo). De regreso a Noruega, su salud comenzó a decaer y en medio de la
  2342. pobreza le fue diagnosticada una tuberculosis, enfermedad que lo llevo a la
  2343. muerte en 1.819. Su vida fue corta y sumida en la pobreza. No tuvo reconocimiento
  2344. a pesar de su monumental obra.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2345. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2346. &lt;br /&gt;&lt;/div&gt;
  2347. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;&quot;&gt;
  2348. &lt;br /&gt;&lt;/div&gt;
  2349. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/5492484464027680051/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/niels-henrik-abel.html#comment-form' title='1 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5492484464027680051'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5492484464027680051'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/niels-henrik-abel.html' title='Niels Henrik Abel'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheAMg4Kuy1tQkehQU6RyoShyqu_tFClvAQd9UcHbjoDukzpvJNM0kFcxUN-mxiWcIgDuBU6HRdXWcKCf-XJl00MV_piMMRYkMxZEezc93oV-LTqEt5ijWMfQla2PhapTeWZ9zO-1VlRZc/s72-c/abel.bmp" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-4833553142766965826</id><published>2012-09-25T08:07:00.000-07:00</published><updated>2012-09-25T09:23:33.568-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="álgebra"/><title type='text'>Grupo (Definición)</title><content type='html'>&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  2350. &lt;br /&gt;
  2351. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2352. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: large; line-height: 150%;&quot;&gt;Un conjunto G no vacio con una ley de composición
  2353. interna *, decimos que es un grupo respecto a esa ley, si (G, *) verifica las
  2354. siguientes propiedades: &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2355. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2356. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2357. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2358. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Symbol; line-height: 150%;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  2359. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;La ley de composición * es asociativa,
  2360. es decir: &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2361. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2362. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: large; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2363. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-indent: 35.4pt;&quot;&gt;
  2364. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;(x*y)*z = x*(y*z),
  2365. cualquiera sean x, y, z &lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2366. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-indent: 35.4pt;&quot;&gt;
  2367. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2368. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2369. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Symbol; line-height: 150%;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  2370. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;Existe un elemento neutro e &lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G. Es decir, existe e &lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G tal que:&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2371. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2372. &lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; font-size: large; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2373. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-indent: 35.4pt;&quot;&gt;
  2374. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;e*x = x*e = x, para
  2375. todo x &lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2376. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-indent: 35.4pt;&quot;&gt;
  2377. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2378. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2379. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Symbol; line-height: 150%;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
  2380. &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;Para todo x &lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G, existe un elemento simétrico de x. Es decir ,
  2381. existe x’&lt;/span&gt; &amp;nbsp;&lt;span style=&quot;background-color: white; font-family: &#39;Cambria Math&#39;, serif; line-height: 150%;&quot;&gt;∈&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt; G tal que:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2382. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; text-align: justify;&quot;&gt;
  2383. &lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; font-size: large; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2384. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; text-align: justify;&quot;&gt;
  2385. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;x* x’&lt;/span&gt; = x’*x = e.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2386. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; text-align: justify;&quot;&gt;
  2387. &lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2388. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2389. &lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;Si además de
  2390. cumplirse estas propiedades y la ley de composición es conmutativa, se dice que
  2391. el grupo G es conmutativo o abeliano.&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-size: small;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
  2392. &lt;span style=&quot;background-color: white; font-family: &#39;Times New Roman&#39;, serif; line-height: 150%;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;
  2393. &lt;a href=&quot;http://linaresgsj.blogspot.com/2012/09/niels-henrik-abel.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;font-family: Times New Roman, serif; font-size: large;&quot;&gt;Biografía de&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Trebuchet MS&#39;, Trebuchet, Verdana, sans-serif; font-size: 22px; line-height: normal; text-align: start;&quot;&gt;Niels Henrik Abel&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;
  2394. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/4833553142766965826/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/grupo-definicion.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/4833553142766965826'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/4833553142766965826'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/grupo-definicion.html' title='Grupo (Definición)'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-7228569835496863802</id><published>2012-09-23T10:37:00.000-07:00</published><updated>2012-09-23T10:59:52.571-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="matemáticas"/><title type='text'>La matemática de Thales de Mileto</title><content type='html'>&lt;br /&gt;
  2395. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2396. &lt;/div&gt;
  2397. &lt;div class=&quot;MsoNormal&quot;&gt;
  2398. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 14pt; line-height: 115%; text-indent: 0cm;&quot;&gt;No está claro que descubrió o conoció Thales, sin
  2399. embargo los siguientes teoremas se le atribuyen:&lt;/span&gt;&lt;/div&gt;
  2400. &lt;div class=&quot;MsoNormal&quot;&gt;
  2401. &lt;br /&gt;&lt;/div&gt;
  2402. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2403. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 14.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;Los
  2404. ángulos de la base de un triangulo isósceles son iguales.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2405. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2406. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 14.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;Un
  2407. círculo es bisecado por cualquier diámetro.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2408. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2409. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 14.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;Los
