{
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  "sourcesContent": ["import{jsx as e,jsxs as r}from\"react/jsx-runtime\";import{ComponentPresetsConsumer as n,Link as t}from\"framer\";import{motion as i}from\"framer-motion\";import*as l from\"react\";import a from\"https://framerusercontent.com/modules/pVk4QsoHxASnVtUBp6jr/HTBsNkEMAb7TUGaO3DBy/CodeBlock.js\";export const richText=/*#__PURE__*/r(l.Fragment,{children:[/*#__PURE__*/e(\"p\",{children:\"Differentialregning kan lyde sv\\xe6rt, men det er faktisk ikke s\\xe5 sv\\xe6rt, n\\xe5r man f\\xf8rst kn\\xe6kker koden. Hvis du nogensinde har undret dig over, hvordan man m\\xe5ler h\\xe6ldningen p\\xe5 en graf eller finder ud af, hvor hurtigt noget \\xe6ndrer sig, s\\xe5 er differentialregning din ven.\\xa0\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"Indholdsfortegnelse\"})}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Hvad er differentialregning?\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Regler for differentialregning\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"S\\xe5dan finder du en differentialkvotient\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Guide til tangenters h\\xe6ldning\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Hvad er den anden afledte?\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"K\\xe6dereglen forklaret\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Produktreglen i differentialregning\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Differentialregning i Excel\"})})]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvad er differentialregning?\"})}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(t,{href:\"https://ordnet.dk/ddo/ordbog?query=differentialregning\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"Differentialregning\"})}),\" handler om at finde ud af, hvor hurtigt noget \\xe6ndrer sig i et bestemt punkt i et \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/koordinatsystemer\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"koordinatsystem\"})}),\". T\\xe6nk p\\xe5 det som at m\\xe5le h\\xe6ldningen p\\xe5 en bakke. Hvis bakken bliver stejlere, \\xe6ndrer h\\xe6ldningen sig.\\xa0\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"Et simpelt eksempel\"})}),/*#__PURE__*/e(\"p\",{children:\"Forestil dig, at du har en graf for en funktion, fx f(x)=x2f(x) = x^2. Hvis du vil vide, hvor stejl grafen er i punktet x=2x = 2, skal du bruge differentialregning til at finde h\\xe6ldningen der.\"}),/*#__PURE__*/r(\"p\",{children:[\"Resultatet? Den afledte funktion, som viser h\\xe6ldningen i alle punkter. For f(x)=x2f(x) = x^2 er den \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/funktioner\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"afledte funktion\"})}),\" f\u2032(x)=2xf'(x) = 2x. Ved x=2x = 2 er h\\xe6ldningen alts\\xe5 4. Nemt, ikke?\"]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Regler for differentialregning\"})}),/*#__PURE__*/r(\"p\",{children:[\"F\\xf8r vi hopper til eksempler, skal du kende de \",/*#__PURE__*/e(t,{href:\"https://bestaamatematik.dk/goer-differentialregning-leg/\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"grundl\\xe6ggende regler.\"})}),\" Her er de vigtigste:\"]}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Potensreglen\"}),\": Hvis f(x)=xnf(x) = x^n, s\\xe5 er f\u2032(x)=n\u22C5xn\u22121f'(x) = n*x^{n-1}.\"]})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Konstantreglen\"}),\": Hvis f(x)=kf(x) = k, s\\xe5 er f\u2032(x)=0f'(x) = 0 (en konstant \\xe6ndrer sig ikke).\"]})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Sumreglen\"}),\": Hvis f(x)=g(x)+h(x)f(x) = g(x) + h(x), s\\xe5 er f\u2032(x)=g\u2032(x)+h\u2032(x)f'(x) = g'(x) + h'(x).\"]})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Produktreglen\"}),\": Hvis f(x)=g(x)\u22C5h(x)f(x) = g(x)*h(x), s\\xe5 er f\u2032(x)=g\u2032(x)\u22C5h(x)+g(x)\u22C5h\u2032(x)f'(x) = g'(x)*h(x) + g(x)*h'(x).\"]})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Kvotientreglen\"}),\": Hvis f(x)=g(x)h(x)f(x) ={g(x)}/{h(x)}, s\\xe5 er f\u2032(x)=g\u2032(x)\u22C5h(x)\u2212g(x)\u22C5h\u2032(x)h(x)2f'(x) ={g'(x)*h(x) - g(x)*h'(x)}{h(x)^2}.\"]})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"K\\xe6dereglen\"}),\": Hvis f(x)=g(h(x))f(x) = g(h(x)), s\\xe5 er f\u2032(x)=g\u2032(h(x))\u22C5h\u2032(x)f'(x) = g'(h(x))*h'(x).\"]})})]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"S\\xe5dan finder du en differentialkvotient\"})}),/*#__PURE__*/r(\"p\",{children:[\"Differentialkvotienten er bare et fint ord for \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/funktioner\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"h\\xe6ldningen\"})}),\" i et bestemt punkt. Du kan finde den ved hj\\xe6lp af denne formel:\"]}),/*#__PURE__*/e(\"p\",{children:\"f\u2032(x)=lim\u2061h\u21920f(x+h)\u2212f(x)hf'(x) = \\\\lim_{h -> 0}/{f(x + h) - f(x)}{h}\"}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Et eksempel\"})}),/*#__PURE__*/e(\"p\",{children:\"Lad os tage f(x)=x2f(x) = x^2 og finde h\\xe6ldningen i x=2x = 2:\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Start med formlen: f\u2032(x)=lim\u2061h\u21920(x+h)2\u2212x2hf'(x) = \\\\lim_{h -> 0}/{(x + h)^2 - x^2}{h}\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Inds\\xe6t f(x)=x2f(x) = x^2: (2+h)2\u221222h/{(2 + h)^2 - 2^2}{h}\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Udregn: 4+4h+h2\u22124h=4h+h2h/{4 + 4h + h^2 - 4}{h} = /{4h + h^2}{h}\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Forkort: 4+h4 + h\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Lad h\u21920h \\\\to 0: 44\"})})]}),/*#__PURE__*/e(\"p\",{children:\"H\\xe6ldningen i x=2x = 2 er alts\\xe5 4.