{"id":4035,"date":"2025-03-01T06:05:19","date_gmt":"2025-03-01T06:05:19","guid":{"rendered":"https:\/\/lash.utrng.edu.mx\/?p=4035"},"modified":"2025-03-01T06:08:03","modified_gmt":"2025-03-01T06:08:03","slug":"2-continuidad","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=4035","title":{"rendered":"2. Continuidad"},"content":{"rendered":"\n<p>En un problema sobre continuidad podemos:<\/p>\n\n\n\n<p><strong>Primero<\/strong>. Determinar si una funci\u00f3n <em>f<\/em>(.x) es continua o discontinua en un punto dado.<br><strong>Segundo<\/strong>. Determinar en qu\u00e9 puntos una funci\u00f3n\/(.v) es discontinua.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-green-cyan-color has-text-color has-link-color wp-elements-10cda8c2e5725e496469b77eba34d024\">Continuidad y Discontinuidad.<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"709\" height=\"267\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image.png\" alt=\"\" class=\"wp-image-4036\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image.png 709w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-300x113.png 300w\" sizes=\"auto, (max-width: 709px) 100vw, 709px\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/2.jpg\" alt=\"\" class=\"wp-image-4038\" style=\"width:449px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/2.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/2-300x300.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/2-150x150.jpg 150w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/2-768x768.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<!--more-->\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-ffaf336c5d0f054dfb08a9597d17ccdf\">Ejemplos:<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"349\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-1.png\" alt=\"\" class=\"wp-image-4037\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-1.png 601w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-1-300x174.png 300w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"608\" height=\"108\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-2.png\" alt=\"\" class=\"wp-image-4039\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-2.png 608w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-2-300x53.png 300w\" sizes=\"auto, (max-width: 608px) 100vw, 608px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"688\" height=\"314\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-3.png\" alt=\"\" class=\"wp-image-4040\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-3.png 688w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-3-300x137.png 300w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"352\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-4.png\" alt=\"\" class=\"wp-image-4041\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-4.png 616w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-4-300x171.png 300w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>En algunos casos la discontinuidad es evitable asignando a la funci\u00f3n otro valor para <em>f<\/em>(a ).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"71\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-5.png\" alt=\"\" class=\"wp-image-4042\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-5.png 507w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-5-300x42.png 300w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"702\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-6.png\" alt=\"\" class=\"wp-image-4043\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-6.png 618w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-6-264x300.png 264w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<p>En este caso, la discontinuidad es evitable porque si asignamos a la funci\u00f3n<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"59\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-7.png\" alt=\"\" class=\"wp-image-4044\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-7.png 507w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-7-300x35.png 300w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-vivid-green-cyan-color has-text-color has-link-color wp-elements-202f654deb0c11b491ad393e50650924\">L\u00edmites al infinito;<br>l\u00edmites infinitos<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"84\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-8.png\" alt=\"\" class=\"wp-image-4045\" style=\"width:629px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-8.png 601w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-8-300x42.png 300w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"166\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-9.png\" alt=\"\" class=\"wp-image-4046\" style=\"width:327px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-9.png 253w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-9-75x50.png 75w\" sizes=\"auto, (max-width: 253px) 100vw, 253px\" \/><\/figure><\/div>\n\n\n<p>Cuando escribimos x \u21fe \u221e, no queremos dar a entender que en un lugar muy alejado a la derecha del eje x exista un n\u00famero \u2014m\u00e1s grande que todos los dem\u00e1s\u2014 al cual se aproxima x. En lugar de eso utilizamos x \u21fe \u221e como una forma breve de decir que x se hace cada vez m\u00e1s grande sin cota.<\/p>\n\n\n\n<p>En la siguiente tabla de la figura, hemos listado valores de g(x) = x \/ (1 + x<sup>2<\/sup>) para diversos valores de x. Parece que g(x) se hace cada vez m\u00e1s peque\u00f1o conforme x se hace cada vez m\u00e1s grande. Escribimos<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"126\" height=\"44\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-11.png\" alt=\"\" class=\"wp-image-4048\" style=\"width:176px;height:auto\"\/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"116\" height=\"170\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-10.png\" alt=\"\" class=\"wp-image-4047\" style=\"width:158px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Al experimentar <strong>con n\u00fameros<\/strong> negativos cada vez m\u00e1s lejanos del cero nos conducir\u00eda a escribir<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"132\" height=\"43\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-12.png\" alt=\"\" class=\"wp-image-4049\" style=\"width:192px;height:auto\"\/><\/figure><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"108\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-13.png\" alt=\"\" class=\"wp-image-4050\" style=\"width:633px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-13.png 601w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-13-300x54.png 300w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"324\" height=\"52\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-14.png\" alt=\"\" class=\"wp-image-4051\" style=\"width:362px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-14.png 324w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-14-300x48.png 300w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"236\" height=\"210\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/03\/image-15.png\" alt=\"\" class=\"wp-image-4052\" style=\"width:316px;height:auto\"\/><\/figure><\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>En un problema sobre continuidad podemos: Primero. Determinar si una funci\u00f3n f(.x) es continua o discontinua en un punto dado.Segundo. Determinar en qu\u00e9 puntos una funci\u00f3n\/(.v) es discontinua. Continuidad y Discontinuidad.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[95],"tags":[],"class_list":["post-4035","post","type-post","status-publish","format-standard","hentry","category-calculodiferencial2do-ti"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4035"}],"version-history":[{"count":1,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4035\/revisions"}],"predecessor-version":[{"id":4053,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4035\/revisions\/4053"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}