{"id":26572,"date":"2023-08-01T14:18:38","date_gmt":"2023-08-01T14:18:38","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=26572"},"modified":"2023-08-04T15:30:11","modified_gmt":"2023-08-04T15:30:11","slug":"clase-digital-3-limites","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-limites\/","title":{"rendered":"Clase digital 3. L\u00edmites"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-26604\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites.png\" style=\"object-position:52% 66%\" data-object-fit=\"cover\" data-object-position=\"52% 66%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1500\" height=\"700\" class=\"wp-block-cover__image-background wp-image-26604\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites.png\" style=\"object-position:52% 66%\" data-object-fit=\"cover\" data-object-position=\"52% 66%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites.png 1500w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites-300x140.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites-1024x478.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Limites-768x358.png 768w\" sizes=\"auto, (max-width: 1500px) 100vw, 1500px\" \/><\/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\">L\u00edmites<\/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\">Este tema es fundamental para entender el concepto de <strong>derivadas<\/strong> y <strong>l\u00edmites<\/strong>. Seguro que has escuchado la palabra l\u00edmite, normalmente lo traducimos como <em>el lugar donde no debemos ir m\u00e1s all\u00e1<\/em>. Pues bien, en matem\u00e1ticas es similar, y es en base a este l\u00edmite que se puede definir la derivada.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tenemos varios tipos de l\u00edmites: laterales, infinitos, al infinito; todos ellos nos permiten analizar m\u00e1s r\u00e1pido una funci\u00f3n que grafic\u00e1ndola. Veamos pues algo de l\u00edmites \u00a1Adelante!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00bfQu\u00e9 entendemos por <strong>l\u00edmite<\/strong>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una manera de expresarlo es \u201chasta aqu\u00ed\u201d o \u201cya no m\u00e1s\u201d. Sabemos que se trata de una instancia en la que no debemos pasar. Bueno en matem\u00e1ticas es igual, existe una \u201coperaci\u00f3n\u201d que se llama l\u00edmite y que matem\u00e1ticamente se expresa como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-8.48.55.png\" alt=\"\" class=\"wp-image-26909\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"56\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-8.48.55.png\" alt=\"\" class=\"wp-image-26909\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Y se lee: \u201cEl l\u00edmite de una funci\u00f3n cuando x se acerca a <em>a<\/em> es L\u201des decir, nos acercamos a <em>x=a <\/em>pero no lo tocamos.<\/p>\n\n\n<div class=\"wp-block-image\">\n<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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.01.07.png\" alt=\"\" class=\"wp-image-26910\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"251\" height=\"224\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.01.07.png\" alt=\"\" class=\"wp-image-26910\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Veremos cu\u00e1l es su l\u00edmite si nos acercamos a <em>x=3. <\/em>Podr\u00edamos simplemente sustituir el valor de&nbsp; <em>x=3,<\/em> pero as\u00ed no estar\u00edamos tomando del l\u00edmite, estar\u00edamos evaluando la funci\u00f3n en <em>x=3.<\/em>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces, \u00bfC\u00f3mo ser\u00eda sacar el l\u00edmite? Veamos, acerqu\u00e9monos al 3 pero sin llegar a \u00e9l.<\/p>\n\n\n<div class=\"wp-block-image\">\n<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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.29.png\" alt=\"\" class=\"wp-image-26911\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"475\" height=\"275\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.29.png\" alt=\"\" class=\"wp-image-26911\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.29.png 475w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.29-300x174.png 300w\" sizes=\"auto, (max-width: 475px) 100vw, 475px\" \/><\/noscript><\/figure>\n<\/div>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.55.png\" alt=\"\" class=\"wp-image-26912\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"929\" height=\"204\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.55.png\" alt=\"\" class=\"wp-image-26912\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.55.png 929w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.55-300x66.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.04.55-768x169.png 768w\" sizes=\"auto, (max-width: 929px) 100vw, 929px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">De manera que, gr\u00e1ficamente lo ver\u00edamos como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.05.47.png\" alt=\"\" class=\"wp-image-26913\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"761\" height=\"357\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.05.47.png\" alt=\"\" class=\"wp-image-26913\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.05.47.png 761w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.05.47-300x141.png 300w\" sizes=\"auto, (max-width: 761px) 100vw, 761px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Podemos ver que hay un peque\u00f1o espacio alrededor de <strong><em>a<\/em><\/strong> dado por <strong><em>\u03b4<\/em><\/strong>, que nos permite acercarnos a<strong> <em>x=a<\/em><\/strong>, y al hacerlo nos acercamos al l\u00edmite <strong><em>L<\/em><\/strong>.<\/p>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.07.57.png\" alt=\"\" class=\"wp-image-26916\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"519\" height=\"446\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.07.57.png\" alt=\"\" class=\"wp-image-26916\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.07.57.png 519w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.07.57-300x258.png 300w\" sizes=\"auto, (max-width: 519px) 100vw, 519px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Veamos otro ejemplo:<\/p>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.09.36.png\" alt=\"\" class=\"wp-image-26919\" width=\"866\" height=\"633\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.09.36.png\" alt=\"\" class=\"wp-image-26919\" width=\"866\" height=\"633\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.09.36.png 934w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.09.36-300x219.