MATH 222 Midterm: Kansas State MATH 222 222t3u94

• School: Kansas State University
• Department: Mathematics
• Course: MATH 222
• Professor: All

Document Summary

You have to show all your work to receive full credit. The point value is indicated at the left of each problem. (14pts) 1. The temperature at each point of the circular disk. D = {(x, y) : x2 + y2 4} is given by t = x2 + 2y2 2y . Find the hottest and the coldest points of the disk. (14pts) 2. Use the method of lagrange multipliers to answer the following question: what point of the surface. = 1 is closest to the origin? (hint: consider the square of the distance. ) 0 z 1 x the order of integration. ) page 3 e y2 dydx . (hint: reverse (12pts) 4. Use double integration to nd the area of region bounded by. Evaluate the double integral r rd ex2+y2 described by 1 x2 + y2 4 . page 4 da where d is the ring (12pts) 6.