calculus

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 + 1

x +

1

y .

2. Use Lagrange multipliers to find 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 = {(x,y) : x ≥ 0 y ≥ 0, x2 + y2 ≤ 3} .

4. Use the Midpoint rule with m = 4 and n = 2 to estimate the value of the integral∫∫ D

(3−3x2y + 5y4)dA , where D = [0,2]× [0,4] .

What is the error?

5. Evaluate the integral∫∫ D

y sin(xy)dA , where D = [0,π]× [0,π/2].