  2410. ángulos entre dos líneas rectas que se cortan son iguales (opuesto por el vértice).&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2411. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2412. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 14.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;Dos
  2413. triángulos son congruentes si ellos tienen dos ángulos y un lado igual.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2414. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2415. &lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: Symbol; font-size: 14.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;·&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;Todo
  2416. ángulo inscrito en una semicircunferencia es recto.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2417. &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto;&quot;&gt;
  2418. &lt;br /&gt;&lt;/div&gt;
  2419. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto;&quot;&gt;
  2420. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 14.0pt; line-height: 150%;&quot;&gt;&lt;a href=&quot;http://www.linaresgsj.blogspot.com/2012/01/tales-de-mileto.html&quot; target=&quot;_blank&quot;&gt;&lt;span style=&quot;color: red;&quot;&gt;Biografía de Thales de Mileto&lt;/span&gt;&lt;/a&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2421. &lt;br /&gt;
  2422. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2423. &lt;br /&gt;&lt;/div&gt;
  2424. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2425. &lt;span style=&quot;font-family: Times New Roman, serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2426. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; margin-left: 17.85pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: 0cm;&quot;&gt;
  2427. &lt;br /&gt;&lt;/div&gt;
  2428. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/7228569835496863802/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/la-matematica-de-thales-de-mileto.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/7228569835496863802'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/7228569835496863802'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/la-matematica-de-thales-de-mileto.html' title='La matemática de Thales de Mileto'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-8518064547365017663</id><published>2012-09-16T07:49:00.000-07:00</published><updated>2012-09-16T07:49:10.011-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Biografías"/><title type='text'>Nota histórica sobre la Transformada de Laplace</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2429. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtDLO9lrSXnR95YHzdc-w8yIL4j7gjE8fRkWwWWO2N6bIQ6N6yH9i-S0rs8tO7Vj_M-uVv8xbwMjr094b9ekJj5AlqV33G-Q70yqlGvAn4y6yFW-MiJ0lYUPt3HI1hwas1Rhb0G_Yv_dE/s1600/laplace.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: right; float: right; margin-bottom: 1em; margin-left: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtDLO9lrSXnR95YHzdc-w8yIL4j7gjE8fRkWwWWO2N6bIQ6N6yH9i-S0rs8tO7Vj_M-uVv8xbwMjr094b9ekJj5AlqV33G-Q70yqlGvAn4y6yFW-MiJ0lYUPt3HI1hwas1Rhb0G_Yv_dE/s1600/laplace.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2430. &lt;br /&gt;
  2431. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2432. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Pierre-Simon de Laplace nació el 23 de
  2433. marzo de 1749 en Beaumont-en-Auge y falleció el 5 de marzo de 1827. A los 19
  2434. años viajó a Paris a estudiar matemáticas, donde rápidamente impresionó a d’Alembert,
  2435. quien lo apadrinó y le consiguió trabajo de profesor de matemáticas en la École
  2436. Militaire. Debido a la gran cantidad de trabajos de calidad que presentó y la
  2437. variedad de temas que abordó, ya a los 24 años se le conocía como “el Newton de
  2438. Francia”. El matemático Anders Lexell, contemporáneo de Laplace, escribió que
  2439. Laplace mismo se consideraba el mejor matemático de Francia, y que “quería
  2440. opinar acerca de todo”. Entre los trabajos de Laplace destaca sobre todo su
  2441. “Tratado de Mecánica Celeste”, obra que publicó en cinco volúmenes entre 1799 y
  2442. 1825 y que suele considerarse como la culminación de la teoría newtoniana de la
  2443. gravitación. El otro gran aporte de Laplace se encuentra en el campo de la
  2444. Teoría de Probabilidades. La primera edición de la “Teoría Analítica de las
  2445. Probabilidades” fue publicada en 1812 y en ella consideró las probabilidades
  2446. desde todos los puntos de vista: presenta el método de los mínimos cuadrados,
  2447. el problema de la aguja de Bufón, aplicaciones a la mortalidad, expectativa de
  2448. vida y a problemas legales; incluye también aplicaciones para determinar la
  2449. masa de Júpiter, Saturno y Urano, métodos de triangulación y un método para
  2450. determinar el meridiano de Francia. Y contiene lo que hoy conocemos como la
  2451. Transformada de Laplace. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2452. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2453. &lt;br /&gt;&lt;/div&gt;
  2454. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2455. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;La transformada de Laplace aparece por
  2456. primera vez en el trabajo de Euler de 1769, “Institutiones Calculi Integralis”,
  2457. al resolver la ecuación: &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2458. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2459. &lt;br /&gt;&lt;/div&gt;
  2460. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2461. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Ly”+ My’+ Ny = U&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2462. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2463. &lt;br /&gt;&lt;/div&gt;
  2464. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;&quot;&gt;
  2465. &lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; line-height: 150%;&quot;&gt;Sin embargo, quizás por la frecuencia
  2466. con que Laplace la usó y por la profundidad de los resultados que logró, la
  2467. transformada lleva su nombre. Durante el siglo XIX se le conocía con el nombre
  2468. “Método de Laplace” y aunque hubo muchos matemáticos que contribuyeron a la
  2469. teoría, fue Poincaré quien desarrolla de nuevo la transformada de Laplace. Sin
  2470. embargo, la transformada de Laplace como la conocemos hoy, se debe al trabajo
  2471. de Gustav Doetsch de 1937.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2472. &lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/8518064547365017663/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/nota-historica-sobre-la-transformada-de.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/8518064547365017663'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/8518064547365017663'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/nota-historica-sobre-la-transformada-de.html' title='Nota histórica sobre la Transformada de Laplace'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtDLO9lrSXnR95YHzdc-w8yIL4j7gjE8fRkWwWWO2N6bIQ6N6yH9i-S0rs8tO7Vj_M-uVv8xbwMjr094b9ekJj5AlqV33G-Q70yqlGvAn4y6yFW-MiJ0lYUPt3HI1hwas1Rhb0G_Yv_dE/s72-c/laplace.bmp" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-2524960190918716639</id><published>2012-09-14T19:15:00.000-07:00</published><updated>2012-09-14T19:16:51.345-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="integrales"/><title type='text'>Tabla de Integrales</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2473. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv2nS6OCb_E9uTh2-GHJNtrBLARINwdrdv9BLzqOFHZUBHey8smrQetDZFTpPv7Uf8NMqCRCT7q-a7JgZzmMMT03rrZf_sP2CBdooPis_RajS-HoM686YjgEHn24t6_ExZP-ZF7uKtls8/s1600/tabla.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; height=&quot;200&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv2nS6OCb_E9uTh2-GHJNtrBLARINwdrdv9BLzqOFHZUBHey8smrQetDZFTpPv7Uf8NMqCRCT7q-a7JgZzmMMT03rrZf_sP2CBdooPis_RajS-HoM686YjgEHn24t6_ExZP-ZF7uKtls8/s400/tabla.bmp&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2474. &lt;br /&gt;
  2475. &lt;br /&gt;
