{"id":101,"date":"2020-01-12T22:23:22","date_gmt":"2020-01-12T22:23:22","guid":{"rendered":"https:\/\/henriksenmatematik.wordpress.com\/?p=101"},"modified":"2026-04-09T22:44:30","modified_gmt":"2026-04-09T20:44:30","slug":"graensevaerdibegrebet","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=101","title":{"rendered":"Gr\u00e6nsev\u00e6rdibegrebet"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Gr\u00e6nsev\u00e6rdibegrebet er vigtigt for differential- og integralregningen. Vi kigger her n\u00e6rmere p\u00e5 begrebet.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed alignwide is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/N9kaSmJhxHM?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<blockquote class=\"is-style-default wp-block-quote eplus-wrapper is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\" eplus-wrapper\">   <strong>Definition<\/strong><br>   En funktion <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=f&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"f\" class=\"latex\" \/> siges at have en gr\u00e6nsev\u00e6rdi <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=L&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"L\" class=\"latex\" \/> for <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x\" class=\"latex\" \/> g\u00e5ende mod <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x_0&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x_0\" class=\"latex\" \/>, hvis <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=f%28x%29&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"f(x)\" class=\"latex\" \/> n\u00e6rmer sig <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=L&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"L\" class=\"latex\" \/>, n\u00e5r <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x\" class=\"latex\" \/> n\u00e6rmer sig <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x_0&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x_0\" class=\"latex\" \/>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">  Med matematiksymboler ser de s\u00e5dan ud<\/p>\n\n\n\n<p class=\" eplus-wrapper\">  <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Clim_%7Bx+%5Cto+x_0%7D+f%28x%29+%3DL&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"&#92;lim_{x &#92;to x_0} f(x) =L\" class=\"latex\" \/><\/p>\n\n\n\n<p class=\" eplus-wrapper\">  eller<\/p>\n\n\n\n<p class=\" eplus-wrapper\">  <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Clim_%7Bh+%5Cto+0%7D+f%28x_0%2Bh%29%3DL&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"&#92;lim_{h &#92;to 0} f(x_0+h)=L\" class=\"latex\" \/> <\/p>\n<\/blockquote>\n\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/matbhtx.systime.dk\/?id=c12671\" target=\"_blank\" rel=\"noopener\">matBhtx 9.1<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matbhtx.systime.dk\/?id=c12684\" target=\"_blank\" rel=\"noopener\">matBhtx 9.3<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c269\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.12<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/matbhtx.systime.dk\/?id=c12678\" target=\"_blank\" rel=\"noopener\">matBhtx 9.2<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matbhtx.systime.dk\/?id=c12686\" target=\"_blank\" rel=\"noopener\">matBhtx 9.5<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c1541\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.13<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c262\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.10<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c254\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.06<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c255\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.07<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c268\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.11<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c1542\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.14<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=120#c1544\" target=\"_blank\" rel=\"noopener\">matAB2stx 2.16<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Gr\u00e6nsev\u00e6rdibegrebet er vigtigt for differential- og integralregningen. Vi kigger her n\u00e6rmere p\u00e5 begrebet.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[11,3],"tags":[74],"class_list":["post-101","post","type-post","status-publish","format-standard","hentry","category-differentialregning","category-matematik","tag-htx"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=101"}],"version-history":[{"count":8,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/101\/revisions"}],"predecessor-version":[{"id":4313,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/101\/revisions\/4313"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}