\"}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Guide til tangenters h\\xe6ldning\"})}),/*#__PURE__*/r(\"p\",{children:[\"En tangent er en linje, der r\\xf8rer \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/funktioner\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"grafen\"})}),\" i \\xe9t punkt. H\\xe6ldningen p\\xe5 tangenten er det samme som differentialkvotienten i det punkt.\"]}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvordan finder du tangenth\\xe6ldningen?\"})}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Find den afledte funktion (f\u2032(x)f'(x)).\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"S\\xe6t den \\xf8nskede xx-v\\xe6rdi ind i f\u2032(x)f'(x).\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Resultatet er h\\xe6ldningen p\\xe5 tangenten i det punkt.\"})})]}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempel\"})}),/*#__PURE__*/e(\"p\",{children:\"For f(x)=x3f(x) = x^3, find h\\xe6ldningen af tangenten ved x=1x = 1:\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Den afledte funktion er f\u2032(x)=3x2f'(x) = 3x^2.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"S\\xe6t x=1x = 1 ind: f\u2032(1)=3(1)2=3f'(1) = 3(1)^2 = 3.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Tangenth\\xe6ldningen er 3.\"})})]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvad er den anden afledte?\"})}),/*#__PURE__*/e(\"p\",{children:\"Den anden afledte, skrevet som f\u2032\u2032(x)f''(x), viser, hvordan h\\xe6ldningen \\xe6ndrer sig. Det kaldes ogs\\xe5 krumningen af grafen.\"}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempel\"})}),/*#__PURE__*/e(\"p\",{children:\"For f(x)=x3f(x) = x^3:\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"F\\xf8rstefunktion: f\u2032(x)=3x2f'(x) = 3x^2.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Anden afledte: f\u2032\u2032(x)=6xf''(x) = 6x.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Ved x=2x = 2 er f\u2032\u2032(2)=6(2)=12f''(2) = 6(2) = 12.\"})})]}),/*#__PURE__*/e(\"p\",{children:\"Det betyder, at h\\xe6ldningen \\xe6ndrer sig hurtigt her.\"}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"K\\xe6dereglen forklaret\"})}),/*#__PURE__*/r(\"p\",{children:[\"K\\xe6dereglen er genial, n\\xe5r du har en \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/funktioner\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"funktion\"})}),\" indeni en anden funktion, fx f(x)=(2x+3)2f(x) = (2x + 3)^2.\"]}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempel\"})}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Ydre funktion: g(x)=x2g(x) = x^2.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Indre funktion: h(x)=2x+3h(x) = 2x + 3.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Brug k\\xe6dereglen: g\u2032(h(x))\u22C5h\u2032(x)g'(h(x))*h'(x).\"})}),/*#__PURE__*/r(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:[/*#__PURE__*/e(\"p\",{children:\"L\\xf8sning:\"}),/*#__PURE__*/r(\"ul\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"g\u2032(x)=2xg'(x) = 2x, s\\xe5 g\u2032(h(x))=2(2x+3)g'(h(x)) = 2(2x + 3).\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"h\u2032(x)=2h'(x) = 2.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Sammenlagt: 2(2x+3)\u22C52=4(2x+3)2(2x + 3)*2 = 4(2x + 3).\"})})]})]})]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Produktreglen i differentialregning\"})}),/*#__PURE__*/e(\"p\",{children:\"Hvis du har to funktioner, der ganges sammen, skal du bruge produktreglen.\"}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempel\"})}),/*#__PURE__*/e(\"p\",{children:\"Lad f(x)=x\u22C5exf(x) = x*e^x. Her er g(x)=xg(x) = x og h(x)=exh(x) = e^x.\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Differentier g(x)g(x): g\u2032(x)=1g'(x) = 1.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Differentier h(x)h(x): h\u2032(x)=exh'(x) = e^x.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Brug produktreglen: g\u2032(x)\u22C5h(x)+g(x)\u22C5h\u2032(x)g'(x)*h(x) + g(x)*h'(x).\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"L\\xf8sning: 1\u22C5ex+x\u22C5ex=ex+xex1*e^x + x*e^x = e^x + xe^x.\"})})]}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Differentialregning i Excel\"})}),/*#__PURE__*/r(\"p\",{children:[\"Vidste du, at du kan bruge \",/*#__PURE__*/e(t,{href:\"https://real-statistics.com/other-mathematical-topics/differentiation/\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"Excel til at lave differentialregning\"})}),\"? 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Det lyder m\\xe5ske teknisk, men her er en simpel m\\xe5de at g\\xf8re det p\\xe5:\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/r(\"p\",{children:[\"Find de to\",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/funktioner\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\" linjers ligninger\"})}),\" (fx y = 2x + 1 og y = -x + 3).\"]})}),/*#__PURE__*/r(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:[/*#__PURE__*/e(\"p\",{children:\"S\\xe6t de to ligninger lig med hinanden:\"}),/*#__PURE__*/e(\"ul\",{children:/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"2x + 1 = -x + 3.\"})})})]}),/*#__PURE__*/r(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:[/*#__PURE__*/e(\"p\",{children:\"L\\xf8s for x:\"}),/*#__PURE__*/e(\"ul\",{children:/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"3x = 2 \u2192 x = 2/3.\"})})})]}),/*#__PURE__*/r(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:[/*#__PURE__*/e(\"p\",{children:\"Find y ved at inds\\xe6tte x i en af ligningerne.\"}),/*#__PURE__*/e(\"ul\",{children:/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"y = 2(2/3) + 1 = 7/3.\"})})})]}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Sk\\xe6ringspunktet er (2/3, 7/3).\"})})]}),/*#__PURE__*/e(\"p\",{children:\"Du har nu fundet det magiske m\\xf8depunkt.\"}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvordan finder jeg h\\xe6ldningskoefficienten af en linje?\\xa0\"})}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvad er h\\xe6ldningskoefficienten?\"})}),/*#__PURE__*/e(\"p\",{children:'H\\xe6ldningskoefficienten, ofte kaldet \"h\\xe6ldningen af en graf\", beskriver, hvor stejl en linje er. 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For at finde h\\xe6ldningen:\"}),/*#__PURE__*/r(\"ol\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Beregn: a=(y2-y1)/(x2-x1)=(6-2)/(3-1)\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Beregn: a=42\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"Beregn: a=2\\xa0\"})})]}),/*#__PURE__*/e(\"p\",{children:\"H\\xe6ldningen af linjen er alts\\xe5 2, hvilket betyder, at linjen stiger med 2 enheder for hver 1 enhed, den bev\\xe6ger sig til h\\xf8jre.\"}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"strong\",{children:\"Hvorfor er det vigtigt?\"})}),/*#__PURE__*/r(\"p\",{children:[\"At kende \",/*#__PURE__*/e(t,{href:\"https://www.toptutors.com/blog/gratis-matematik-opgaver-faerdighedsregning\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"h\\xe6ldningen hj\\xe6lper dig\"})}),\" med at forst\\xe5, hvordan linjer opf\\xf8rer sig. For eksempel:\"]}),/*#__PURE__*/r(\"ul\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"En positiv h\\xe6ldning betyder, at linjen stiger.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"En negativ h\\xe6ldning betyder, at linjen falder.\"})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"En h\\xe6ldning p\\xe5 0 betyder, at linjen er vandret.\"})})]}),/*#__PURE__*/e(\"p\",{children:\"Pr\\xf8v selv med forskellige punkter og bliv en ekspert i at finde h\\xe6ldninger!\"}),/*#__PURE__*/e(\"h2\",{children:/*#__PURE__*/e(\"strong\",{children:\"Sjove fakta om koordinatsystemer\"})}),/*#__PURE__*/r(\"ul\",{children:[/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:'Koordinatsystemet blev opfundet af Ren\\xe9 Descartes i 1600-tallet. Jep, ham fra \"Jeg t\\xe6nker, derfor er jeg\"!'})}),/*#__PURE__*/e(\"li\",{\"data-preset-tag\":\"p\",style:{\"--framer-font-size\":\"11px\",\"--framer-text-color\":\"rgb(0, 0, 0)\",\"--framer-text-decoration\":\"none\"},children:/*#__PURE__*/e(\"p\",{children:\"GPS-en p\\xe5 din telefon bruger faktisk en 3D-version af koordinatsystemet til at finde din position.\"})})]}),/*#__PURE__*/e(\"p\",{children:\"Jeg h\\xe5ber, du nu f\\xf8ler dig som en mester i koordinatsystemer.\"})]});export const richText3=/*#__PURE__*/r(l.Fragment,{children:[/*#__PURE__*/e(\"p\",{children:\"I dag er det ikke l\\xe6ngere nok at kunne l\\xe6se, skrive og regne \u2013 i hvert fald ikke, hvis man sp\\xf8rger fremtidens arbejdsmarked. Teknologiske f\\xe6rdigheder er blevet en central del af den moderne dannelse, og det er aldrig for tidligt at begynde at l\\xe6re dem. Men hvorfor er det egentlig s\\xe5 vigtigt, at vores b\\xf8rn l\\xe6rer at mestre teknologi? Og hvordan kan man som for\\xe6lder sikre, at ens barn f\\xe5r de bedste foruds\\xe6tninger i en verden, hvor koder, apps og algoritmer spiller en stadig st\\xf8rre rolle? Lad os dykke ned i det!\"}),/*#__PURE__*/e(\"h3\",{children:\"Teknologi er fremtiden \u2013 og fremtiden er her\"}),/*#__PURE__*/e(\"p\",{children:\"Det er ingen hemmelighed, at vi lever i en digital tidsalder. Fra smartphones til smarte k\\xf8leskabe \u2013 teknologi er overalt. Og det er ikke kun i vores daglige liv, at teknologi spiller en rolle; det er ogs\\xe5 i fremtidens jobmarked. Mange af de jobs, som vil eksistere om 10-20 \\xe5r, er jobs, vi ikke engang kan forestille os endnu \u2013 men \\xe9n ting er sikkert: de vil kr\\xe6ve teknologiske f\\xe6rdigheder.\"}),/*#__PURE__*/e(\"p\",{children:\"Ved at l\\xe6re b\\xf8rnene teknologiske f\\xe6rdigheder tidligt, giver vi dem en fordel, som kan hj\\xe6lpe dem b\\xe5de i skolen og senere i livet. Det handler ikke kun om at l\\xe6re at bruge en computer, men om at forst\\xe5, hvordan teknologi fungerer, hvordan man kan skabe med den, og hvordan man kan bruge den til at l\\xf8se problemer.\"}),/*#__PURE__*/e(\"h3\",{children:\"Skabere af fremtidens innovationer\"}),/*#__PURE__*/e(\"p\",{children:\"B\\xf8rn, der l\\xe6rer at kode eller arbejde med teknologi, bliver ikke bare brugere af teknologi \u2013 de bliver skabere. De f\\xe5r mulighed for at t\\xe6nke kreativt, l\\xf8se problemer og skabe noget nyt og unikt. Det er som at give dem en superkraft! T\\xe6nk bare p\\xe5, hvor fantastisk det m\\xe5 v\\xe6re for et barn at kunne sige: \u201CJeg har lavet min egen app!