{"id":4621,"date":"2022-01-14T21:01:07","date_gmt":"2022-01-14T21:01:07","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=4621"},"modified":"2022-02-08T18:59:19","modified_gmt":"2022-02-08T18:59:19","slug":"clase-digital-6-nocion-de-limite-definicion-de-limite-de-una-funcion-propiedades-de-los-limites","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-6-nocion-de-limite-definicion-de-limite-de-una-funcion-propiedades-de-los-limites\/","title":{"rendered":"Clase digital 6: Nocio\u0301n de li\u0301mite. Definicio\u0301n de li\u0301mite de una funcio\u0301n. Propiedades de los li\u0301mites."},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-4765\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"759\" class=\"wp-block-cover__image-background wp-image-4765\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1-300x142.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1-1024x486.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1-768x364.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/e6ppicj05jg-1-1536x729.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Nocio\u0301n de li\u0301mite. Definicio\u0301n de li\u0301mite de una funcio\u0301n. Propiedades de los li\u0301mites.<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es un placer encontrarte, espero que sigas gozando de una excelente salud y tengas buen \u00e1nimo por aprender cosas nuevas de este curso, por ello te invito a la sexta clase titulada L\u00cdMITE del curso<strong> C\u00e1lculo Diferencial<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En esta sexta clase, se abordar\u00e1 la definici\u00f3n de l\u00edmite, que es quiz\u00e1 el concepto matem\u00e1tico m\u00e1s importante que ha permitido el desarrollo y soluci\u00f3n de los problemas que dieron origen al c\u00e1lculo. La noci\u00f3n de l\u00edmite aparece no solo en c\u00e1lculo diferencial, sino que se relaciona con los cursos de an\u00e1lisis y c\u00e1lculo vectorial. El concepto conforma una pareja indisoluble con el de continuidad, tal para que el primero exista, debe existir aqu\u00e9l.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entendido lo anterior, te invito a continuar la clase.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"limites\">L\u00edmites<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Recordemos algunos conceptos, de la siguiente funci\u00f3n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-1.png\" alt=\"\" class=\"wp-image-4642\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"141\" height=\"56\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-1.png\" alt=\"\" class=\"wp-image-4642\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u00bfCu\u00e1l es el dominio de la funci\u00f3n?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De acuerdo con lo aprendido en la clase 4, se observa que es una funci\u00f3n polinomial, por lo tanto q(x) debe ser diferente de cero, entonces se plantea la igualdad para as\u00ed conocer el dominio de la funci\u00f3n. Al resolver se sabe que el dominio de la funci\u00f3n es D<sub>f<\/sub>=R{-4}, por tanto, se podr\u00eda decir que se pueden elegir valores de menos infinito hasta antes del -4 y poquito despu\u00e9s del -4 hasta m\u00e1s infinito donde la funci\u00f3n es v\u00e1lida. Observa la tabla, en donde se eligieron valores de <strong>x <\/strong>muy cerca a -4 por la derecha y por la izquierda y se sustituyen en la funci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En la tabla se acerca al -4 por la izquierda, observ\u00e1ndose que cada vez que se acerca m\u00e1s al -4 el valor tiende a 8<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/4.png\" alt=\"\" class=\"wp-image-4652\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"849\" height=\"309\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/4.png\" alt=\"\" class=\"wp-image-4652\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/4.png 849w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/4-300x109.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/4-768x280.png 768w\" sizes=\"auto, (max-width: 849px) 100vw, 849px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">En la tabla se acerca al -4 por la derecha, observ\u00e1ndose que cada vez que se acerca m\u00e1s al -4 el valor tiende a 8<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/linea.png\" alt=\"\" class=\"wp-image-4656\" width=\"657\" height=\"161\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/linea.png\" alt=\"\" class=\"wp-image-4656\" width=\"657\" height=\"161\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/linea.png 890w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/linea-300x73.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/linea-768x188.png 768w\" sizes=\"auto, (max-width: 657px) 100vw, 657px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al acercarse por la izquierda y por la derecha el valor tiende al mismo n\u00famero, se dice que el l\u00edmite de la funci\u00f3n en x=4 tiende a 8. Generalizando el concepto, el l\u00edmite de una funci\u00f3n en un valor a existe si cuando se acerca por la derecha y por la izquierda tiende a l mismo valor<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"existencia-o-no-existencia\">Existencia o no existencia<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Un l\u00edmite (por un lado o por dos lados) no tiene por qu\u00e9 existir. Pero es importante recordar: La existencia de un l\u00edmite de una funci\u00f3n f cuando x tiene a a (desde un lado o desde ambos lados) no depende de si f esta definida en a, si no solo si esta definida para x cerca del n\u00famero a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si la funci\u00f3n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx.png\" alt=\"\" class=\"wp-image-4661\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"94\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx.png\" alt=\"\" class=\"wp-image-4661\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">se modifica de la siguiente forma<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx-2.png\" alt=\"\" class=\"wp-image-4662\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"793\" height=\"130\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx-2.png\" alt=\"\" class=\"wp-image-4662\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx-2.png 793w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx-2-300x49.