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Unformatted text preview: minimum value on D . (b) (2pts) Explain why T does not attain a maximum or a minimum value in the interior of D . (c) (6pts) Use Lagrange multipliers to ﬁnd the maximum and minimum values of T ( x,y ) on the boundary D ( x 2 + y 2 = 1). 5. Let Z Z D ( x + y ) 2 e ( xy ) dxdy where D is the region bounded by y = 0, y =x , and y = x4. (a) (3pts) Sketch the region of integration, D , in xyspace. (b) (1pt) Find an appropriate change of variables u = g ( x,y ) and v = h ( x,y ) to simplify the integral. (c) (3pts) Sketch the region of integration, D * , in uvspace. 5. Continued. (d) (8pts) Use the Change of Variables Theorem to setup, but do not evaluate , the integral in uvspace equal to Z Z D ( x + y ) 2 e ( xy ) dxdy ....
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 Summer '08
 Staff
 Math, Calculus, 2pts, Quadratic form, 1pt, Joseph Louis Lagrange, secondorder Taylor formula

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