Exam 3 Choike Fall 2010

Exam 3 Choike Fall 2010 - MATH 2163 Calculus III m3 Name...

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.' MATH 2163, Calculus III m3 Name: Instructions: Answers given without work indicating the algebra or an explanation of how the answer was obtained may not receive full credit. I. (10 pts.) A functionj{x,y) has the values in the table below. Let R be the rectangle o ,; x,; 1,0,; Y ,; 2. Using the tabular data given below for the functionj, find the double Riemann sum for If j(x,y)dA that corresponds to congruent rectangles with dimensions fu = 0.5 R and L'.y = 0.5 and that uses the largest value available for jin each of these rectangles. y 0 1.5 2 0 3 0.25 3 x 0.5 3 0.75 3 I 3 2. (25 pts.) a. Sketch and label the region of integration in the xy-plane for s o S-2H'(3x)dydx. -2 3x+2 s o S-2H2 b. Evaluate the integral (3x)dydx. -2 3x+2 s o S-2H2 c. Interchange the order of integration for the iterated integral (3x )dydx . -2 3x+2 YOU DO NOT HAVE TO INTEGRATE THIS INTEGRAL. \ 3. (20 pts.) Evaluate the double integral If er' dA over the region.R, where R R = {(x,y)1 0::::; x::::;I,x::::; y::::; I}.
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4. (15 pts.)
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Exam 3 Choike Fall 2010 - MATH 2163 Calculus III m3 Name...

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