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fx-2-768x126.png 768w\" sizes=\"auto, (max-width: 793px) 100vw, 793px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se sabe que la funci\u00f3n <em>f(-4)<\/em> esta definida y es <em>f(-4)=5<\/em>, sin embargo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/deciseis-cuartos.png\" alt=\"\" class=\"wp-image-4665\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"173\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/deciseis-cuartos.png\" alt=\"\" class=\"wp-image-4665\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto el l\u00edmite por los dos lados<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim.png\" alt=\"\" class=\"wp-image-4668\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"115\" height=\"46\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim.png\" alt=\"\" class=\"wp-image-4668\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">no existe, para dejar m\u00e1s claro el concepto, observa la imagen, en donde, la funci\u00f3n por partes, respeta que la primer parte no toma el valor de -4 y en la segunda parte si.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica.png\" alt=\"\" class=\"wp-image-4671\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"421\" height=\"409\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica.png\" alt=\"\" class=\"wp-image-4671\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica.png 421w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-300x291.png 300w\" sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Encuentra el l\u00edmite de&nbsp;f(x)=-x<sup>2<\/sup>+2x+2 cuando <strong>x<\/strong> tiende a 4 por la izquierda y por la derecha<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Elige los valores a sustituir por la izquierda y por la derecha, por ello se llena la tabla.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla.png\" alt=\"\" class=\"wp-image-4676\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"217\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla.png\" alt=\"\" class=\"wp-image-4676\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla.png 700w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla-300x93.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al observar las tablas, se puede inferir que el l\u00edmite de la funci\u00f3n cuando x tiende a 4, es -6.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Anal\u00edticamente se resuelve de la siguiente forma<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calculando el l\u00edmite por la izquierda<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"x2-2x-2-6\"><strong>-x<sup>2<\/sup>+2x+2 =-6<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Calculando el l\u00edmite por la derecha<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"x2-2x-2-6\">-x<sup>2<\/sup>+2x+2 =-6<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Al ser los dos l\u00edmites iguales se dice que el l\u00edmite de la funci\u00f3n es: -x<sup>2<\/sup>+2x+2 =-6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calcula el l\u00edmite de la funci\u00f3n cuando <strong>x<\/strong> tiende a <strong>2<\/strong><\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"f-x-x2-x-2-x-6-x-2\"><em>f(x)={x<sup>2<\/sup>,&nbsp; &nbsp; &nbsp; x&lt;2 -x+6, &nbsp; &nbsp; &nbsp; &nbsp; x&gt;<\/em>2&nbsp;<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La gr\u00e1fica de la funci\u00f3n es la siguiente:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-2.png\" alt=\"\" class=\"wp-image-4683\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"552\" height=\"250\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-2.png\" alt=\"\" class=\"wp-image-4683\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-2.png 552w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-2-300x136.png 300w\" sizes=\"auto, (max-width: 552px) 100vw, 552px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se coloca la recta num\u00e9rica para visualizar los valores de acercamiento por la izquierda y por la derecha.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-3.png\" alt=\"\" class=\"wp-image-4685\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"152\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-3.png\" alt=\"\" class=\"wp-image-4685\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-3.png 438w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Grafica-3-300x104.