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a:5:{s:8:"template";s:17358:"<!DOCTYPE html> <html lang="da-DK"> <head> <meta charset="utf-8"/> <meta content="width=device-width, initial-scale=1" name="viewport"/> <link href="http://gmpg.org/xfn/11" rel="profile"/> <title>{{ keyword }}</title> <style id="scribbles-css" media="all" rel="stylesheet" type="text/css"> @charset "UTF-8"; html { font-family: sans-serif; -ms-text-size-adjust: 100%; -webkit-text-size-adjust: 100%; } body { margin: 0; } aside, footer, header, nav { display: block; } a { background-color: transparent; -webkit-text-decoration-skip: objects; } a:active, a:hover { outline-width: 0; } input { font: inherit; margin: 0; } input { overflow: visible; } [type="submit"] { -webkit-appearance: button; } [type="submit"]::-moz-focus-inner { border-style: none; padding: 0; } [type="submit"]:-moz-focusring { outline: 1px dotted ButtonText; } [type="search"] { -webkit-appearance: textfield; outline-offset: -2px; } [type="search"]::-webkit-search-cancel-button, [type="search"]::-webkit-search-decoration { -webkit-appearance: none; 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} } .menu-toggle div { background-color: #ffffff; height: 0.25rem; margin: 0.43rem; -webkit-transform: rotate(0deg); -ms-transform: rotate(0deg); transform: rotate(0deg); -webkit-transition: .15s ease-in-out; transition: .15s ease-in-out; -webkit-transform-origin: left center; -ms-transform-origin: left center; transform-origin: left center; } /* Text meant only for screen readers. */ .screen-reader-text { clip: rect(1px, 1px, 1px, 1px); position: absolute !important; height: 1px; width: 1px; overflow: hidden; } .screen-reader-text:focus { background-color: #fff; -webkit-border-radius: 3px; border-radius: 3px; -webkit-box-shadow: 0 0 2px 2px rgba(0, 0, 0, 0.6); box-shadow: 0 0 2px 2px rgba(0, 0, 0, 0.6); clip: auto !important; color: #21759b; display: block; font-size: 14px; font-size: 0.875rem; font-weight: bold; height: auto; left: 5px; line-height: normal; padding: 15px 23px 14px; text-decoration: none; top: 5px; width: auto; z-index: 100000; /* Above WP toolbar. */ } .site-header:before, .site-header:after, .site-content:before, .site-content:after, .site-footer:before, .site-footer:after { content: ""; 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} </style> <style id="scribbles-inline-css" type="text/css"> .hero{ background-image:url(); } .site-title a,.site-title a:visited{ color:#ffffff; } .site-title a:hover,.site-title a:visited:hover{ color:rgba(255, 255, 255, 0.8); } .site-search-wrapper .widget .search-field{ border-color:rgba(153, 153, 153, 0.25); } .hero{ color:#ffffff; } .main-navigation ul li a,.main-navigation ul li a:visited,.main-navigation ul li a:hover,.main-navigation ul li a:visited:hover{ color:#ffffff; } .menu-toggle div{ background-color:#ffffff; } .main-navigation ul li a,.main-navigation ul li a:visited,.main-navigation ul li a:hover,.main-navigation ul li a:visited:hover{ color:#ffffff; } .main-navigation ul li a:hover{ color:rgba(255, 255, 255, 0.8); } .main-navigation ul li a:hover{ color:rgba(255, 255, 255, 0.8); } h4,label,.widget-title{ color:#ffffff; } .footer-widget .widget-title{ color:#ffffff; border-color:#ffffff; } body,input,input[type="search"]:focus{ color:#e5e5e5; } input[type="search"]{ color:rgba(229, 229, 229, 0.5); 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} .main-navigation-container,.main-navigation-container:before,.main-navigation-container:after{ background-color:#333333; } .site-footer{ background-color:#282828; } .site-footer .widget{ background-color:#333333; } .site-info-wrapper{ background-color:#222222; } </style> <style type="text/css"> .site-title a,.site-title a:visited{color:#ffffff;} </style><style id="custom-background-css" type="text/css"> body.custom-background { background-color: ##222222; } </style> </head> <body class="custom-background custom-header-image layout-two-column-default"> <div class="hfeed site" id="page"> <a class="skip-link screen-reader-text" href="#">Skip to content</a> <header class="site-header" id="masthead" role="banner"> <div class="site-header-wrapper"> <div class="site-title-wrapper"> <div class="site-title"><a href="#" rel="home">{{ keyword }}</a></div> </div> <div class="hero"> <div class="hero-inner"> </div> </div> <div class="site-search-wrapper"> <div class="widget widget_search"><form action="#" class="search-form" method="get" role="search"> <label> <span class="screen-reader-text">Search