\u201D\"}),/*#__PURE__*/e(\"p\",{children:\"Og netop det med at skabe noget selv er en uvurderlig oplevelse. Lad os sige, at dit barn har en god id\\xe9 til en webshop \u2013 m\\xe5ske s\\xe6lger de hjemmelavede armb\\xe5nd, eller m\\xe5ske har de en dr\\xf8m om at starte en lille virksomhed. Med de rette teknologiske f\\xe6rdigheder kan de ikke bare bygge en webshop, men ogs\\xe5 omdanne den til en app!\"}),/*#__PURE__*/r(\"p\",{children:[\"Her kommer BravoShop ind i billedet. \",/*#__PURE__*/e(t,{href:\"https://getbravoshop.com/\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"BravoShop\"})}),\" er en fantastisk platform, der kan omdanne din webshop til en app for dig \u2013 helt uden at du beh\\xf8ver at l\\xf8fte en finger! Det betyder, at dit barn kan f\\xe5 sin webshop omdannet til en \",/*#__PURE__*/e(t,{href:\"https://www.getbravoshop.com/features\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!0,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"professionel app\"})}),\", som kan n\\xe5 ud til et bredere publikum, uden at I skal bekymre jer om det tekniske.\"]}),/*#__PURE__*/e(\"p\",{children:\"Men selvom BravoShop klarer den tekniske del, er det stadig vigtigt, at dit barn har en grundl\\xe6ggende forst\\xe5else af teknologi. Denne forst\\xe5else g\\xf8r dem bedre rustet til at tr\\xe6ffe informerede beslutninger og giver dem en st\\xe6rkere position i at videreudvikle og forbedre deres projekter i fremtiden. Teknologisk kunnen giver dem n\\xf8glen til at v\\xe6re kreative og innovative \u2013 ogs\\xe5 n\\xe5r de har v\\xe6rkt\\xf8jer som BravoShop til at g\\xf8re det tunge arbejde.\"}),/*#__PURE__*/e(\"h3\",{children:\"3. Bedre forst\\xe5else af verden\"}),/*#__PURE__*/e(\"p\",{children:\"Teknologi handler ikke kun om at lave apps eller bygge hjemmesider. Det handler ogs\\xe5 om at forst\\xe5 den verden, vi lever i. Teknologi er en del af n\\xe6sten alle aspekter af vores liv \u2013 fra sundhed til transport, fra kommunikation til underholdning. Ved at l\\xe6re, hvordan teknologi fungerer, f\\xe5r b\\xf8rnene en dybere forst\\xe5else af de kr\\xe6fter, der former vores verden.\"}),/*#__PURE__*/e(\"p\",{children:\"Det kan ogs\\xe5 hj\\xe6lpe dem med at blive mere kritiske t\\xe6nkere. I en tid, hvor fake news og misinformation florerer p\\xe5 nettet, er det vigtigt at kunne skelne mellem, hvad der er \\xe6gte, og hvad der ikke er. Teknologiske f\\xe6rdigheder kan hj\\xe6lpe b\\xf8rnene med at navigere i denne komplekse informationsverden og l\\xe6re dem at finde, vurdere og bruge information korrekt.\"}),/*#__PURE__*/e(\"h3\",{children:\"4. \\xd8get selvtillid og uafh\\xe6ngighed\"}),/*#__PURE__*/e(\"p\",{children:\"N\\xe5r b\\xf8rn l\\xe6rer nye f\\xe6rdigheder, vokser deres selvtillid. N\\xe5r de ser, at de kan mestre teknologi \u2013 noget, som m\\xe5ske virker komplekst og skr\\xe6mmende i starten \u2013 opdager de ogs\\xe5, at de kan mestre mange andre ting. Det giver dem en f\\xf8lelse af uafh\\xe6ngighed og styrker deres tro p\\xe5 egne evner.\"}),/*#__PURE__*/e(\"p\",{children:\"Forestil dig, hvor stolt dit barn vil v\\xe6re, n\\xe5r de kan vise deres venner (og dig!) en app, de selv har v\\xe6ret med til at udvikle. Det er en oplevelse, som kan inspirere dem til at forf\\xf8lge st\\xf8rre dr\\xf8mme og tage flere chancer i fremtiden.\"}),/*#__PURE__*/e(\"h3\",{children:\"Konklusion\"}),/*#__PURE__*/e(\"p\",{children:\"At undervise b\\xf8rn i teknologiske f\\xe6rdigheder er en uvurderlig investering i deres fremtid. Gennem programmering og andre teknologi rettede fag f\\xe5r de v\\xe6rkt\\xf8jer til at forst\\xe5, skabe og forme den verden, de vokser op i. Teknologi handler ikke kun om at f\\xf8lge med, men om at lede vejen.\"}),/*#__PURE__*/e(\"p\",{children:\"Med hj\\xe6lp fra en tutor, der kan undervise i programmeringsfagene, f\\xe5r dit barn ikke kun styrket deres tekniske kunnen, men ogs\\xe5 deres evne til at t\\xe6nke kritisk, l\\xf8se problemer og udfolde deres kreativitet. Det giver dem en konkurrencefordel i b\\xe5de skole og arbejdsliv, og \\xe5bner d\\xf8ren til utallige muligheder i en digital fremtid.\"}),/*#__PURE__*/e(\"p\",{children:\"S\\xe5 hvis du vil sikre, at dit barn st\\xe5r st\\xe6rkt i en teknologisk verden, kan det v\\xe6re en god id\\xe9 at overveje ekstra undervisning. P\\xe5 den m\\xe5de kan de blive de innovative skabere, som morgendagens verden har brug for!\"})]});export const richText4=/*#__PURE__*/r(l.Fragment,{children:[/*#__PURE__*/r(\"p\",{children:[\"Velkommen til min ultimative guide om cirkler. Her viser jeg dig alt om \",/*#__PURE__*/e(\"strong\",{children:\"areal af cirkel\"}),\", omkreds, diameter, radius og meget mere. \"]}),/*#__PURE__*/e(\"p\",{children:\"Denne artikel er designet til skoleelever i Danmark, der vil have en dybere forst\\xe5else af cirklers geometri. Jeg lover, at du f\\xe5r al den viden, du har brug for, n\\xe5r du skal arbejde med cirkler i matematik!\"}),/*#__PURE__*/e(\"p\",{children:\"Jeg anbefaler dig at l\\xe6se med hele vejen og gemme guiden til senere. Den er nemlig fyldt med vigtige formler, eksempler og praktiske r\\xe5d, der g\\xf8r det nemt for dig at mestre alt om cirkler. \"}),/*#__PURE__*/r(\"p\",{children:[\"Cirklers geometri er en del af \",/*#__PURE__*/e(t,{href:{pathVariables:{ShClwuvpU:\"matematik-laereplan-i-folkeskolen\"},unresolvedPathSlugs:{ShClwuvpU:{collectionId:\"APEGY5MZP\",collectionItemId:\"yMgERIhX3\"}},webPageId:\"c04VI30oM\"},motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"l\\xe6replanen for elever i udskoling\"})}),\" (7. - 9. klasse). Derfor er det vigtigt at have styr p\\xe5 emnet f\\xf8r man skal op til ens afgangspr\\xf8ve i 9. klasse i \",/*#__PURE__*/e(t,{href:{pathVariables:{Ihpb1g38u:\"matematik\"},unresolvedPathSlugs:{Ihpb1g38u:{collectionId:\"Y2uTJM8up\",collectionItemId:\"sA2GJYud_\"}},webPageId:\"JJ3B6BQzG\"},motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"matematik\"})}),\".