  2476. &lt;br /&gt;
  2477. &lt;br /&gt;
  2478. &lt;br /&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/2524960190918716639/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/tabla-de-integrales.html#comment-form' title='0 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2524960190918716639'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/2524960190918716639'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/09/tabla-de-integrales.html' title='Tabla de Integrales'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv2nS6OCb_E9uTh2-GHJNtrBLARINwdrdv9BLzqOFHZUBHey8smrQetDZFTpPv7Uf8NMqCRCT7q-a7JgZzmMMT03rrZf_sP2CBdooPis_RajS-HoM686YjgEHn24t6_ExZP-ZF7uKtls8/s72-c/tabla.bmp" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-3396485665399624067</id><published>2012-07-08T07:31:00.000-07:00</published><updated>2012-07-08T07:33:51.615-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="ecuación diferencial"/><title type='text'>Ecuación diferencial de primer orden</title><content type='html'>&lt;br /&gt;
  2479. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2480. Hola, la ecuación diferencial&lt;/div&gt;
  2481. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2482. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK9BTCZ46RN6oahamTsnUBxDZ5vSgoTbf2H0Qi5tKLFTPK1JlWzvhT5hefZwAFt97riX6IE5zNaXYx0JddtCoI6F-KLfTn8rpUVUHFBtA37iRUQUjiO18NRabRNsQwQE3l9ScJTGwTVjo/h104/6.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2483. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2484. Es una ecuación lineal de primer orden. Es de la forma:&lt;/div&gt;
  2485. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2486. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBglgkZPwI7VTVecNTy6s64SHC4p3vfTo_l5E6MA75lvh369X1N8x1zEix6ZEh3wdzZJZ8UOqiqwflRhA3XaqTmm6hUwEdZXa4aq6cCPE0rfiUoPSciL_BZE1aRmtsr0aVWjuW1OfqAIg/h119/1.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2487. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2488. Este tipo de ecuacion diferencial se resuelve por medio de un factor integrante de la forma&lt;/div&gt;
  2489. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2490. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4oZngBg32EiFWxv4VsZfiKJBhYHeAT2DbSs1MdVYJJ32SRSy3KPtWpjkTI7wCeT2TA1Zp9KL1qFBGqyk3JxA7Rbq8sHPjy7YYX8__ePrqZyXVpjMnSDoNWl6qC6Z3jA2uRhGHztCgOA0/h120/2.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2491. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2492. Para este caso tenemos:&lt;/div&gt;
  2493. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2494. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1w2233ODcUx4HEYFCsVwIkQARRUMqrLWNiRpWZZQwWp2jFtW98uE4j8QPuen31d-st0WNqHzjbzL99Tkj0Ns92mWF7DNXAnlyUFlCsy4qkfH9SXTd9GNaVvJuNJzgaH1mZfoJlx4RFn4/h120/3.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2495. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2496. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTrLe434f64HjfaLz3GuhbA3Cmnm5KdiSrG8afhNyg6vjArJ8EFNinXbCXs_c1gnUdoKJ9Yxca3ihiC2bu88t2t4PRxK2UVnkDAhHLsxstEzEUECgi0UXaIEEZY8j2d6rTO9r_Zhk6-i8/h120/4.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2497. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2498. Esta última expresión es el factor integrante, ese factor debe multiplicarse por la ecuación diferencial dada. Haciendo esa operacion tenemos:&lt;/div&gt;
  2499. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2500. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0OKjL_imyGow1e7pT682U1DQEX1mTSdUaaOWASa4P53SvPNeSwUIjSXXs0ga5qwC757JfIHzkDaWDNhS_k2HV_UAgjO9JWzNoN_J60CgrszfE2BMIp3X4xb1DZWrNIJSm4yx-olq6n0k/h65/7.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2501. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2502. Simplificando&lt;/div&gt;
  2503. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2504. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgizB0iD05p14-SoIJSZdvDFODb4A3j0m19-RjR1hyphenhyphen9lo15e5w6O_OH_lenfoid9T9seF1jGYDWdM0dtWQs1gL66Y70HDX-Rz8HbUi0u8vJU78R-ED4_g-lz_p2U87lHAbyhyphenhyphenFUKyMVgms/h58/8.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2505. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2506. El primer miembro de la ecuación es una diferencial exacta, se transforma a:&lt;/div&gt;
  2507. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2508. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHybBscTT_Enhs3DgCOm47nnrWTW7YRO-FuiOKPCkWDFMsAh_YEWHLUJF2aNHEnfQXZ-hCH9ARQbGAAg2ZdDmUAUMTtfC91UsDTULzLpJPvcz9GcTVn0VyGY8qOq-2oTsM574w-yjUXcs/h72/9.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2509. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2510. Transponiendo el diferencial (dx) al segundo miembro, tenemos:&lt;/div&gt;
  2511. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2512. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOVhWl_b4O-oDDfv5OD7yrTv3c5oF4yqur49QnSNk9Szbag4-_QScPQiYs-YsjpnVWjruE2PmvIZepMQNokvAbMi5IQGc0wS24sY38bQE9YKujfy3sbol6MwS5rB5m6VgcMSYxMeCYCCs/h49/10.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2513. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2514. Aplicando integrales queda&lt;/div&gt;
  2515. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2516. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFuDZLt1fVvVRMwIVvk7df2MTO4teLWl0elsQohEQiY79k_RBFQ5NXPBQ_n87e4474XQc7xu5oLT7EYr-EA1wWhpoMI3D-G1jgv0MHTso_CKu6XeKW_fxGsbhZjr3ObRb44GaJFl7avFc/h67/11.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2517. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2518. Resolviendo las integrales tenemos&lt;/div&gt;
  2519. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2520. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9jKWIdvQImpzT0aja-wbJkGn2BVqRSvw615jPghIzxOIvV9ZOrCt4LJOtAzncMbLhx8FfyVJXQFzVLvh5Vx3VDkvYNl0AuCOdATyxJ8kD1VJ6UOZXcGrKzZEt_Qbc_Om4s9ccKIgYD9w/h83/12.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2521. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2522. Despejando &quot;y&quot; se obtiene la solución:&lt;/div&gt;
  2523. &lt;br /&gt;
  2524. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2525. &lt;img src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3lwjwlOgKlJJaw0tkQG2OazNYmIl0rubhmFzcuyYJ-fCi4Rmj0GD3Q1btgZTo8pDeuyZTgupje8fr_anGbH5c8LGezRzvIWa9WlTMR2NYbqz9sek8YUOWltDEy4XyqVhTkFisPeU4FRE/h111/13.bmp&quot; style=&quot;border: 0px;&quot; /&gt;&lt;/div&gt;
  2526. &lt;div style=&quot;border: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 12px; margin-bottom: 10px; outline: 0px; padding: 0px;&quot;&gt;
  2527. Fin.&lt;/div&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/3396485665399624067/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/07/ecuacion-diferencial-de-primer-orden.html#comment-form' title='1 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3396485665399624067'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/3396485665399624067'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/07/ecuacion-diferencial-de-primer-orden.html' title='Ecuación diferencial de primer orden'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK9BTCZ46RN6oahamTsnUBxDZ5vSgoTbf2H0Qi5tKLFTPK1JlWzvhT5hefZwAFt97riX6IE5zNaXYx0JddtCoI6F-KLfTn8rpUVUHFBtA37iRUQUjiO18NRabRNsQwQE3l9ScJTGwTVjo/s72-h104-c/6.bmp" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-1269960585318326134</id><published>2012-02-02T18:06:00.000-08:00</published><updated>2014-07-03T14:24:11.312-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="integrales"/><title type='text'>Integral por partes</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2528. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg5xXOQm0xmmaDNJFt-m5oy1Znb2Owsa904EkXsUTRHC7-X23xL83aKUQmwQr-wjlrCIWF6VFzBBpl4SeXDFDqtISQ2o6NjlCTpUzemBRlDqmcuCsXpxENnYqrk1ZNKuzqc6RAWzqOalM/s1600/B1.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg5xXOQm0xmmaDNJFt-m5oy1Znb2Owsa904EkXsUTRHC7-X23xL83aKUQmwQr-wjlrCIWF6VFzBBpl4SeXDFDqtISQ2o6NjlCTpUzemBRlDqmcuCsXpxENnYqrk1ZNKuzqc6RAWzqOalM/s200/B1.bmp&quot; height=&quot;74&quot; width=&quot;200&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2529. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
  2530. &lt;/div&gt;
  2531. &lt;h1&gt;
  2532.  
