A U M FACULTY OF ENGINEERING MAT 310

A U M FACULTY OF ENGINEERING MAT 310 (Calculus III Assignment 2 (100 pts) Groups: F2-7,F2-8,F2-9 No partial credit will be given for unsupported answers. 1. Find the local extrema of the function. f(x; y) = xy + 1x + 1y . 2. Use Lagrange multipliers to nd the absolute extrema of f subject to the given constraint. f(x; y) = 2x2 + 3y2 ?? 4x ?? 5 , x2 + y2 = 16 . 3. Find the absolute extrema of f on the set D . f(x; y) = xy2 , D = f(x; y) : x 0 y 0; x2 + y2 3g . 4. Use the Midpoint rule with m = 4 and n = 2 to estimate the value of the integral ZZ D (3 ?? 3x2y + 5y4) dA , where D = [0; 2] [0; 4] . What is the error? 5. Evaluate the integral ZZ D y sin(xy) dA , where D = [0; ] [0; =2]: