MATH 241 Midterm: MATH241H_HERB-R_FALL2002_0101_MID_EXAM_1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: ALL

Document Summary

Math 241h - exam 2 - nov. 13, 2002 (20) 1. Find all critical points of the function f (x, y) = x3 + y3 + 3x2 3y2 and determine whether each is a local maximum, local minimum, or saddlepoint. (20) 2. Find the absolute maximum and minimum of f (x, y, z) = x + 2y 3z restricted to the ellipsoid x2 + y2 + 3z2 = 2. (20) 3. Sketch the region on integration, reverse the order of integration, and evaluate the integral r 1. Let r be the region inside the ellipse x2 + 4y2 = 4. Use the change of variables x = 2r cos , y = r sin to evaluate the integral.