{"id":332,"date":"2021-01-19T10:25:32","date_gmt":"2021-01-19T09:25:32","guid":{"rendered":"http:\/\/172.105.246.247\/?p=332"},"modified":"2021-01-19T10:25:32","modified_gmt":"2021-01-19T09:25:32","slug":"opgave","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=332","title":{"rendered":"DG001"},"content":{"rendered":"\n<p class=\"has-text-align-center\">Gr\u00e6nsev\u00e6rdi og differentialregning<\/p>\n\n\n\n<blockquote class=\"reddit-card\" data-card-created=\"1611045789\"><a href=\"https:\/\/www.reddit.com\/r\/3Blue1Brown\/comments\/kyc9u1\/my_mind_goes_in_interesting_directions_when_im\/\">My mind goes in interesting directions when I&#8217;m trying to sleep.<\/a> from <a href=\"http:\/\/www.reddit.com\/r\/3Blue1Brown\">r\/3Blue1Brown<\/a><\/blockquote>\n<script async=\"\" src=\"\/\/embed.redditmedia.com\/widgets\/platform.js\" charset=\"UTF-8\"><\/script>\n\n\n\n<p>I det ovenst\u00e5ende indl\u00e6g p\u00e5 Reddit er svaret p\u00e5 et differentialregningssp\u00f8rgsm\u00e5l <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/a5\/ql_514adf52af85c7e872adc81ffb825ea5_l3.png?resize=17%2C19&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#94;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: 0px;\"\/> hele to gange. Vi vil her se lidt p\u00e5 dette udtryk. Vi starter med at se p\u00e5 hvilken v\u00e6rdi udtrykket har.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>argumenter for at <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/a5\/ql_514adf52af85c7e872adc81ffb825ea5_l3.png?resize=17%2C19&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#94;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: 0px;\"\/> er det samme som <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/05\/ql_29844bccae0a95708724822766e4fa05_l3.png?resize=24%2C18&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#93;&#123;&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\"\/>.<\/li><li>hvilket tal ganget med sig selv <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/62\/ql_2bfff8897aa1969e4895189c8a66fd62_l3.png?resize=9%2C9&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"9\" style=\"vertical-align: 0px;\"\/> gange giver <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/62\/ql_2bfff8897aa1969e4895189c8a66fd62_l3.png?resize=9%2C9&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#109;&#97;&#116;&#104;&#115;&#102;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"9\" style=\"vertical-align: 0px;\"\/>?<\/li><\/ol>\n\n\n\n<p>Vi ser nu p\u00e5 udtrykket som en funktion <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/52\/ql_9846804274726b8ec5213053695bc752_l3.png?resize=73%2C18&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#120;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\"\/> og starter med at se p\u00e5 lidt intuition.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>tegn en skitse p\u00e5 papir af, hvordan du forventer funktionen <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/24\/ql_c229f1194b21740ffc7a238013f06624_l3.png?resize=27%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -3px;\"\/> ser ud.<\/li><\/ol>\n\n\n\n<p>Vi vil nu unders\u00f8ge funktionen for at se hvordan den opf\u00f8rer sig.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>hvad er den h\u00f8jeste v\u00e6rdi som <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/24\/ql_c229f1194b21740ffc7a238013f06624_l3.png?resize=27%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -3px;\"\/> kan antage?<\/li><li>hvad er definitions- og v\u00e6rdim\u00e6ngden for <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/24\/ql_c229f1194b21740ffc7a238013f06624_l3.png?resize=27%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -3px;\"\/>?<\/li><li>argumenter for, hvad gr\u00e6nsev\u00e6rdien for <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/24\/ql_c229f1194b21740ffc7a238013f06624_l3.png?resize=27%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -3px;\"\/> er, n\u00e5r <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/41\/ql_968f7ca0ca00def350ebd65e56c97541_l3.png?resize=10%2C9&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> g\u00e5r mod <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/ea\/ql_cfb82fea55a7728d1ca093877ec8c1ea_l3.png?resize=9%2C12&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/li><li>tegn basere p\u00e5 din unders\u00f8gelse, hvordan du nu forventer at funktionen ser ud.<\/li><li>plot <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/24\/ql_c229f1194b21740ffc7a238013f06624_l3.png?resize=27%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -3px;\"\/> og se om det passer overens med det du har fundet ud af og din forventning.<\/li><\/ol>\n\n\n","protected":false},"excerpt":{"rendered":"<p>Gr\u00e6nsev\u00e6rdi og differentialregning My mind goes in interesting directions when I&#8217;m trying to sleep. from r\/3Blue1Brown I det ovenst\u00e5ende indl\u00e6g p\u00e5 Reddit er svaret p\u00e5 et differentialregningssp\u00f8rgsm\u00e5l hele to gange. Vi vil her se lidt p\u00e5 dette udtryk. Vi starter med at se p\u00e5 hvilken v\u00e6rdi udtrykket har. argumenter for at er det samme som [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4],"tags":[15,16],"class_list":["post-332","post","type-post","status-publish","format-standard","hentry","category-opgave","tag-differentialregning","tag-graensevaerdi"],"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\/332","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=332"}],"version-history":[{"count":1,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/332\/revisions"}],"predecessor-version":[{"id":616,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/332\/revisions\/616"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}