  2533.  
  2534.  
  2535. &lt;span lang=&quot;ES&quot; style=&quot;font-weight: normal;&quot;&gt;&lt;span style=&quot;font-size: small;&quot;&gt;Es una integral por partes, se resuelve por medio de la formula&lt;/span&gt;&lt;/span&gt;&lt;/h1&gt;
  2536. &lt;br /&gt;
  2537. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2538. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidshS0IURhkEi_FwioIJpcYTrRZNn2jcACmKbLSLINMvtF8g-iQOLD7noeIU13zfCzrHYLtT1jepfy_C08PaZcoILh8gOFdLA_WgG3KgiCtgqe3YLNnF7gMoLncjrxCmrQ9toBGDYhK3k/s1600/B2.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidshS0IURhkEi_FwioIJpcYTrRZNn2jcACmKbLSLINMvtF8g-iQOLD7noeIU13zfCzrHYLtT1jepfy_C08PaZcoILh8gOFdLA_WgG3KgiCtgqe3YLNnF7gMoLncjrxCmrQ9toBGDYhK3k/s1600/B2.bmp&quot; /&gt;&lt;/a&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidshS0IURhkEi_FwioIJpcYTrRZNn2jcACmKbLSLINMvtF8g-iQOLD7noeIU13zfCzrHYLtT1jepfy_C08PaZcoILh8gOFdLA_WgG3KgiCtgqe3YLNnF7gMoLncjrxCmrQ9toBGDYhK3k/s1600/B2.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidshS0IURhkEi_FwioIJpcYTrRZNn2jcACmKbLSLINMvtF8g-iQOLD7noeIU13zfCzrHYLtT1jepfy_C08PaZcoILh8gOFdLA_WgG3KgiCtgqe3YLNnF7gMoLncjrxCmrQ9toBGDYhK3k/s1600/B2.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;/div&gt;
  2539. &lt;span style=&quot;text-align: left;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
  2540. &lt;div style=&quot;text-align: left;&quot;&gt;
  2541. &lt;br /&gt;&lt;/div&gt;
  2542. &lt;div style=&quot;text-align: left;&quot;&gt;
  2543. &lt;br /&gt;&lt;/div&gt;
  2544. &lt;div style=&quot;text-align: left;&quot;&gt;
  2545. &lt;br /&gt;&lt;/div&gt;
  2546. &lt;span style=&quot;text-align: left;&quot;&gt;Si (a) y (s) son constantes, tenemos;&lt;/span&gt;&lt;span style=&quot;text-align: left;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
  2547. &lt;div style=&quot;text-align: left;&quot;&gt;
  2548. &lt;br /&gt;&lt;/div&gt;
  2549. &lt;div style=&quot;text-align: left;&quot;&gt;
  2550. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8rHEW10LJmDYXH2dNHOvSishvpxYYjMf7fZhlH32lG1fyO36pAUMICaTXbUbg71gCpAIBaclhcb5thHzNowwqTniMtXA-LmNd9l-IS08wIcA5z57WmjIrp5Wvv5re1iJKRkwZ_7hZPv8/s1600/B3.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8rHEW10LJmDYXH2dNHOvSishvpxYYjMf7fZhlH32lG1fyO36pAUMICaTXbUbg71gCpAIBaclhcb5thHzNowwqTniMtXA-LmNd9l-IS08wIcA5z57WmjIrp5Wvv5re1iJKRkwZ_7hZPv8/s400/B3.bmp&quot; height=&quot;122&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2551. &lt;div style=&quot;text-align: left;&quot;&gt;
  2552. &lt;br /&gt;&lt;/div&gt;
  2553. &lt;div style=&quot;text-align: left;&quot;&gt;
  2554. &lt;br /&gt;&lt;/div&gt;
  2555. &lt;div style=&quot;text-align: left;&quot;&gt;
  2556. &lt;/div&gt;
  2557. &lt;div class=&quot;MsoNormal&quot;&gt;
  2558. &lt;span lang=&quot;ES&quot;&gt;Sustituyendo&lt;span style=&quot;font-size: small;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2559. &lt;br /&gt;
  2560. &lt;div style=&quot;text-align: left;&quot;&gt;
  2561. &lt;br /&gt;&lt;/div&gt;
  2562. &lt;div style=&quot;text-align: left;&quot;&gt;
  2563. &lt;br /&gt;&lt;/div&gt;
  2564. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2565. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3gsBEIBM8a_r84GU4Fn_Yf5cpUa_J7gK2bH4zSlPcegivv3KOXf_418D8zPPharIPzNk3rGvbYvr0F-fQTrFd3SVkl7jRmK2F22CGJ2ACTXSGqAL8lFSTaigqnEx_dFrHAkNs4qYyak/s1600/B4.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3gsBEIBM8a_r84GU4Fn_Yf5cpUa_J7gK2bH4zSlPcegivv3KOXf_418D8zPPharIPzNk3rGvbYvr0F-fQTrFd3SVkl7jRmK2F22CGJ2ACTXSGqAL8lFSTaigqnEx_dFrHAkNs4qYyak/s400/B4.bmp&quot; height=&quot;68&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2566. &lt;br /&gt;
  2567. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2568. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguJRsm2P0SIZmN20CNYE42sk64CQ5E77L9Bd9qFkXoi2-bTmZ0pjR7oIg9-sujl8O6PRsEs-x_mn0XVjwhwkj_CkQ016ir9RPN36rbCxyL6R05ehTI7nuhiYjRakRFRZFevGDlTyYhGWc/s1600/B5.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguJRsm2P0SIZmN20CNYE42sk64CQ5E77L9Bd9qFkXoi2-bTmZ0pjR7oIg9-sujl8O6PRsEs-x_mn0XVjwhwkj_CkQ016ir9RPN36rbCxyL6R05ehTI7nuhiYjRakRFRZFevGDlTyYhGWc/s400/B5.bmp&quot; height=&quot;70&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2569. &lt;br /&gt;
  2570. &lt;br /&gt;
  2571. &lt;br /&gt;
  2572. &lt;br /&gt;
  2573. &lt;br /&gt;
  2574. &lt;br /&gt;
  2575. &lt;br /&gt;
  2576. La integral
  2577. del lado derecho de la expresión es otra integral por partes, resolviendo;&lt;br /&gt;
  2578. &lt;br /&gt;
  2579. &lt;br /&gt;
  2580. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2581. &lt;br /&gt;&lt;/div&gt;
  2582. &lt;br /&gt;
  2583. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2584. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8nJj2Ws6XK-jS4nHgqx_gSF4kG6Jbw0Tc3xQbzBjTK6smIGCjDqyZLXtVzVe4Z5xDgfnDSLB3futUjtcUAaomFNI9lh8Y86pj3A0MCy13lRgsgZmDbsTEcOR5WcR_CdP-X23iVxYAUfw/s1600/B6.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8nJj2Ws6XK-jS4nHgqx_gSF4kG6Jbw0Tc3xQbzBjTK6smIGCjDqyZLXtVzVe4Z5xDgfnDSLB3futUjtcUAaomFNI9lh8Y86pj3A0MCy13lRgsgZmDbsTEcOR5WcR_CdP-X23iVxYAUfw/s400/B6.bmp&quot; height=&quot;102&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2585. &lt;br /&gt;
  2586. &lt;br /&gt;
  2587. &lt;br /&gt;
  2588. &lt;br /&gt;
  2589. &lt;br /&gt;
  2590. &lt;br /&gt;
  2591. &lt;br /&gt;
