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| (27 mellanliggande sidversioner av samma användare visas inte) |
| Rad 1: |
Rad 1: |
| == Intro - Primitiva funktionen ==
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| Gissa och öva.
| | == [[Derivatan av y = e^x]] == |
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| Fundera över det inversa sambandet
| | == [[Naturliga logaritmer]] == |
| | |
| | == [[Derivatan av 2^x]] == |
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| Öva på [http://olleh.se/start/frageprogramMa3.php OlleH]
| | == [[Problemlösning exponentialfunktioner]] == |
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| {{flipped|'''Till nästa gång:''' se filmen om Riemannsumma}}
| | == [[Primitiva funktioner]] == |
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| == Intro - Riemannsumma == | | == [[Beräkna integraler]] == |
| | |
| | == [[Arean av ett område mellan två kurvor]] == |
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| {{#ev:youtube|lPOUB0fLuUk|340|right|Integral - Riemannsumma}}
| | == [[Mer om integraler]] == |
| | |
| | == [[Tillämpningar av integraler]] == |
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| Kan man tänka sig någon trevlig frågeställning som ingång till integralerna?
| | == Newtons Integralbevis == |
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| Börja med att visa Riemannsumman för att ta reda på arean under en graf.
| | <html> |
| {{clear}}
| | <script type='text/javascript' src='http://demonstrations.wolfram.com/javascript/embed.js' ></script><script type='text/javascript'>var demoObj = new DEMOEMBED(); demoObj.run('NewtonsIntegrabilityProof', '', '549', '620');</script><div id='DEMO_NewtonsIntegrabilityProof'><a class='demonstrationHyperlink' href='http://demonstrations.wolfram.com/NewtonsIntegrabilityProof/' target='_blank'>Newton's Integrability Proof</a> from the <a class='demonstrationHyperlink' href='http://demonstrations.wolfram.com/' target='_blank'>Wolfram Demonstrations Project</a> by Michael Rogers</div> |
| | | </html> |
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" /> | |
| | |
| === Övning Riemannsumma i GGb===
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| {{uppgruta|laborera själv i Geogebra
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| Denna GGB ger dig möjlighet att flytta stapeln och att testa olika funktioner.
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| Du kan ändra på antalet staplar och se hur det påverkar beräkningen.
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| [http://www.geogebratube.org/student/m14091 Här är GGB:n:]
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| Vad lärde du dig av denna övning?}}
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| === uppg 2 ===
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| Testa denna: http://www.geogebratube.org/student/m11330
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| Hur hanteras negativa areor?
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| === Uppg 3 === | |
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| Man kan skapa Riemannsummor mellan två funktioner:
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| * http://www.geogebratube.org/student/m26214
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| * http://www.geogebratube.org/student/m26213
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| == Mer om integraler ==
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| {{#ev:youtube|OAN8qa-pnIo|340|left}} {{#ev:youtube|i8JPiQ3Ujyc|340|right}}
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| {{clear}}
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| [http://www.proofwiki.org/wiki/Fundamental_Theorem_of_Calculus ProofWiki]
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| == Mekaniken ==
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| Jämför med mekaniken, sträckan är arean under en vt-graf.
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| == problemlösning med integraler ==
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| {Ma3C|229-232{}
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