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IX. Opgaver – 2. Januar 2003 566 2.29. Løs differentialligning ☞ Matematik Alfa 1, Januar 2003 Opgave 5 - figur y 1 0 1 x Løsningskurve y(x) = 6 + 2 x 2.30. Angiv potensrække ☞ Matematik Alfa 1, Januar 2003 Opgave 6 1) Angiv en potensrækkefremstilling for x − sin x. 2) Angiv grænseværdien x − sin x lim x→0 x3 cos x .
IX. Opgaver – 2. Januar 2003 567 Løsning 1) Benyt potensrækken sin x = ∞ (−1) n 1 (2n + 1)! x2n+1 n=0 2.31. Angiv potensrække ☞ Matematik Alfa 1, Januar 2003 Opgave 6 - løsning sin x = 1 1 x − 1! 3! x3 + 1 5! x5 − ... til at få ∞ x − sin x = (−1) n+1 1 (2n + 1)! x2n+1 skrevet ud n=1 x − sinx = 1 3! x3 − 1 5! x5 + ... 2.32. Angiv potensrække ☞ Matematik Alfa 1, Januar 2003 Opgave 6 - løsning 2) Dermed er f(x) = x − sinx x 3 = ∞ (−1) n+1 1 (2n + 1)! x2n−2 n=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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I. Differentiation - 2. Partielle a
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I. Differentiation - 3. Tangentplan
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 5. Gradient 88
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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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II. Integration - 2. Itereret integ
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II. Integration - 3. Generelle omr
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II. Integration - 4. Koordinatskift
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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III. Potensrækker - 3. Potensrækk
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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IV. Differentialligninger - 2. 1. o
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IV. Differentialligninger - 3. Gene
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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 - 2. Lineære afbildnin
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V. Matricer - 3. Lineære ligninger
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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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VII. Skalarprodukt og projektion -
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VIII. Appendiks - 1. Polære koordi
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