{"id":80,"date":"2020-01-11T18:42:06","date_gmt":"2020-01-11T18:42:06","guid":{"rendered":"https:\/\/henriksenmatematik.wordpress.com\/?p=80"},"modified":"2026-04-09T22:15:26","modified_gmt":"2026-04-09T20:15:26","slug":"kontinuitet-3","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=80","title":{"rendered":"Kontinuitet"},"content":{"rendered":"\n

Definition<\/h3>

kontinuitet,<\/strong> uafbrudt sammenh\u00e6ng. I matematik siges en funktion at v\u00e6re kontinuert, hvis den ikke overspringer v\u00e6rdier, det vil sige at dens grafiske billede forl\u00f8ber ubrudt uden huller eller spring<\/p>

denstoredanske.dk\n<\/p><\/blockquote>\n\n\n\n

En funktion \"f(x)\" siges at v\u00e6re kontinuert i et interval \"[a;, n\u00e5r den uden \u201cbrud\u201d genneml\u00f8ber intervallet. Hvis du kan tegne grafen uden at l\u00f8fte blyantspidsen fra papiret, er den kontinuert.<\/p>\n\n\n\n

Et eksempel p\u00e5 en kontinuert funktion kunne for eksempel v\u00e6re<\/p>\n\n\n\n

\"Kontinuert<\/figure><\/div>\n\n\n\n

Det ses her, at funktionen er sammenh\u00e6ngende i hele definitionsintervallet og derfor er den en kontinuert funktion, selv om det laver et kn\u00e6k.<\/p>\n\n\n\n

En funktion der ikke er kontinuert hedder en diskontinuert funktion og kunne for eksempel v\u00e6re<\/p>\n\n\n\n

\"Diskontinuert<\/figure>\n\n\n\n

Men den kunne ogs\u00e5 godt v\u00e6re<\/p>\n\n\n\n

\"Diskontinuert<\/figure>\n\n\n\n

Begge funktioner er defineret i hele definitionsintervallet, men begge springer n\u00e5r x bliver lig med -1.<\/p>\n\n\n\n

De funktioner som vi har m\u00f8dt indtil videre er alle kontinuerte.<\/p>\n\n\n\n

Generelt vil der for funktioner g\u00e6lde at<\/p>\n\n\n\n

S\u00e5fremt funktionerne \"f(x)\" og \"g(x)\" er kontinuerte i punktet \"x_0\", da vil f\u00f8lgende kombinationer af \"f\" og \"g\" ogs\u00e5 v\u00e6re kontinuerte i punktet \"x_0\"<\/p>

\"f(x_0)<\/p>

\"f(x_0)<\/p>

\"f(x)\cdot<\/p>

\"\frac{f(x_0)}{g(x_0)}\", \"g(x_0)\neq<\/p>

\"f(g(x_0))\" og \"g(f(x_0))\" <\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

Definition kontinuitet, uafbrudt sammenh\u00e6ng. I matematik siges en funktion at v\u00e6re kontinuert, hvis den ikke overspringer v\u00e6rdier, det vil sige at dens grafiske billede forl\u00f8ber ubrudt uden huller eller spring denstoredanske.dk En funktion siges at v\u00e6re kontinuert i et interval , n\u00e5r den uden \u201cbrud\u201d genneml\u00f8ber intervallet. Hvis du kan tegne grafen uden at l\u00f8fte […]<\/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":[],"class_list":["post-80","post","type-post","status-publish","format-standard","hentry","category-differentialregning","category-matematik"],"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\/80","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=80"}],"version-history":[{"count":1,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions"}],"predecessor-version":[{"id":4299,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions\/4299"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=80"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=80"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}