  2592. &lt;div class=&quot;MsoNormal&quot;&gt;
  2593. &lt;br /&gt;
  2594. &lt;span lang=&quot;ES&quot;&gt;Sustituyendo
  2595. tenemos;&lt;span style=&quot;font-size: small;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2596. &lt;br /&gt;
  2597. &lt;br /&gt;
  2598. &lt;br /&gt;
  2599. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2600. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiq2pJ0ZnVwS7rptEDV6EwBn0dglMXzkEbfc2Ww8PWRKJ-IZ8eEwjxk-fmDk46V053MqAA5CvycP9ojunHScV6UlvFlBhkcErl-MpJ6k2cBU0F42TPC20JXHm6fvMkGWyVq_HX7JfTtYk/s1600/B7.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiq2pJ0ZnVwS7rptEDV6EwBn0dglMXzkEbfc2Ww8PWRKJ-IZ8eEwjxk-fmDk46V053MqAA5CvycP9ojunHScV6UlvFlBhkcErl-MpJ6k2cBU0F42TPC20JXHm6fvMkGWyVq_HX7JfTtYk/s1600/B7.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2601. &lt;br /&gt;
  2602. &lt;br /&gt;
  2603. &lt;br /&gt;
  2604. &lt;br /&gt;
  2605. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2606. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwdenTfJn4UjXDXsEmS3OrfRWqz6EN2veviuwPd7CMIvKNlqn1c-o71ru-ZNybUe2kSiDaWhnkpFzM_tJnNdJN2P8ZhavGKaAQw1HWnrMXRw2g2Vb9I6FHbUPlfHEz07Z4VQb_P3FRpys/s1600/B8.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwdenTfJn4UjXDXsEmS3OrfRWqz6EN2veviuwPd7CMIvKNlqn1c-o71ru-ZNybUe2kSiDaWhnkpFzM_tJnNdJN2P8ZhavGKaAQw1HWnrMXRw2g2Vb9I6FHbUPlfHEz07Z4VQb_P3FRpys/s1600/B8.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2607. &lt;br /&gt;
  2608. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2609. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6WQ5cA-zG6iWB4WW62uY61PG_ZOgbEseo3c_aG7_Rx-gHKB0S_QCNsgQT9R1VZSo7g9e88c_ua3GtzFLYRtx8bES8Jo0piiuTP7cpbRJ_9k95pGCn1uwaaR3lgqGAAc_TnU8OSn9y9Q0/s1600/B14.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6WQ5cA-zG6iWB4WW62uY61PG_ZOgbEseo3c_aG7_Rx-gHKB0S_QCNsgQT9R1VZSo7g9e88c_ua3GtzFLYRtx8bES8Jo0piiuTP7cpbRJ_9k95pGCn1uwaaR3lgqGAAc_TnU8OSn9y9Q0/s1600/B14.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2610. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2611. &lt;br /&gt;&lt;/div&gt;
  2612. &lt;br /&gt;
  2613. &lt;br /&gt;
  2614. &lt;div class=&quot;MsoNormal&quot;&gt;
  2615. &lt;span lang=&quot;ES&quot;&gt;La integral de lado derecho de esta última expresión es igual a la
  2616. integral de lado izquierdo, transponiendo términos tenemos;&lt;span style=&quot;font-size: small;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2617. &lt;br /&gt;
  2618. &lt;br /&gt;
  2619. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2620. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_IpraqFO_fqHVl97w5T9LgOM_xt-8NI7FGqTccAwKbCoEyoAv9u4blGnTuwEARktgYcgsuoSJs0UYaf9mEzoR8dc2DGX_UmH21QOaJrfD51qnVVvY1dRkaQm9DeLW7xShAbIGDkLNIeo/s1600/B13.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;/div&gt;
  2621. &amp;nbsp;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcO0zevbuz2SV7h2ETA_BDwadxKVMsU5thMpIuOA7M-mlgYs7n5x60Snmg1WhQQd6hMIsY1nA0PrOHYY6G3crdEYi3pXAlC-gUdNkkYeoqHrVM5WeeBd8tgKnTHLDSVK6tHiH9j81KgHY/s1600/B10.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcO0zevbuz2SV7h2ETA_BDwadxKVMsU5thMpIuOA7M-mlgYs7n5x60Snmg1WhQQd6hMIsY1nA0PrOHYY6G3crdEYi3pXAlC-gUdNkkYeoqHrVM5WeeBd8tgKnTHLDSVK6tHiH9j81KgHY/s1600/B10.bmp&quot; /&gt;&lt;/a&gt;&lt;br /&gt;
  2622. &lt;br /&gt;
  2623. &lt;br /&gt;
  2624. &lt;br /&gt;
  2625. &lt;div class=&quot;MsoNormal&quot;&gt;
  2626. &lt;span lang=&quot;ES&quot;&gt;Sumando ambas integrales&lt;span style=&quot;font-size: small;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2627. &lt;div class=&quot;MsoNormal&quot;&gt;
  2628. &lt;span lang=&quot;ES&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2629. &lt;br /&gt;
  2630. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2631. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcO0zevbuz2SV7h2ETA_BDwadxKVMsU5thMpIuOA7M-mlgYs7n5x60Snmg1WhQQd6hMIsY1nA0PrOHYY6G3crdEYi3pXAlC-gUdNkkYeoqHrVM5WeeBd8tgKnTHLDSVK6tHiH9j81KgHY/s1600/B10.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;/div&gt;
  2632. &lt;br /&gt;
  2633. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP9UVVHcJxdv9fUBTUfVWLUAvKKNA8tq8U7R9ddbsIOHimYlEMjizJ9YEaQNKxjm5mb9owc2Ipu9dkGOH9hImYQV3XyS08yjSM1_YDDVNHDjIYRaxmvQtL-MZDVQ6xfgJfeWlotdov9HE/s1600/B11.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP9UVVHcJxdv9fUBTUfVWLUAvKKNA8tq8U7R9ddbsIOHimYlEMjizJ9YEaQNKxjm5mb9owc2Ipu9dkGOH9hImYQV3XyS08yjSM1_YDDVNHDjIYRaxmvQtL-MZDVQ6xfgJfeWlotdov9HE/s400/B11.bmp&quot; height=&quot;65&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;
  2634. &lt;br /&gt;
  2635. &lt;br /&gt;
  2636. &lt;br /&gt;
  2637. &lt;br /&gt;
  2638. &lt;span style=&quot;font-size: 12pt;&quot;&gt;E&lt;/span&gt;liminando el
  2639. coeficiente de la integral y transponiendo al lado derecho:&lt;br /&gt;
  2640. &lt;br /&gt;
  2641. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2642. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP9UVVHcJxdv9fUBTUfVWLUAvKKNA8tq8U7R9ddbsIOHimYlEMjizJ9YEaQNKxjm5mb9owc2Ipu9dkGOH9hImYQV3XyS08yjSM1_YDDVNHDjIYRaxmvQtL-MZDVQ6xfgJfeWlotdov9HE/s1600/B11.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;/div&gt;
  2643. &lt;br /&gt;
