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III. Potensrækker – 2. Talfølger og rækker 264 → 3 for t → 0 1.28. Sammenligning af uegentlige integraler ☞ [S] 5.10 Improper integrals Sætning (Sammenligning) Antag at kontinuerte funktioner f,g opfylder uligheden f(x) ≥ g(x) ≥ 0 for x ≥ a. (a) ∞ (b) ∞ a f(x)dx konvergent ⇒ ∞ a a g(x)dx divergent ⇒ ∞ a 2. Talfølger og rækker g(x)dx konvergent. f(x)dx divergent. 2.1. Oversigt ☞ [S] 8.1, 8.2 Nøgleord og begreber ✌ Grænseværdi af talfølge ✌ Test grænseværdi ✌ Monotone og begrænsede talfølger ✌ Talrække og afsnitssum ✌ Konvergente rækker har små led
III. Potensrækker – 2. Talfølger og rækker 265 ✌ Regneregler 2.2. Grænse for talfølge ☞ [S] 8.1 Sequences 1 Definition En talfølge {an} har grænseværdi L lim n→∞ an = L Hvis an kommer vilkårligt tæt på L, når n er tilstrækkeligt stor. Skrives også an → L når n → ∞ Følgen kaldes da konvergent og i modsat fald divergent. 2.3. Grænse tydeligere ☞ [S] 8.1 Sequences Definition præcis En talfølge {an} har grænseværdi L lim n→∞ an = L Hvis der for ethvert ǫ > 0 findes et tal N så |an − L| < ǫ for n > N 2.4. Simpel følge ☞ [S] 8.1 Sequences Eksempel
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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