for:</span> <input class="search-field" name="s" placeholder="Search " type="search" value=""/> </label> <input class="search-submit" type="submit" value="Search"/> </form></div> </div> </div> </header> <div class="main-navigation-container"> <div class="menu-toggle" id="menu-toggle"> <div></div> <div></div> <div></div> </div> <nav class="main-navigation" id="site-navigation"> <div class="menu-primary-menu-container"><ul class="menu" id="menu-primary-menu"><li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-170" id="menu-item-170"><a href="#">Home</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-172" id="menu-item-172"><a href="#">About Us</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-169" id="menu-item-169"><a href="#">Make A Difference</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page current_page_parent menu-item-166" id="menu-item-166"><a href="#">Blog</a></li> <li class="menu-item menu-item-type-post_type menu-item-object-page menu-item-171" id="menu-item-171"><a href="#">Contact Us</a></li> </ul></div> </nav> </div> <div class="page-title-container"> </div> <div class="site-content" id="content"> {{ text }} </div> <footer class="site-footer" id="colophon"> <div class="site-footer-inner"> {{ links }} <div class="footer-widget-area columns-1"> <div class="footer-widget"> <aside class="widget wpcw-widgets wpcw-widget-social" id="wpcw_social-3"><h4 class="widget-title">Social Media</h4><ul><li class="no-label"><a href="#" target="_blank" title="Visit {{ keyword }} on Google+"><span class="fa fa-2x fa-google-plus"></span></a></li><li class="no-label"><a href="#" target="_blank" title="Visit {{ keyword }} on Twitter"><span class="fa fa-2x fa-twitter"></span></a></li><li class="no-label"><a href="#" target="_blank" title="Visit {{ keyword }} on LinkedIn"><span class="fa fa-2x fa-linkedin-square"></span></a></li><li class="no-label"><a href="#" target="_blank" title="Visit {{ keyword }} on Facebook"><span class="fa fa-2x fa-facebook-official"></span></a></li></ul></aside> </div> </div> </div> </footer> <div class="site-info-wrapper"> <div class="site-info"> <div class="site-info-inner"> <nav class="social-menu"> </nav> <div class="site-info-text"> Copyright 2017 {{ keyword }} </div> </div> </div> </div> </div> </body> </html>";s:4:"text";s:2161:"Man kan integrere en konstant (fast tal) gange en funktion ved simpelthen at lade konstanten så og så integrere funktionen. Tangentens ligning Vi ser på hvordan man bestemmer ligningen/forskriften for tangenten i et punkt. Her gennemgår vi sumreglen, konstantreglen, produktreglen samt kvotientreglen for differentialkvotienter. Her gennemgår vi sumreglen, konstantreglen, produktreglen samt kvotientreglen for differentialkvotienter. ... Bevis for sumreglen er (hvis det er godtaget at tretrinsreglen er tilstrækkelig bevisførelse) at putte (f(x)+g(x)) igennem tretrinsreglen istedet for bare f(x). Bevis v.h.a tretrinsreglen, at funktionen f(x) = x^2 er differentiabel i x0 meddifferentialkvotienten f '(x0) = 2 * x0. Produktreglen er nævnt og brugt til bevis for konstantreglen. Torsdag 17. juli: Modul 14 Bevis med arealfunktionen og for regneregler for bestemte integraler Bevise at man kan udregne arealer under grafer med integraler. MatWiki - Matematik A - Differentiation Af Produkt Her er nogle regneregler for produkt. denne. Husk at kigge efter figuren og beregninger nederst. For at integrere bruger vi først sumreglen og dernæst konstantreglen: Vi kan nu bruge de ovenstående regler for x og sinus til at integrere: Da k kan være hvilken som helst konstant kan vi … Omfang 20 timer Særlige fokuspunkter Formuleringsevne Beviskompetence Anvendelse af CAS til at finde differentialkvotienter, afledede, væksthastigheder og tangentligninger. Det forudsættes at alle funktioner er differentiable og dermed kontinuerte for den givne definitionsmængde:. Interaktivt bevis for differentialkvotient af differens af 2 funktioner Ved at klikke i boksene får du beviset for (f(x)-g(x))'=f'(x)-g'(x) frem. Brøkreglen er nævnt og enkelte opgaver regnet vha. 7. Redegør for andre simple funktioners differentialkvotienter i x0. - Konstantreglen - Produktreglen - Kvotientreglen Generelt står der rigtig meget på nettet, hvilket jeg også selv har brugt flittigt da jeg gik på HTX. Indføre arealfunktionen (og forstå dens virkemåde), bevise af den er en stamfunktion til den funktion der gælder for. Konstantreglen for integration. 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