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Asignaci\u00f3n de valor por la izquierda<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla-1.png\" alt=\"\" class=\"wp-image-4687\" width=\"516\" height=\"88\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla-1.png\" alt=\"\" class=\"wp-image-4687\" width=\"516\" height=\"88\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla-1.png 598w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tabla-1-300x51.png 300w\" sizes=\"auto, (max-width: 516px) 100vw, 516px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Asignaci\u00f3n de valores por la derecha<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TAbla-2.png\" alt=\"\" class=\"wp-image-4688\" width=\"529\" height=\"85\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TAbla-2.png\" alt=\"\" class=\"wp-image-4688\" width=\"529\" height=\"85\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TAbla-2.png 596w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TAbla-2-300x48.png 300w\" sizes=\"auto, (max-width: 529px) 100vw, 529px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al ser los dos l\u00edmites iguales se sabe que<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-1.png\" alt=\"\" class=\"wp-image-4691\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"436\" height=\"129\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-1.png\" alt=\"\" class=\"wp-image-4691\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-1.png 436w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-1-300x89.png 300w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Encuentra el l\u00edmite de la funci\u00f3n<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"f-x-x-2-x-5-x-10-x-5\">f(x)={x+2, x\u22645 -x+10, x&gt;5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se dibuja la recta num\u00e9rica para identificar el acercamiento por la derecha y por la izquierda, y posteriormente el llenado de la tabla.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Recta.png\" alt=\"\" class=\"wp-image-4697\" width=\"565\" height=\"337\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Recta.png\" alt=\"\" class=\"wp-image-4697\" width=\"565\" height=\"337\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Recta.png 675w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Recta-300x179.png 300w\" sizes=\"auto, (max-width: 565px) 100vw, 565px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se concluye que en la funci\u00f3n el l\u00edmite no existe.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"teoremas-de-los-limites\">Teoremas de los l\u00edmites<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Teoremas.png\" alt=\"\" class=\"wp-image-4700\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"879\" height=\"743\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Teoremas.png\" alt=\"\" class=\"wp-image-4700\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Teoremas.png 879w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Teoremas-300x254.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Teoremas-768x649.png 768w\" sizes=\"auto, (max-width: 879px) 100vw, 879px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Eval\u00faa 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por el teorema de l\u00edmites 8 es la constante por tanto el l\u00edmite es: 8=8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Eval\u00faa 8 x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utilizando los teoremas de l\u00edmite<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/8x.png\" alt=\"\" class=\"wp-image-4705\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"438\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/8x.png\" alt=\"\" class=\"wp-image-4705\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/8x.png 469w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/8x-300x280.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.4.png\" alt=\"\" class=\"wp-image-4707\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"736\" height=\"150\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.4.png\" alt=\"\" class=\"wp-image-4707\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.4.png 736w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.4-300x61.png 300w\" sizes=\"auto, (max-width: 736px) 100vw, 736px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Eval\u00fae el x<sup>3<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando el teorema de l\u00edmite de una potencia<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/x3.png\" alt=\"\" class=\"wp-image-4710\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"391\" height=\"77\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/x3.png\" alt=\"\" class=\"wp-image-4710\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/x3.png 391w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/x3-300x59.png 300w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2.png\" alt=\"\" class=\"wp-image-4714\" width=\"910\" height=\"254\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2.png\" alt=\"\" class=\"wp-image-4714\" width=\"910\" height=\"254\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2.png 709w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2-300x84.png 300w\" sizes=\"auto, (max-width: 910px) 100vw, 910px\" \/><\/noscript><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/3.png\" alt=\"\" class=\"wp-image-4718\" width=\"847\" height=\"278\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/3.png\" alt=\"\" class=\"wp-image-4718\" width=\"847\" height=\"278\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/3.png 609w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/3-300x99.png 300w\" sizes=\"auto, (max-width: 847px) 100vw, 847px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ese resultado indica una indeterminaci\u00f3n, pero es incorrecto decir que el l\u00edmite no existe, cuando suceda esto se deben realizar diversas operaciones algebraicas que validen o no la existencia del l\u00edmite.