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III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 260 og divergent for p ≤ 1. 1.21. Test uegentlig integral ☞ [S] 5.10 Improper integrals Test ∞ 2 Integralet 3√ dx er konvergent. x Løsning 1 t 2x −1/3 dx = (Alternativt p = 1/3 < 1 i Eksempel 4) 1 3x 2/3 t → ∞ for t → ∞ 1 = 3t 2/3 − 3 Afkryds: ja nej 1.22. Uendelige funktioner 3 Definition ☞ [S] 5.10 Improper integrals Det uegentlige integral er konvergent, hvis grænseværdien findes; i modsat fald divergent. b (a) f(x)dx = lim t→b− t f(x)dx a a
III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 261 (b) (c) b a f(x)dx = lim t→a + b f(x)dx b c b f(x)dx = f(x)dx + f(x)dx a a 1.23. Uendelige funktioner ☞ [S] 5.10 Improper integrals Eksempel (1) Det uegentlige integral er divergent. 1 0 1 dx = lim x t→0 + 1 1 dx = lim t x t→0 + [lnx] 1 t = lim t→0 + −ln t = ∞ 1.24. Uendelige funktioner ☞ [S] 5.10 Improper integrals Eksempel (1) Det uegentlige integral 1 0 1 √ x dx = lim t→0 + 1 t t c x −1/2 dx = lim t→0 + 2x 1/2 1 t
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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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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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0-række/søjle, 423 n-te afsnitssu
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