# Find the Absolute Maximum and Minimum Values Calculus Questions

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Carnegie Mellon University Department of Mathematical Sciences 21-256, Spring 2021 Homework 5 Instructions: Please show all your work. 1. Let R = [0; 1] [0; 1] : Approximate ZZ xy dA (x; y) R by using m = 2 and n = 2 sub-intervals on the x and y axes, and taking the midpoint of each sub-rectangle as the sampling point. 2. Let R = [0; 2] [1; 3] : Calculate ZZ x dA (x; y) Ry by using Fubini’s Theorem, and iterating the integrals in both orders. 3. Consider the rectangle Ra = [0; a] (a) Evaluate ZZ e x y [0; a] ; where a > 0: dA (x; y) Ra as an expression in a: (b) Now evaluate ZZ lim a !1 e x y dA (x; y) Ra 4. Let D be the region bounded by the curves y = x2 + 6 and y = 5x: Evaluate ZZ x2 y dA (x; y) D 5. Let D be the region in the …rst quadrant with x ZZ x dA (x; y) 1 + y D 6. Evaluate Z 4Z 0 8 e x2 y y 2 : Evaluate dx dy 2y by using

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