This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 nd 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 ( x-y ) dxdy where D is the region bounded by y = 0, y =-x , and y = x-4. (a) (3pts) Sketch the region of integration, D , in xy-space. (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 uv-space. 5. Continued. (d) (8pts) Use the Change of Variables Theorem to set-up, but do not evaluate , the integral in uv-space equal to Z Z D ( x + y ) 2 e ( x-y ) dxdy ....
View Full Document