Let S be the cylinder defined by x + y = 4 and 2 ...
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Let S be the cylinder defined by x² + y² = 4 and −2 ≤ ≈ ≤ 2. (a) Note that as = C₁ C₂ where C₁ (resp. C₂) is the circle at the top (resp. bottom) of the cylinder. Give parametrizations c₁ and c2 of C₁ and C2₂ with the orientation corresponding to outwards pointing normal vectors for S. (b) Use part (a) and Stokes' theorem to evaluate 1₂0 (V x F). dS for F(x, y, z) = x²i+y²j+xye²k. Here S is oriented with outwards pointing normal vectors. Let W be the top half of the ball of radius R> 0 centered at (0, 0, 0), i.e., the surface given by x² + y² + z² ≤ R² and z ≥ 0. (a) Describe W as an elementary region in R³. (b) Use part (a) and Gauss' divergence theorem to evaluate How F.dS, where F(x, y, z) = (x³ + eª, y³ − z, xy + z³) and OW is oriented with outwards pointing normal vectors. 7 Let S be the cylinder defined by x² + y² = 4 and −2 ≤ ≈ ≤ 2. (a) Note that as = C₁ C₂ where C₁ (resp. C₂) is the circle at the top (resp. bottom) of the cylinder. Give parametrizations c₁ and c2 of C₁ and C2₂ with the orientation corresponding to outwards pointing normal vectors for S. (b) Use part (a) and Stokes' theorem to evaluate 1₂0 (V x F). dS for F(x, y, z) = x²i+y²j+xye²k. Here S is oriented with outwards pointing normal vectors. Let W be the top half of the ball of radius R> 0 centered at (0, 0, 0), i.e., the surface given by x² + y² + z² ≤ R² and z ≥ 0. (a) Describe W as an elementary region in R³. (b) Use part (a) and Gauss' divergence theorem to evaluate How F.dS, where F(x, y, z) = (x³ + eª, y³ − z, xy + z³) and OW is oriented with outwards pointing normal vectors. 7
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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