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Factorizando el denominador<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Factorizar.png\" alt=\"\" class=\"wp-image-4721\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"708\" height=\"653\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Factorizar.png\" alt=\"\" class=\"wp-image-4721\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Factorizar.png 708w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Factorizar-300x277.png 300w\" sizes=\"auto, (max-width: 708px) 100vw, 708px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al tener esta indeterminaci\u00f3n se procede a factorizar para determinar que en efecto el l\u00edmite no exista<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Factorizando numerador<\/strong><\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"x-5-x-5\">(x &#8211; 5) (x-5)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Factorizando denominador<\/strong><\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"x-5-x-1\"> (x &#8211; 5) (x+1) <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituyendo en el l\u00edmite<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-2.png\" alt=\"\" class=\"wp-image-4725\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"644\" height=\"105\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-2.png\" alt=\"\" class=\"wp-image-4725\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-2.png 644w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-2-300x49.png 300w\" sizes=\"auto, (max-width: 644px) 100vw, 644px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se concluye que el l\u00edmite si existe y es cero<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.6.png\" alt=\"\" class=\"wp-image-4726\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"861\" height=\"199\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.6.png\" alt=\"\" class=\"wp-image-4726\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.6.png 861w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.6-300x69.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/TEorema-3.2.6-768x178.png 768w\" sizes=\"auto, (max-width: 861px) 100vw, 861px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1.png\" alt=\"\" class=\"wp-image-4727\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"625\" height=\"395\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1.png\" alt=\"\" class=\"wp-image-4727\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1.png 625w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1-300x190.png 300w\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Al ser 0\/0 no significa que el l\u00edmite no exista, cuando se tienen ra\u00edces cuadradas la operaci\u00f3n algebraica que se realiza es la racionalizaci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Racionalizando<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Solucion-del-ejemplo-1.png\" alt=\"\" class=\"wp-image-4728\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"775\" height=\"364\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Solucion-del-ejemplo-1.png\" alt=\"\" class=\"wp-image-4728\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Solucion-del-ejemplo-1.png 775w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Solucion-del-ejemplo-1-300x141.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Solucion-del-ejemplo-1-768x361.png 768w\" sizes=\"auto, (max-width: 775px) 100vw, 775px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se concluye que el l\u00edmite existe y es<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Raiz.png\" alt=\"\" class=\"wp-image-4729\" width=\"246\" height=\"131\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Raiz.png\" alt=\"\" class=\"wp-image-4729\" width=\"246\" height=\"131\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Continuidad<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas.png\" alt=\"\" class=\"wp-image-4730\" width=\"890\" height=\"516\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas.png\" alt=\"\" class=\"wp-image-4730\" width=\"890\" height=\"516\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas.png 758w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas-300x174.png 300w\" sizes=\"auto, (max-width: 890px) 100vw, 890px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si alguna de estas condiciones no se cumple se dice que la funci\u00f3n no es continua en a: Determinar si cada una de las siguientes funciones es continua en 1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/a.png\" alt=\"\" class=\"wp-image-4735\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"855\" height=\"194\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/a.png\" alt=\"\" class=\"wp-image-4735\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/a.png 855w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/a-300x68.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/a-768x174.png 768w\" sizes=\"auto, (max-width: 855px) 100vw, 855px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo.png\" alt=\"\" class=\"wp-image-4737\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"729\" height=\"582\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo.png\" alt=\"\" class=\"wp-image-4737\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo.png 729w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-300x240.png 300w\" sizes=\"auto, (max-width: 729px) 100vw, 729px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">La primera parte de la funci\u00f3n no puede tomar el valor de 1, por ello se toma la segunda parte de la funci\u00f3n.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"g-1-2\">g(1) = 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">La funci\u00f3n se encuentra definida, por lo tanto se procede al segundo paso que es evaluar el l\u00edmite de la funci\u00f3n cuando x tiende a 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Evaluando el l\u00edmite<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Al observar la funci\u00f3n la parte del numerador se puede factorizar como una diferencia de cubos, utilizando la f\u00f3rmula de factorizaci\u00f3n.