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IX. Opgaver – 2. Januar 2003 558 y 1 0 1 2 (2,1) T = {(x,y)|0 ≤ x ≤ 2, 1 2x ≤ y ≤ 1} = {(x,y)|0 ≤ y ≤ 1,0 ≤ x ≤ 2y} 2.17. Beregn et dobbeltintegral ☞ Matematik Alfa 1, Januar 2003 Opgave 3 - løsning Dobbeltintegralet er Type I: T = {(x,y)|0 ≤ x ≤ 2, 1 2x ≤ y ≤ 1} = {(x,y)|0 ≤ y ≤ 1,0 ≤ x ≤ 2y} T f(x,y)dA = 2 1 0 1 2 x f(x,y)dy dx x
IX. Opgaver – 2. Januar 2003 559 Dobbeltintegralet er Type II: T f(x,y)dA = 1 2y 0 0 f(x,y)dx dy 2.18. Beregn et dobbeltintegral Opgave 3 - løsning ☞ Matematik Alfa 1, Januar 2003 x sin(y 3 1 2y )dA = x sin(y 3 )dx dy T = = = 0 0 1 1 0 2 x2 sin(y 3 ) x=0 1 2y 0 2 sin(y 3 )dy 1 − 2 3 cos(y3 ) = 2 (1 − cos(1)) 3 ≈ 0.31 0 x=2y dy
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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 - 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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etningsafledede, 89, 102 retningsfe
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