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HW6-510-soln

# HW6-510-soln - AMS 510 HW6 Solution 9.25(a It is the volume...

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AMS 510 HW6 Solution 9.25 (a) It is the volume between z = 0, z = x y , x = 1, y = 0, y = 4 – x 2 (b) 1 2 0 4 x 2 x y dxdy (c) 1 2 0 4 x 2 x y dxdy = 241 / 60 9.27 0 a 0 b b a x 0 c c a x c b y 1 dzdydx = abc / 6 9.28 a a a a 0 x 2 y 2 1 dzdydx = 8a 4 / 3 9.32 { x y = u y = uv { u = x y v = y x y ,also { 0 x 1 0 y 1 { 0 u 1 0 v 1 , and ∂ x , y ∂ u,v = 1 – v –u v u = u then 0 1 0 1 x e y / x y dydx = 0 1 0 1 e v udvdu = e 1 2 9.33

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{ xy = u xy 3 = v { 4 u 8 5 v 15 , then Area = ∫∫ dxdy = 4 8 5 15 ∂ x, y ∂ u,v dvdu = 4 8 5 15 1 2v dvdu = 2ln3 9.37 0 1 0 1 x 2 y 2 2 xyz dzdydx = 0 1 0 1 1 2 xy 4 x 2 y 2 dydx = 3 / 8 9.40 0 2 0 4 x 2 0 4 x 2 y 2 xyz dzdydx = 4 / 3 9.41 If we project the intersection curve of surface z = x 2 y 2 and z = 2 x onto the plane x-y, we can see the projected curve is
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