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III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 262 er konvergent. = lim t→0 + 2√ t − 2 = 2 1.25. Uendelige funktioner ☞ [S] 5.10 Improper integrals y 1√ t t y = 1 √ x Uendelige værdier, endeligt areal 1 x
III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 263 1.26. Uendelige funktioner ☞ [S] 5.10 Improper integrals Eksempel (4) Det uegentlige integral p = 1 1 0 1 dx = lim xp t→0 + er konvergent for p < 1 med værdi og divergent for p ≥ 1. = lim t→0 + 1 t 1 1 − p 1 0 1 dx = lim xp t→0 + 1 1 − p · 1 − 1 tp−1 1 1 dx = xp p − 1 1 xp−1 1 t 1.27. Test uegentlig integral ☞ [S] 5.10 Improper integrals Test 1 2 Integralet 3√ dx er konvergent. x Løsning 0 1 t 2x −1/3 dx = 3x 2/3 1 = 3 − 3t 2/3 t Afkryds: ja nej
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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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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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IV. Differentialligninger - 1. Graf
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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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VIII. Appendiks - 1. Polære koordi
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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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