MATH 241 Midterm: MATH 241 UIUC Math241_Fall08_9AM_Exam3

• School: University of Illinois
• Department: Mathematics
• Course: MATH 241
• Professor: All

Document Summary

Math 241 exam 3 9am v1. , 0, 0 is a critical point of f . 0: (8pts) find the maximum and minimum values of f (x, y) = y2 constraint x2 + y2 = 1. X + 200 subject to the: (5pts) let d be the region bounded by xy2 = 1, y = x, x = 0, and y = 3. Zzdr x + y x 2y da: (7pts) express the integral z 3. 0 dydx px2 + y2 as an iterated integral in polar coordinates. 9. (5pts) let w be the region in r3 above the xy-plane bounded by the two spheres x2 + y2 + z2 = 9 and x2 + y2 + z2 = 25. Set up, but do not evaluate, an iterated integral(s) that will calculate the volume of w . Math 241 exam 3 2pm v1. 55 points possible: let f : rn.