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.09.36-768x562.png 768w\" sizes=\"auto, (max-width: 866px) 100vw, 866px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span id=\"docs-internal-guid-d6c9f7bc-7fff-1fcc-8c01-9b675ed0df10\"><p dir=\"ltr\" style=\"line-height:1.3800000000000001;text-align: justify;margin-top:0pt;margin-bottom:0pt\"><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;vertical-align: baseline\">Siempre que nos acerquemos por valores mayores que<\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-style: italic;vertical-align: baseline\"> <\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-weight: 700;font-style: italic;vertical-align: baseline\">a<\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;vertical-align: baseline\">, a <\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-weight: 700;font-style: italic;vertical-align: baseline\">a<\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-style: italic;vertical-align: baseline\"> <\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;vertical-align: baseline\">diremos que el l\u00edmite es por la derecha y si nos acercamos por valores menores que <\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-weight: 700;font-style: italic;vertical-align: baseline\">a<\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;vertical-align: baseline\">, a <\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;font-weight: 700;font-style: italic;vertical-align: baseline\">a<\/span><span style=\"font-size: 11pt;font-family: Raleway, sans-serif;background-color: transparent;vertical-align: baseline\"> diremos que el l\u00edmite es por la izquierda<\/span><\/p><\/span><\/p>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.09.png\" alt=\"\" class=\"wp-image-26921\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"929\" height=\"377\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.09.png\" alt=\"\" class=\"wp-image-26921\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.09.png 929w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.09-300x122.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.09-768x312.png 768w\" sizes=\"auto, (max-width: 929px) 100vw, 929px\" \/><\/noscript><\/figure>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.44.png\" alt=\"\" class=\"wp-image-26922\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"931\" height=\"841\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.44.png\" alt=\"\" class=\"wp-image-26922\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.44.png 931w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.44-300x271.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.15.44-768x694.png 768w\" sizes=\"auto, (max-width: 931px) 100vw, 931px\" \/><\/noscript><\/figure>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.28.png\" alt=\"\" class=\"wp-image-26923\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"263\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.28.png\" alt=\"\" class=\"wp-image-26923\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.28.png 934w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.28-300x84.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.28-768x216.png 768w\" sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><\/noscript><\/figure>\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\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.53.png\" alt=\"\" class=\"wp-image-26924\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"931\" height=\"757\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.53.png\" alt=\"\" class=\"wp-image-26924\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.53.png 931w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.53-300x244.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.16.53-768x624.png 768w\" sizes=\"auto, (max-width: 931px) 100vw, 931px\" \/><\/noscript><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"L\u00cdMITES - Clase Completa: Explicaci\u00f3n desde Cero | El Traductor\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/pYVVPqphPS0?start=1&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Por supuesto que hay una manera m\u00e1s f\u00e1cil de encontrar los l\u00edmites de las funciones y esto es aplicando los teoremas de la secci\u00f3n 1.5 del libro Leithold, te recomiendo que los leas y estudies, as\u00ed como las siguientes secciones 1.6 y 1.7<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Calculo-louis-leithold-1.5-1.6-1.7.pdf\" type=\"application\/pdf\" style=\"width:100%;height:846px\" aria-label=\"Incrustado de Calculo-louis-leithold-1.5-1.6-1.7.\"><\/object><a id=\"wp-block-file--media-c97da6e1-8bdb-4b63-b28f-ca67bcbc9054\" href=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Calculo-louis-leithold-1.5-1.6-1.7.pdf\">Calculo-louis-leithold-1.5-1.6-1.7<\/a><a href=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Calculo-louis-leithold-1.5-1.6-1.7.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-c97da6e1-8bdb-4b63-b28f-ca67bcbc9054\">Descarga<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que ha concluido con el estudio de material escrito y video, realiza la siguiente consigna correspondiente.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Has aprendido el tema de los l\u00edmites, qu\u00e9 tipos de l\u00edmites hay y c\u00f3mo se llaman, adem\u00e1s de c\u00f3mo se calculan. Debes recordar que NUNCA deber\u00e1s evaluar un l\u00edmite sustituyendo el valor, a menos que hagas uso de los teoremas, Los teoremas nos facilitan el trabajo, procura recordarlos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Bien hecho!<\/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\">\n<li><a href=\"https:\/\/luiscastellanos.files.wordpress.com\/2007\/02\/calculo-louis-leithold.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/luiscastellanos.files.wordpress.com\/2007\/02\/calculo-louis-leithold.pdf<\/a>, p\u00e1ginas 38-67 numeraci\u00f3n del libro.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n Este tema es fundamental para entender el concepto de derivadas y l\u00edmites. Seguro que has escuchado la palabra l\u00edmite, normalmente lo traducimos como el lugar donde no debemos ir m\u00e1s all\u00e1. Pues bien, en matem\u00e1ticas es similar, y es en base a este l\u00edmite que se puede definir la derivada. Tenemos varios tipos de &#8230; <a title=\"Clase digital 3. L\u00edmites\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-limites\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 3. L\u00edmites\">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":[19,685],"tags":[41,176,64],"class_list":["post-26572","post","type-post","status-publish","format-standard","hentry","category-ingenieria-en-sistemas-computacionales","category-uda-calculo-diferencial-ingenieria-en-sistemas-computacionales","tag-clase-digital","tag-monica-trejo-duran","tag-neli06002"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26572","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=26572"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26572\/revisions"}],"predecessor-version":[{"id":26927,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26572\/revisions\/26927"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=26572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=26572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=26572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}