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IX. Opgaver – 1. August 2002 536 Angiv også grænseværdien lim x→0 f(x). 1.22. Angiv potensrække ☞ Matematik Alfa 1, August 2002 Opgave 4 - løsning Benyt potensrækken ∞ n 1 cos x = (−1) til at få n=0 cos x 2 − 1 = (2n)! x2n ∞ n 1 (−1) n=1 (2n)! x4n 1.23. Angiv potensrække ☞ Matematik Alfa 1, August 2002 Opgave 4 - løsning Dermed er ∞ n 1 f(x) = (−1) n=1 (2n)! x4(n−1) = − 1 1 + 2! 4! x4 − 1 6! x8 + 1 8! x12 − ...
IX. Opgaver – 1. August 2002 537 Det følger, at lim f(x) = −1 x→0 2 1.24. Angiv potensrække ☞ Matematik Alfa 1, August 2002 Opgave 4 - figur Grafen for y 0 1 1 y = cos(x2 ) − 1 x 4 1.25. Find gradient ☞ Matematik Alfa 1, August 2002 Opgave 5 Betragt funktionen f(x,y) = y 2 + ln(x 3 + y + 1). 1. Angiv gradientvektoren ∇f(0,2). x
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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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IX. Opgaver - 4. August 2004 586 vi
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IX. Opgaver - 5. Januar 2005 592 De
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IX. Opgaver - 5. Januar 2005 594 (t
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IX. Opgaver - 5. Januar 2005 598 De
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IX. Opgaver - 5. Januar 2005 600 Gr
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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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etningsafledede, 89, 102 retningsfe
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