  2644. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuNAP27RgRKRnUP7F15nsHRZV9m8cXWJl_7A-8hTlltQ_AvWzNvHdS1sywAb-v2XTlxtW7krN174MBmgukg0oleTue4EBxZVBcYHTeOunz3fNgm6MGOLjjsrfJktRc-SdW_F0x-9PywlM/s1600/B12.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuNAP27RgRKRnUP7F15nsHRZV9m8cXWJl_7A-8hTlltQ_AvWzNvHdS1sywAb-v2XTlxtW7krN174MBmgukg0oleTue4EBxZVBcYHTeOunz3fNgm6MGOLjjsrfJktRc-SdW_F0x-9PywlM/s400/B12.bmp&quot; height=&quot;66&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;
  2645. &lt;br /&gt;
  2646. &lt;br /&gt;
  2647. &lt;br /&gt;
  2648. &lt;br /&gt;
  2649. Solución:&lt;br /&gt;
  2650. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2651. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuNAP27RgRKRnUP7F15nsHRZV9m8cXWJl_7A-8hTlltQ_AvWzNvHdS1sywAb-v2XTlxtW7krN174MBmgukg0oleTue4EBxZVBcYHTeOunz3fNgm6MGOLjjsrfJktRc-SdW_F0x-9PywlM/s1600/B12.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; float: left; margin-bottom: 1em; margin-right: 1em;&quot;&gt;&lt;br /&gt;&lt;/a&gt;&lt;/div&gt;
  2652. &lt;br /&gt;
  2653. &lt;br /&gt;
  2654. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_IpraqFO_fqHVl97w5T9LgOM_xt-8NI7FGqTccAwKbCoEyoAv9u4blGnTuwEARktgYcgsuoSJs0UYaf9mEzoR8dc2DGX_UmH21QOaJrfD51qnVVvY1dRkaQm9DeLW7xShAbIGDkLNIeo/s1600/B13.bmp&quot; imageanchor=&quot;1&quot; style=&quot;clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_IpraqFO_fqHVl97w5T9LgOM_xt-8NI7FGqTccAwKbCoEyoAv9u4blGnTuwEARktgYcgsuoSJs0UYaf9mEzoR8dc2DGX_UmH21QOaJrfD51qnVVvY1dRkaQm9DeLW7xShAbIGDkLNIeo/s400/B13.bmp&quot; height=&quot;78&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;
  2655. &lt;br /&gt;
  2656. &lt;br /&gt;
  2657. &lt;br /&gt;
  2658. &lt;br /&gt;
  2659. &lt;br /&gt;
  2660. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2661. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;color: #4f81bd;&quot;&gt;Entradas
  2662. Interesantes&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2663. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2664. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/biografias-de-matematicos.html&quot;&gt;Biografías
  2665. de Matemáticos&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2666. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2667. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2011/02/completacion-de-cuadrados.html&quot;&gt;Completación
  2668. de cuadrados&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2669. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2670. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2011/12/solucion-la-ecuacion-de-segundo-grado.html&quot;&gt;Solución
  2671. a la ecuación de segundo grado&lt;/a&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/div&gt;
  2672. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2673. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/matematicas-y-la-vida.html&quot;&gt;Matemáticas
  2674. y la vida&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2675. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2676. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/sistema-de-numeracion-indoarabigo.html&quot;&gt;Sistema
  2677. de numeración Indoarábigo&lt;/a&gt;&lt;span class=&quot;MsoHyperlink&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2678. &lt;div class=&quot;MsoNormal&quot;&gt;
  2679. &lt;br /&gt;&lt;/div&gt;
  2680. &lt;div class=&quot;MsoNormal&quot;&gt;
  2681. &lt;b&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Arial, sans-serif; font-size: 18pt; line-height: 115%;&quot;&gt;Si
  2682. consideras que este artículo ha aclarado tus dudas, te invitamos a dejar un
  2683. comentario. Gracias.&lt;/span&gt;&lt;/b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/div&gt;
  2684. &lt;br /&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/1269960585318326134/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/02/integral-por-partes.html#comment-form' title='7 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/1269960585318326134'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/1269960585318326134'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/02/integral-por-partes.html' title='Integral por partes'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg5xXOQm0xmmaDNJFt-m5oy1Znb2Owsa904EkXsUTRHC7-X23xL83aKUQmwQr-wjlrCIWF6VFzBBpl4SeXDFDqtISQ2o6NjlCTpUzemBRlDqmcuCsXpxENnYqrk1ZNKuzqc6RAWzqOalM/s72-c/B1.bmp" height="72" width="72"/><thr:total>7</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7029771534698050015.post-5050043770366620700</id><published>2012-01-25T22:59:00.000-08:00</published><updated>2012-01-25T23:02:35.943-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="integrales"/><title type='text'>Propiedades de la integral definida</title><content type='html'>&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 18.0pt; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2685. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%; text-indent: -18pt;&quot;&gt;&amp;nbsp;Si f(x) y g(x) son dos funciones continuas en el intervalo de
  2686. integración [a,b] y k una constante cualquiera:&lt;/span&gt;&lt;/div&gt;
  2687. &lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 18pt; text-align: justify; text-indent: -18pt;&quot;&gt;
  2688. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2689. &lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 18pt; text-align: justify; text-indent: -18pt;&quot;&gt;