\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Indhold\"}),/*#__PURE__*/r(\"p\",{children:[\"1. \",/*#__PURE__*/e(\"strong\",{children:\"Hvad er en cirkel?\"})]}),/*#__PURE__*/r(\"p\",{children:[\"2. \",/*#__PURE__*/e(\"strong\",{children:\"Grundl\\xe6ggende begreber: radius, diameter og pi\"})]}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Areal af cirkel \u2013 formel og eksempler\"})]}),/*#__PURE__*/r(\"p\",{children:[\"4. \",/*#__PURE__*/e(\"strong\",{children:\"Halvcirkel \u2013 hvordan beregner man det?\"})]}),/*#__PURE__*/r(\"p\",{children:[\"5. \",/*#__PURE__*/e(\"strong\",{children:\"Omkreds af cirkel \u2013 forst\\xe5 formlen\"})]}),/*#__PURE__*/r(\"p\",{children:[\"6. \",/*#__PURE__*/e(\"strong\",{children:\"Line\\xe6re elementer i en cirkel (tangent, korde, sekant)\"})]}),/*#__PURE__*/r(\"p\",{children:[\"7. \",/*#__PURE__*/e(\"strong\",{children:\"Vigtige vinkler i en cirkel (central, perifer, etc.)\"})]}),/*#__PURE__*/r(\"p\",{children:[\"8. \",/*#__PURE__*/e(\"strong\",{children:\"Udvidede cirkelbegreber: ellipser og cirkeludsnit\"})]}),/*#__PURE__*/r(\"p\",{children:[\"9. \",/*#__PURE__*/e(\"strong\",{children:\"Historien bag cirklens geometri\"})]}),/*#__PURE__*/r(\"p\",{children:[\"10. \",/*#__PURE__*/e(\"strong\",{children:\"Praktiske eksempler og \\xf8velser\"})]}),/*#__PURE__*/r(\"p\",{children:[\"11. \",/*#__PURE__*/e(\"strong\",{children:\"Ofte stillede sp\\xf8rgsm\\xe5l (FAQ)\"})]}),/*#__PURE__*/r(\"p\",{children:[\"12. \",/*#__PURE__*/e(\"strong\",{children:\"Konklusion\"})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Hvad er en cirkel?\"}),/*#__PURE__*/e(\"p\",{children:\"En cirkel er en perfekt, kontinuerlig kurve, hvor alle punkter p\\xe5 kurven ligger i samme afstand fra \\xe9t f\\xe6lles midtpunkt (centrum). Den simple definition rummer dog et stort potentiale. \"}),/*#__PURE__*/e(\"p\",{children:\"Cirkler indg\\xe5r i alt fra cykelhjul til planeters baner. For dig som skoleelev er forst\\xe5elsen af cirkler en vigtig grundsten, fordi det knytter sig til geometri, trigonometri og mange former for beregninger.\"}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Kort sagt:\"}),\" En cirkel er m\\xe6ngden af punkter, der har samme afstand til et centrum.\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"De tre vigtigste formler\"}),/*#__PURE__*/r(\"p\",{children:[\"1. \",/*#__PURE__*/e(\"strong\",{children:\"Areal af cirkel:\"}),\" A = \\\\pi r^2\"]}),/*#__PURE__*/r(\"p\",{children:[\"2. \",/*#__PURE__*/e(\"strong\",{children:\"Omkreds af cirkel:\"}),\" O = 2\\\\pi r\"]}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Diameter:\"}),\" d = 2r\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Typiske fejl at undg\\xe5\"}),/*#__PURE__*/r(\"p\",{children:[\"1. \",/*#__PURE__*/e(\"strong\",{children:\"Forkert radius:\"}),\" Du glemmer at halvere diameteren.\"]}),/*#__PURE__*/r(\"p\",{children:[\"2. \",/*#__PURE__*/e(\"strong\",{children:\"Forveksling af \"}),\"\\\\pi\",/*#__PURE__*/e(\"strong\",{children:\" og 3,14:\"}),\" Husk at 3,14 bare er en tiln\\xe6rmelse.\"]}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Manglende enheder:\"}),\" Skriv altid om arealet er i\\xa0 \\\\text{cm}^2 , \\\\text{m}^2 osv.\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Hurtige huskeregler\"}),/*#__PURE__*/r(\"p\",{children:[\"\u2022 \",/*#__PURE__*/e(\"strong\",{children:\"Radius\"}),\" = halvdelen af diameter\"]}),/*#__PURE__*/r(\"p\",{children:[\"\u2022 \",/*#__PURE__*/e(\"strong\",{children:\"Omkreds\"}),\" = l\\xe6ngden rundt om cirklen\"]}),/*#__PURE__*/r(\"p\",{children:[\"\u2022 \",/*#__PURE__*/e(\"strong\",{children:\"Areal\"}),\" = alt det \u201Cindre\u201D i cirklen\"]}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"N\\xf8dvendigt grej til cirkelopgaver\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Passer\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Lineal\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Lommeregner med \\\\pi-funktion\"}),/*#__PURE__*/e(\"h3\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Mine personlige tips\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Tegn altid en figur, hvis du kan.\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Marker radius og diameter tydeligt.\"}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Tjek altid enheder og om du regner i cm, m eller mm.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Hvorn\\xe5r bruger du cirkler i hverdagen?\"}),/*#__PURE__*/r(\"p\",{children:[\"1. \",/*#__PURE__*/e(\"strong\",{children:\"M\\xe5ling af rum:\"}),\" Fx runde borde, runde haver.\"]}),/*#__PURE__*/r(\"p\",{children:[\"2. \",/*#__PURE__*/e(\"strong\",{children:\"Byggeri og arkitektur:\"}),\" Udregning af kupler, runde vinduer, trapper.\"]}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Teknologi:\"}),\" Hjul, lejer, gear, alt med rotation.\"]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Grundl\\xe6ggende begreber: radius, diameter og pi\"}),/*#__PURE__*/e(\"p\",{children:\"For at forst\\xe5 en cirkel, er det n\\xf8dvendigt at kende nogle n\\xf8glebegreber.