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 ( 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 ....
View
Full
Document
This note was uploaded on 02/15/2011 for the course MATH 380 taught by Professor Staff during the Summer '08 term at University of Illinois, Urbana Champaign.
 Summer '08
 Staff
 Math, Calculus

Click to edit the document details