  2690. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2691. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2692. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;a)&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;Si los límites que
  2693. integración coinciden, la integral
  2694. definida vale cero.&lt;/span&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2695. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2696. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2697. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2698. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5_rwtL8XIfHmpHdZQOaxQBv5MHryhIcmc5n31Gza6JtmCIILCd6GEAAqEXjjZNK8-HejDz5VTQ5q7-Rx0I0yRd21neneAX8b0MmmX7iwYX2MDs56Y6GM8pQ-3N5YHYjzKPYWspSZo0_o/s1600/A1.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center; text-indent: 0px;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5_rwtL8XIfHmpHdZQOaxQBv5MHryhIcmc5n31Gza6JtmCIILCd6GEAAqEXjjZNK8-HejDz5VTQ5q7-Rx0I0yRd21neneAX8b0MmmX7iwYX2MDs56Y6GM8pQ-3N5YHYjzKPYWspSZo0_o/s1600/A1.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2699. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2700. &lt;/div&gt;
  2701. &lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2702. &lt;br /&gt;&lt;/div&gt;
  2703. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2704. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;b)&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;El valor de la integral definida cambia de signo si se
  2705. permutan los límites de integración.&lt;/span&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2706. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2707. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2708. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2709. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFb_CjMAa5zL702kjwmyZFArOMGK3x_ZjA8Hn3Ut6aO7xnOPeBlKn-1eNdlYB5uouGKVrvBEXxBQY6od6q5Ikv5iHmFiq2289OlqZ8X6PF7sEo1AgURTagQJmDU3oo9nw6IkDRzL8OQ2A/s1600/A2.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center; text-indent: 0px;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFb_CjMAa5zL702kjwmyZFArOMGK3x_ZjA8Hn3Ut6aO7xnOPeBlKn-1eNdlYB5uouGKVrvBEXxBQY6od6q5Ikv5iHmFiq2289OlqZ8X6PF7sEo1AgURTagQJmDU3oo9nw6IkDRzL8OQ2A/s1600/A2.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2710. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2711. &lt;/div&gt;
  2712. &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2713. &lt;br /&gt;&lt;/div&gt;
  2714. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2715. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;c)&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;La integral del producto de una constante por
  2716. una función es igual a la constante por la integral de la función.&lt;/span&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2717. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2718. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2719. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2720. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkMlg4QBMpYODYs3lmRL_8nvwAPEj0bT3hrfhCet1Xsi8u9eU_P1dlP4wmsaYzOK4pRI5MO5VRQ7lIQuQbKoKx8VxymO2NknphhXucXYHHSCjNOdwJA0hXqMoTuw6qQPEvGy9KRwAAqWE/s1600/A3.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center; text-indent: 0px;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkMlg4QBMpYODYs3lmRL_8nvwAPEj0bT3hrfhCet1Xsi8u9eU_P1dlP4wmsaYzOK4pRI5MO5VRQ7lIQuQbKoKx8VxymO2NknphhXucXYHHSCjNOdwJA0hXqMoTuw6qQPEvGy9KRwAAqWE/s1600/A3.bmp&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2721. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2722. &lt;/div&gt;
  2723. &lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 18pt; text-align: justify; text-indent: -18pt;&quot;&gt;
  2724. &lt;br /&gt;&lt;/div&gt;
  2725. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2726. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;d)&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&amp;nbsp;La integral
  2727. definida de una suma de funciones es igual a la suma de integrales
  2728. (Propiedad de linealidad)·&lt;/span&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2729. &lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 18pt; text-align: justify; text-indent: -18pt;&quot;&gt;
  2730. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt;&quot;&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;/span&gt;&lt;span style=&quot;text-align: center;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
  2731. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2732. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBw2twHOOwn7MwBEN5XBiOdKRdLgd4ypziN21ELBHkNwAk3ofu67a7eG726VqO_O_D11f8sMp_iPhHObyYezSaeG6IU8BpfuwIclrFcJpsHZlIi_IEya3vrYCJXdrlIlm1SYIKtpw0xIQ/s1600/A4.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; height=&quot;52&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBw2twHOOwn7MwBEN5XBiOdKRdLgd4ypziN21ELBHkNwAk3ofu67a7eG726VqO_O_D11f8sMp_iPhHObyYezSaeG6IU8BpfuwIclrFcJpsHZlIi_IEya3vrYCJXdrlIlm1SYIKtpw0xIQ/s320/A4.bmp&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2733. &lt;br /&gt;
  2734. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2735. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;e)&lt;span style=&quot;font: normal normal normal 7pt/normal &#39;Times New Roman&#39;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&amp;nbsp;Si c es un punto interior del intervalo [a,