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Hvad er radius?\"}),/*#__PURE__*/e(\"p\",{children:\"Radius er afstanden fra centrum af cirklen til et punkt p\\xe5 cirklens kant (omkredsen). Du bruger radius i n\\xe6sten alle beregninger, der handler om en cirkel.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Hvad er diameter?\"}),/*#__PURE__*/e(\"p\",{children:\"Diameteren er den l\\xe6ngste linje, du kan tegne inden i cirklen. Den g\\xe5r igennem centrum og forbinder to punkter p\\xe5 omkredsen. Den er altid dobbelt s\\xe5 lang som radius.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"em\",{children:\"Formel for diameter:\"})}),/*#__PURE__*/e(\"p\",{children:\"d = 2r\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h3\",{children:\"Hvad er pi?\"}),/*#__PURE__*/e(\"p\",{children:\"Pi er en speciel matematisk konstant, som du bruger til at beregne b\\xe5de areal og omkreds af en cirkel. Pi har uendelig mange decimaler og er irrationel, men i regnestykket kan du ofte bruge 3,14 eller 3,14159 som tiln\\xe6rmelse.\"}),/*#__PURE__*/e(\"p\",{children:\"Fun fact: D. 14. marts (3/14) fejres Pi-dagen over hele verden.\"}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"strong\",{children:\"Ekstern kilde om pi: \"}),/*#__PURE__*/e(t,{href:\"https://en.wikipedia.org/wiki/Pi\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:/*#__PURE__*/e(\"strong\",{children:\"Wikipedia om Pi\"})})})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Areal af cirkel \u2013 formel og eksempler\"}),/*#__PURE__*/e(\"p\",{children:\"En cirkel d\\xe6kker et bestemt areal. Det er altid fascinerende at se, hvor meget plads en cirkel egentlig optager.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Formel for areal af cirkel:\"}),/*#__PURE__*/e(\"p\",{children:\"A = pi * r^2\"}),/*#__PURE__*/e(\"p\",{children:\"Her er r radius. Det er let at huske, hvis du forestiller dig, at du skal gange pi med kvadratet p\\xe5 radius.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Hvorfor virker formlen?\"}),/*#__PURE__*/e(\"p\",{children:\"Forestil dig, at cirklen kan deles op i sm\\xe5 stykker (n\\xe6sten ligesom trekanter), som samlet kan omformes til et rektangel. Bredden af dette \u201Crektangel\u201D svarer nogenlunde til omkredsen halveret, og h\\xf8jden svarer til radius. Matematisk lander det p\\xe5 pi * r^2.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempler:\"})}),/*#__PURE__*/r(\"p\",{children:[\"1. \",/*#__PURE__*/e(\"strong\",{children:\"Radius = 5 cm\"})]}),/*#__PURE__*/e(\"p\",{children:\"A = pi * 5^2 = pi * 25 = 78,5 cm^2\"}),/*#__PURE__*/r(\"p\",{children:[\"2. \",/*#__PURE__*/e(\"strong\",{children:\"Radius = 10 cm\"})]}),/*#__PURE__*/e(\"p\",{children:\"A = pi * 10^2 = pi * 100 = 314 cm^2\"}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Radius = 1 m\"})]}),/*#__PURE__*/e(\"p\",{children:\"A = pi * 1^2 = pi = 3,14 m^2\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Halvcirkel \u2013 hvordan beregner man det?\"}),/*#__PURE__*/e(\"p\",{children:\"En halvcirkel er pr\\xe6cis halvdelen af en hel cirkel. Forestil dig, du har en rund pizza, og du kun vil have halvdelen. Ligesom med en pizza sk\\xe6rer du blot en hel cirkel i to lige store dele.\"}),/*#__PURE__*/e(\"h3\",{children:\"Formel for areal af en halvcirkel:\"}),/*#__PURE__*/e(\"p\",{children:\"A_{\\\\text{halvcirkel}} = \\\\frac{1}{2} \\\\times \\\\pi r^2\"}),/*#__PURE__*/e(\"p\",{children:\"Det kan bruges til fx arealet af en halvm\\xe5neformet have eller et halvcirkelformet vindue. Let og lige til.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Omkreds af cirkel \u2013 forst\\xe5 formlen\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"Formel for omkreds:\"})}),/*#__PURE__*/e(\"p\",{children:\"O = 2 \\\\pi r\"}),/*#__PURE__*/e(\"p\",{children:\"Du kan ogs\\xe5 skrive det som \\\\pi \\\\times d, fordi diameteren d = 2r.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"Eksempler:\"})}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Hvis r = 5 \\\\, \\\\text{cm}, s\\xe5 er omkredsen:\"}),/*#__PURE__*/e(\"p\",{children:\"O = 2 \\\\times \\\\pi \\\\times 5 \\\\approx 31,4 \\\\, \\\\text{cm}\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"p\",{children:\"\u2022 Hvis r = 10 \\\\, \\\\text{cm}, s\\xe5 er omkredsen:\"}),/*#__PURE__*/e(\"p\",{children:\"O = 2 \\\\times \\\\pi \\\\times 10 \\\\approx 62,8 \\\\, \\\\text{cm}\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"p\",{children:\"Omkredsen fort\\xe6ller dig, hvor meget \u201Chegn\u201D du skal bruge for at omringe et cirkelformet areal.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Line\\xe6re elementer i en cirkel (tangent, korde, sekant)\"}),/*#__PURE__*/e(\"p\",{children:\"Udover radius og diameter findes der andre vigtige linjer, der kan tr\\xe6kkes i en cirkel:\"}),/*#__PURE__*/e(\"h4\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Korde\"}),/*#__PURE__*/e(\"p\",{children:\"En korde er en linje, der forbinder to punkter p\\xe5 cirklens kant. Den beh\\xf8ver ikke at g\\xe5 gennem centrum.\"}),/*#__PURE__*/e(\"h4\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Sekant\"}),/*#__PURE__*/e(\"p\",{children:\"En sekant er en linje, der sk\\xe6rer cirklen i to punkter, men den forts\\xe6tter uden for cirklen p\\xe5 begge sider. Du kan se en sekant som en forl\\xe6nget korde.