ca2-2 - Version PREVIEW FinalReview02 Van Ligten (56650) 1...

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Unformatted text preview: Version PREVIEW FinalReview02 Van Ligten (56650) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. CalC15c10a 001 10.0 points Find the slope in the x-direction at the point P (0 , 2 , f (0 , 2)) on the graph of f when f ( x, y ) = 4(2 x + y ) e xy . 1. slope =- 10 2. slope =- 14 3. slope =- 6 4. slope =- 12 5. slope =- 8 correct Explanation: The graph of f is a surface in 3-space and the slope in the x-direction at the point P (0 , 2 , f (0 , 2)) on that surface is the value of the partial derivative f x at (0 , 2). Now f x = 8 e xy- 4(2 xy + y 2 ) e xy . Consequently, at P (0 , 2 , f (0 , 2)) slope =- 8 . CalC15c49a 002 10.0 points Determine the second partial f xy of f when f ( x, y ) = 7 x 2 y + y 2 10 x . 1. f xy = 14 x y 2 + y 5 x 2 2. f xy = 14 x- y 3. f xy =- 14 x y 2- y 5 x 2 correct 4. f xy = 14 x + y 5. f xy = 14 x y 2- y 5 x 2 Explanation: Differentiating with respect to x , we obtain f x = 14 x y- y 2 10 x 2 , and so after differentiation with respect to y we see that f xy =- 14 x y 2- y 5 x 2 . CalC16b16s 003 10.0 points Determine the value of the double integral I = integraldisplay integraldisplay A 3 xy 2 16 + x 2 dA over the rectangle A = braceleftBig ( x, y ) : 0 x 3 ,- 2 y 2 bracerightBig , integrating first with respect to y . 1. I = 4 ln parenleftBig 16 25 parenrightBig 2. I = 8 ln parenleftBig 25 32 parenrightBig 3. I = 8 ln parenleftBig 25 16 parenrightBig correct 4. I = 8 ln parenleftBig 16 25 parenrightBig 5. I = 4 ln parenleftBig 25 16 parenrightBig 6. I = 4 ln parenleftBig 25 32 parenrightBig Explanation: Version PREVIEW FinalReview02 Van Ligten (56650) 2 The double integral over the rectangle A can be represented as the iterated integral I = integraldisplay 3 parenleftbiggintegraldisplay 2 2 3 xy 2 16 + x 2 dy parenrightbigg dx , integrating first with respect to y . Now after integration with respect to y with x fixed, we see that integraldisplay 2 2 3 xy 2 16 + x 2 dy = bracketleftBig xy 3 16 + x 2 bracketrightBig 2 2 = 16 x 16 + x 2 . But integraldisplay 3 16 x 16 + x 2 dx = bracketleftBig 8 ln(16 + x 2 ) bracketrightBig 3 . Consequently, I = 8 ln parenleftBig 25 16 parenrightBig . CalC16c07b 004 10.0 points Find the value of the double integral I = integraldisplay integraldisplay A (8 x- y ) dxdy when A is the region braceleftBig ( x, y ) : y x y, y 1 bracerightBig . 1. I = 9 10 2. I = 4 5 3. I = 7 10 4. I = 3 5 correct 5. I = 1 Explanation: The integral can be written as the repeated integral I = integraldisplay 1 bracketleftBigg integraldisplay y y (8 x- y ) dx bracketrightBigg dy....
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This note was uploaded on 03/31/2010 for the course CH ch302 taught by Professor F during the Spring '09 term at University of Texas-Tyler.

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ca2-2 - Version PREVIEW FinalReview02 Van Ligten (56650) 1...

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