A U MFACULTY OF ENGINEERINGMAT 310 (Calculus IIIAs.docx

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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]. .

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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].

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