\"}),/*#__PURE__*/e(\"h4\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Tangent\"}),/*#__PURE__*/e(\"p\",{children:\"En tangent er en linje, der r\\xf8rer cirklen i pr\\xe6cis \\xe9t punkt. Tangenter er vigtige i b\\xe5de design og matematik. De hj\\xe6lper, n\\xe5r du vil vide, hvor man r\\xf8rer ved en kurve uden at sk\\xe6re ind i den.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Vigtige vinkler i en cirkel (central, perifer, etc.)\"}),/*#__PURE__*/e(\"p\",{children:\"N\\xe5r du tegner vinkler i en cirkel, kan de opst\\xe5 p\\xe5 flere m\\xe5der:\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Central vinkel\"}),/*#__PURE__*/e(\"p\",{children:\"En central vinkel har sit toppunkt i cirklens centrum. Den afsk\\xe6rer en bestemt bue p\\xe5 cirklen, og vinklen er direkte lig med buens gradm\\xe5l.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Perifer (inscribed) vinkel\"}),/*#__PURE__*/e(\"p\",{children:\"En perifer vinkel sidder ude p\\xe5 cirklens omkreds og \u201Ckigger\u201D ind mod centrum. Den vinkel er altid halvt s\\xe5 stor som den centrale vinkel, der afsk\\xe6rer samme bue.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Andre cirkelvinkler\"}),/*#__PURE__*/e(\"p\",{children:\"Der er ogs\\xe5 vinkler dannet af tangenter og sekante-linjer, men de grundl\\xe6ggende er de centrale og perifere.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"em\",{children:\"L\\xe6s ogs\\xe5 \"}),/*#__PURE__*/e(t,{href:{pathVariables:{ShClwuvpU:\"pythagoras-laeresaetning\"},unresolvedPathSlugs:{ShClwuvpU:{collectionId:\"APEGY5MZP\",collectionItemId:\"EUCw7Dd6B\"}},webPageId:\"c04VI30oM\"},motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:/*#__PURE__*/e(\"em\",{children:\"Pythagoras let forklaret \"})})}),/*#__PURE__*/e(\"em\",{children:\"\u2013 relevant n\\xe5r du vil kombinere cirkelgeometri med retvinklede trekanter.\"})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Udvidede cirkelbegreber: ellipser og cirkeludsnit\"}),/*#__PURE__*/e(\"p\",{children:\"En ellipse er ligesom en cirkel, men \u201Ctrykket\u201D eller \u201Cstrukket,\u201D s\\xe5 den ikke er perfekt rund. Planeter bev\\xe6ger sig i elliptiske baner rundt om solen.\"}),/*#__PURE__*/e(\"p\",{children:\"Et cirkeludsnit (sektor) er et \u201Ckagestykke\u201D af en cirkel. Du f\\xe5r et cirkeludsnit, hvis du tegner to radier ud til cirklens kant. Arealet af en sektor med vinkel \\\\theta (i grader) beregnes s\\xe5dan:\"}),/*#__PURE__*/e(\"p\",{children:\"\\\\text{Areal af sektor} = \\\\frac{\\\\theta}{360^\\\\circ} \\\\times \\\\pi r^2\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"em\",{children:\"L\\xe6s ogs\\xe5: \"}),/*#__PURE__*/e(t,{href:\"about:blank#\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:/*#__PURE__*/e(\"em\",{children:\"Forberedelsesopgaver til Matematik F\\xe6rdighedsregning \"})})}),/*#__PURE__*/e(\"em\",{children:\"\u2013 \\xf8v matematikopgaver.\"})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Historien bag cirklens geometri\"}),/*#__PURE__*/e(\"p\",{children:\"Cirkler har fascineret folk i tusindvis af \\xe5r. De gamle egyptere og babyloniere brugte cirkelformler til at bygge templer og m\\xe5le jordstykker. Senere har matematikere som Euclid (fra Gr\\xe6kenland) formuleret mange af de teoremer, du l\\xe6rer i dag.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/r(\"p\",{children:[\"L\\xe6s mere om geometrisk historie: \",/*#__PURE__*/e(t,{href:\"https://www.khanacademy.org/\",motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"Khan Academy \u2013 World of math\"})})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Praktiske eksempler og \\xf8velser\"}),/*#__PURE__*/e(\"p\",{children:\"Jeg tror p\\xe5, at man l\\xe6rer bedst ved at pr\\xf8ve selv. Her er nogle praktiske eksempler:\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Beregning af omkreds:\"}),/*#__PURE__*/e(\"p\",{children:\"Du har en rund l\\xf8bebane med radius 20 m. Hvor meget l\\xf8ber du i \\xe9n runde?\"}),/*#__PURE__*/e(\"p\",{children:\"O = 2 \\\\pi \\\\times 20 \\\\approx 125,6 \\\\, \\\\text{m}\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Areal af en cirkel\"}),/*#__PURE__*/e(\"p\",{children:\"En rund trampolin har diameter p\\xe5 4 m. Hvad er arealet?\"}),/*#__PURE__*/e(\"p\",{children:\"r = \\\\frac{4}{2} = 2 \\\\, \\\\text{m} \\\\quad \\\\Rightarrow \\\\quad A = \\\\pi \\\\times 2^2 = 4\\\\pi \\\\approx 12,57 \\\\, \\\\text{m}^2\"}),/*#__PURE__*/e(\"p\",{children:\"S\\xe5 trampolinen d\\xe6kker ca. 12,57 kvadratmeter.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h4\",{children:\"Halvcirkel i en indk\\xf8rsel\"}),/*#__PURE__*/e(\"p\",{children:\"Forestil dig en halvcirkelformet indk\\xf8rsel med radius 3 m. Arealet bliver\"}),/*#__PURE__*/e(\"p\",{children:\"\\\\frac{1}{2} \\\\times \\\\pi \\\\times 3^2 = \\\\frac{1}{2} \\\\times \\\\pi \\\\times 9 \\\\approx 14,13 \\\\, \\\\text{m}^2.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/r(\"p\",{children:[/*#__PURE__*/e(\"em\",{children:\"Se ogs\\xe5: \"}),/*#__PURE__*/e(t,{href:{pathVariables:{Ihpb1g38u:\"matematik\"},unresolvedPathSlugs:{Ihpb1g38u:{collectionId:\"Y2uTJM8up\",collectionItemId:\"sA2GJYud_\"}},webPageId:\"JJ3B6BQzG\"},motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:/*#__PURE__*/e(\"em\",{children:\"F\\xe5 en mentor i matematik \"})})}),/*#__PURE__*/e(\"em\",{children:\"- f\\xe5 hj\\xe6lp til dine opgaver og lektier.