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III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 258 er divergent. Det uegentlige integral er konvergent. ∞ 1 t 1 dx = lim x2 t→∞ 1 1 dx = 1 x2 1.18. Uendelige intervaller ☞ [S] 5.10 Improper integrals y 1 t Uendeligt interval, uendeligt areal y = 1 x 1.19. Arctan integral ☞ [S] 5.10 Improper integrals x
III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 259 Eksempel 3 ∞ Løsning −∞ t 0 −∞ 1 dx = π 1 + x2 1 dx = [Arctanx]t 1 + x2 0 = Arctan t Grænseovergange limt→±∞ Arctan t = ± π 2 giver ∞ 0 ∞ 1 1 1 dx = dx + dx = π 1 + x2 1 + x2 1 + x2 −∞ 1.20. Reciprok potens ☞ [S] 5.10 Improper integrals Eksempel 4 Det uegentlige integral p = 1 ∞ 1 1 dx = lim xp t→∞ er konvergent for p > 1 med værdi = lim t→∞ t 1 1 1 − p ∞ 1 1 dx = lim xp t→∞ 1 0 1 1 − p · − 1 tp−1 1 1 dx = xp p − 1 1 xp−1 t 1
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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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I. Differentiation - 1. Kontinuitet
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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