  2736. b], la integral definida&lt;b&gt; &lt;/b&gt;se
  2737. descompone como una suma de dos integrales extendidas a los intervalos [a, c] y
  2738. [c, b].&lt;/span&gt;&lt;span lang=&quot;ES-TRAD&quot; style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2739. &lt;div class=&quot;MsoListParagraph&quot; style=&quot;margin-left: 18.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; tab-stops: 14.2pt 21.3pt 35.45pt; text-align: justify; text-indent: -18.0pt;&quot;&gt;
  2740. &lt;span style=&quot;font-family: &#39;Times New Roman&#39;, serif; font-size: 12pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2741. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2742. &lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbj3uYM0xrb8Krk157gaq1a474u_u8F4PImCdLfpD5LUxjnlGadLlg-Eifuuw7ModftOFXoIYvZdojFAY3f-9lWJjuuHdYQ8ZEm5Fc5hIEBRQVP6KUEJejORCNqX0SS_BRADk1mK7zlL8/s1600/A5.bmp&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em; text-align: center; text-indent: 0px;&quot;&gt;&lt;img border=&quot;0&quot; height=&quot;37&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbj3uYM0xrb8Krk157gaq1a474u_u8F4PImCdLfpD5LUxjnlGadLlg-Eifuuw7ModftOFXoIYvZdojFAY3f-9lWJjuuHdYQ8ZEm5Fc5hIEBRQVP6KUEJejORCNqX0SS_BRADk1mK7zlL8/s400/A5.bmp&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
  2743. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2744. &lt;br /&gt;&lt;/div&gt;
  2745. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
  2746. &lt;br /&gt;&lt;/div&gt;
  2747. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
  2748. &lt;/div&gt;
  2749. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2750. &lt;span lang=&quot;ES-TRAD&quot; style=&quot;color: #4f81bd;&quot;&gt;Entradas
  2751. Interesantes&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
  2752. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2753. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/biografias-de-matematicos.html&quot;&gt;Biografías
  2754. de Matemáticos&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2755. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2756. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2011/02/completacion-de-cuadrados.html&quot;&gt;Completación
  2757. de cuadrados&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2758. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2759. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2011/12/solucion-la-ecuacion-de-segundo-grado.html&quot;&gt;Solución
  2760. a la ecuación de segundo grado&lt;/a&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/div&gt;
  2761. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2762. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/matematicas-y-la-vida.html&quot;&gt;Matemáticas
  2763. y la vida&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
  2764. &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm;&quot;&gt;
  2765. &lt;span lang=&quot;ES-TRAD&quot;&gt;&lt;a href=&quot;http://linaresgsj.blogspot.com/2012/01/sistema-de-numeracion-indoarabigo.html&quot;&gt;Sistema
  2766. de numeración Indoarábigo&lt;/a&gt;&lt;span class=&quot;MsoHyperlink&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
  2767. &lt;br /&gt;
  2768. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
  2769. &lt;span style=&quot;line-height: 24px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
  2770. &lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
  2771. &lt;span style=&quot;background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 24px; font-weight: bold; line-height: 27px; text-align: -webkit-auto;&quot;&gt;Si consideras que este artículo ha aclarado tus dudas, te invitamos a dejar un comentario. Gracias.&lt;/span&gt;
  2772. &lt;/div&gt;
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  2774. &lt;/div&gt;&lt;div class=&quot;blogger-post-footer&quot;&gt;Bienvenidos&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://linaresgsj.blogspot.com/feeds/5050043770366620700/comments/default' title='Enviar comentarios'/><link rel='replies' type='text/html' href='http://linaresgsj.blogspot.com/2012/01/propiedades-de-la-integral-definida.html#comment-form' title='3 comentarios'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5050043770366620700'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7029771534698050015/posts/default/5050043770366620700'/><link rel='alternate' type='text/html' href='http://linaresgsj.blogspot.com/2012/01/propiedades-de-la-integral-definida.html' title='Propiedades de la integral definida'/><author><name>saul</name><uri>http://www.blogger.com/profile/15842128268815535198</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='32' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwQzVbIyaO59llwZS5me8CI4LP3imo3NmWAuOp61Kh7vInCcripxU0kCYEricHyU1-BLJ-WCIv0XiI3EXXIcJQQxPyP3gj50fXGklqvAT-Co_dtVJhlrqYmpKC958E-Q/s220/foto_saul_carnet.png'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5_rwtL8XIfHmpHdZQOaxQBv5MHryhIcmc5n31Gza6JtmCIILCd6GEAAqEXjjZNK8-HejDz5VTQ5q7-Rx0I0yRd21neneAX8b0MmmX7iwYX2MDs56Y6GM8pQ-3N5YHYjzKPYWspSZo0_o/s72-c/A1.bmp" height="72" width="72"/><thr:total>3</thr:total></entry></feed>

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