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IX. Opgaver – 1. August 2002 526 Opgave 1 - løsning er et polært rektangel. Integralet er R R = {(r,θ)|0 ≤ r ≤ 2,0 ≤ θ ≤ π 2 } x 2 π/2 y dA = 0 2 r 0 3 cos 2 (θ)sin(θ)rdr dθ 1.6. Beregn et dobbeltintegral Opgave 1 - løsning ☞ Matematik Alfa 1, August 2002 x 2 π/2 2 y dA = r 3 cos 2 (θ)sin(θ)rdr dθ R 0 π/2 = 0 0 1 5 r5 cos 2 r=2 θ sin θ r=0 π/2 32 = 0 5 cos2 θ sinθ dθ = − 32 15 cos3 π/2 θ = 32 15 0 dθ
IX. Opgaver – 1. August 2002 527 1.7. Beregn et dobbeltintegral ☞ Matematik Alfa 1, August 2002 Opgave 1 - ny figur z x R = {(x,y)|0 ≤ x ≤ 2,0 ≤ y ≤ 4 − x 2 } 1.8. Beregn et dobbeltintegral ☞ Matematik Alfa 1, August 2002 Opgave 1 - alternativt er et Type I område. R = {(x,y)|0 ≤ x ≤ 2,0 ≤ y ≤ 4 − x 2 } y
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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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IX. Opgaver - 3. Januar 2004 576 L
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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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