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-3.png\" alt=\"\" class=\"wp-image-4740\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"807\" height=\"414\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-3.png\" alt=\"\" class=\"wp-image-4740\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-3.png 807w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-3-300x154.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-3-768x394.png 768w\" sizes=\"auto, (max-width: 807px) 100vw, 807px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El tercer paso para verificar si la funci\u00f3n es continua en a=1 es verificar la igualdad entre la funci\u00f3n en a y el l\u00edmite; como g(x) \u2260g(1), la funci\u00f3n no esta definida en 1. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3. Determine si la funci\u00f3n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-2.png\" alt=\"\" class=\"wp-image-4742\" width=\"302\" height=\"47\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-2.png\" alt=\"\" class=\"wp-image-4742\" width=\"302\" height=\"47\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Verificando que la funci\u00f3n est\u00e9 definida en a=1<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"f-1-3\">f(1)=3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Al estar la funci\u00f3n definida se calcula el l\u00edmite de la funci\u00f3n, el cual ya fue calculado en el ejercicio anterior el cual es 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Al ser como <strong><em>f(x) =f(1),<\/em><\/strong> la funci\u00f3n esta definida en 1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Continuidad-sobre-un-intervalo.png\" alt=\"\" class=\"wp-image-4744\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"855\" height=\"227\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Continuidad-sobre-un-intervalo.png\" alt=\"\" class=\"wp-image-4744\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Continuidad-sobre-un-intervalo.png 855w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Continuidad-sobre-un-intervalo-300x80.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Continuidad-sobre-un-intervalo-768x204.png 768w\" sizes=\"auto, (max-width: 855px) 100vw, 855px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>L\u00edmites trigonom\u00e9tricos<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/1-1.png\" alt=\"\" class=\"wp-image-4759\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"667\" height=\"500\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/1-1.png\" alt=\"\" class=\"wp-image-4759\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/1-1.png 667w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/1-1-300x225.png 300w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2-2.png\" alt=\"\" class=\"wp-image-4762\" width=\"743\" height=\"449\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/2-2.png\" alt=\"\" class=\"wp-image-4762\" width=\"743\" height=\"449\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Para concluir el tema recordemos lo siguiente:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El l\u00edmite de una funci\u00f3n determina en qu\u00e9 valores la funci\u00f3n esta definida y esto esta aunado con la continuidad de una funci\u00f3n. Si al evaluar el l\u00edmite el resultado es 0\/0, se deber\u00e1 factorizar, racionalizar para verificar que el l\u00edmite no existe. Los l\u00edmites trigonom\u00e9tricos tienen sus propias reglas, y se deben utilizar las identidades correctas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es as\u00ed que, con esta breve conclusi\u00f3n, terminamos la clase y te doy una \u00a1gran felicitaci\u00f3n por este logro! No olvides realizar y enviar correctamente y a tiempo la tarea asignada. Te espero en tu siguiente clase<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.cimat.mx\/ciencia_para_jovenes\/bachillerato\/libros\/%5BPurcell,Varberg,Rigdon%5DCalculo\/%5BPurcell,Varberg,Rigdon%5DCalculo_cap1.pdf\">L\u00edmites<\/a><\/li><li>Zill, D. G., &amp; Wrigth. W. S. (2011). Matem\u00e1ticas 1: C\u00e1lculo Diferencial. M\u00e9xico: MC Graw Hill.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un placer encontrarte, espero que sigas gozando de una excelente salud y tengas buen \u00e1nimo por aprender cosas nuevas de este curso, por ello te invito a la sexta clase titulada L\u00cdMITE del curso C\u00e1lculo Diferencial. En esta sexta clase, se abordar\u00e1 la definici\u00f3n de l\u00edmite, que es quiz\u00e1 el concepto matem\u00e1tico &#8230; <a title=\"Clase digital 6: Nocio\u0301n de li\u0301mite. Definicio\u0301n de li\u0301mite de una funcio\u0301n. Propiedades de los li\u0301mites.\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-6-nocion-de-limite-definicion-de-limite-de-una-funcion-propiedades-de-los-limites\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 6: Nocio\u0301n de li\u0301mite. Definicio\u0301n de li\u0301mite de una funcio\u0301n. Propiedades de los li\u0301mites.\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[10,12],"tags":[41,149,44],"class_list":["post-4621","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-calculo-diferencial","tag-clase-digital","tag-marcela-guadalupe-tellez-martinez","tag-neli04036"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4621","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=4621"}],"version-history":[{"count":5,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4621\/revisions"}],"predecessor-version":[{"id":6950,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4621\/revisions\/6950"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=4621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=4621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=4621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}