\"})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/r(\"p\",{children:[\"3. \",/*#__PURE__*/e(\"strong\",{children:\"Halvcirkel i en indk\\xf8rsel:\"})]}),/*#__PURE__*/e(\"p\",{children:\"Forestil dig en halvcirkelformet indk\\xf8rsel med radius 3 m. 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Vi vil gennemg\\xe5, hvad de st\\xe5r for og hj\\xe6lpe dig med hvilken du skal v\\xe6lge.\"}),/*#__PURE__*/e(\"p\",{children:\"Vi vil gennemg\\xe5:\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"\u2003\uD83C\uDF93STX (Almen Studentereksamen)\"})}),/*#__PURE__*/r(\"p\",{children:[\"\u2003\",/*#__PURE__*/e(\"strong\",{children:\"\uD83C\uDF93 HHX (Merkantil studentereksamen)\"})]}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"\u2003\uD83C\uDF93 HTX (Teknisk Studentereksamen)\"})}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"\u2003\uD83C\uDF93 HF (HF Eksamen)\"})}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"\u2003\uD83C\uDF93 EUX (Erhvervsfaglig Studentereksamen)\"})}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"strong\",{children:\"\u2003\uD83C\uDF93 Overblik over Forskellene Mellem HHX, STX, HTX & HF\"})}),/*#__PURE__*/r(\"p\",{children:[\"\u2003\uD83C\uDF93\",/*#__PURE__*/e(\"strong\",{children:\" Gode R\\xe5d til Valg af Gymnasium\"})]}),/*#__PURE__*/r(\"p\",{children:[\"I Danmark er der 5 muligheder, hvis man v\\xe6lger den gymnasiale vej efter \",/*#__PURE__*/e(t,{href:{webPageId:\"RscCHtWFc\"},motionChild:!0,nodeId:\"APEGY5MZP\",openInNewTab:!1,scopeId:\"contentManagement\",smoothScroll:!1,children:/*#__PURE__*/e(i.a,{children:\"folkeskolen\"})}),\", der er HHX-, HTX-, \\xa0STX-, HF- og EUX-uddannelsen at v\\xe6lge i mellem.\"]}),/*#__PURE__*/e(\"p\",{children:\"Lad os starte med STX, det mest popul\\xe6re valg af gymnasial uddannelse.\"}),/*#__PURE__*/e(\"h1\",{children:\"STX (Almen Studentereksamen)\"}),/*#__PURE__*/e(\"p\",{children:\"STX er derfor et godt valg for dem, der \\xf8nsker en bred uddannelsesm\\xe6ssig baggrund med mange videreg\\xe5ende muligheder.\"}),/*#__PURE__*/e(\"h6\",{children:\"Hvad betyder STX?\"}),/*#__PURE__*/e(\"p\",{children:'STX st\\xe5r for \"Almen Studentereksamen\". 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Nederst p\\xe5 siden er der gratis \\xf8velsesopgaver, s\\xe5 du kan teste dig selv i pythagoras l\\xe6res\\xe6tning.\"}),/*#__PURE__*/r(\"p\",{children:[\"Pythagoras l\\xe6res\\xe6tning siger, at hvis man har en retvinklet trekant (p\\xe5 90 grader), s\\xe5 er hypotenusen i anden lig med summen af \",/*#__PURE__*/e(\"em\",{children:\"a\"}),\" i anden plus \",/*#__PURE__*/e(\"em\",{children:\"b \"}),\"i anden. Pythagoras l\\xe6res\\xe6tning viser alts\\xe5 forholdet mellem de tre sider p\\xe5 en retvinklet trekant.\"]}),/*#__PURE__*/e(\"p\",{children:\"Formlen er:\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"em\",{children:/*#__PURE__*/e(\"strong\",{children:\"\\\\(a^2 + b^2 = c^2\\\\)\"})})}),/*#__PURE__*/e(\"p\",{children:\"Pythagoras l\\xe6res\\xe6tning er en af de mest ber\\xf8mte geometriske s\\xe6tninger og er opkaldt efter den gr\\xe6ske matematiker og filosof Pythagoras, som levede i det 6. \\xe5rhundrede f.Kr.\"}),/*#__PURE__*/e(\"p\",{children:/*#__PURE__*/e(\"br\",{className:\"trailing-break\"})}),/*#__PURE__*/e(\"h2\",{children:\"Hvad er en retvinklet trekant?\"}),/*#__PURE__*/e(\"p\",{children:\"En retvinklet trekant er en trekant, hvor en af vinklerne er 90 grader. Forholdet mellem siderne p\\xe5 trekanten er nemme at forholde sig til, n\\xe5r man bruger Pythagoras l\\xe6res\\xe6tning. Siden, som er modsat den rette vinkel er altid den l\\xe6ngste side og er den man kalder for hypotenusen. Forholdet mellem siderne og andre vinkler i trekanten er basis for emnet trigonometri.\"}),/*#__PURE__*/e(\"h2\",{children:\"Hvad er hypotenusen?\"}),/*#__PURE__*/r(\"p\",{children:[\"Hypotenusen er som sagt den retvinklede trekants l\\xe6ngste side. Siden ligger modsat den rette vinkel. Hypotenusen kan udregnes ved hj\\xe6lp af pythagoras l\\xe6res\\xe6tning og refereres til som \",/*#__PURE__*/e(\"em\",{children:\"c\"}),\". Pythagoras l\\xe6res\\xe6tning angiver som bekendt, at summen af hypotenusen i anden, er lig med summen af trekantens to andre kanter (kateterne) i anden. For eksempel, hvis en af trekantens andre sider er lig med 4 (42=1642=16) og den anden side 3 (32=932=9), s\\xe5 vil hypotenusen l\\xe6ngde v\\xe6re kvadratroden af 25 (25+16=4125+16=41), hvilket er 5.\"]}),/*#__PURE__*/e(\"h2\",{children:\"Hvad er en katete?\"}),/*#__PURE__*/r(\"p\",{children:[\"Trekantens sider som ikke er hypotenusen kaldes for en katete. Retvinklede trekanter vil altid have to kateter og de vil altid v\\xe6re vinkelret p\\xe5 hinanden. Det er alts\\xe5 trekantens to sider, som st\\xf8der til den rette vinkel. \\xa0Trekantens kateter refereres til som \",/*#__PURE__*/e(\"em\",{children:\"a \"}),\"og\",/*#__PURE__*/e(\"em\",{children:\" b\"}),\" i l\\xe6res\\xe6tningen.\"]}),/*#__PURE__*/e(\"h2\",{children:\"Beregn den ubekendte sidel\\xe6ngde p\\xe5 en retvinklet trekant\"}),/*#__PURE__*/e(\"p\",{children:\"I denne video forklarer Yasmin El Youssef hvordan man beregner den ubekendte sidel\\xe6ngde p\\xe5 en retvinklet trekant.\"}),/*#__PURE__*/e(\"p\",{children:\"Pythagoras L\\xe6res\\xe6tning: Beregn den ubekendte sidel\\xe6ngde\"}),/*#__PURE__*/e(\"h4\",{children:\"Eksempel opgave: \\xa0En retvinklet trekant har to kateter p\\xe5 henholdsvis a = 4 cm og b = 3 cm. 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