HW10S - Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00...

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Unformatted text preview: Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00 am Inst: JEGilbert 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Determine f x- f y when f ( x,y ) = 2 x 2 + 2 xy- 4 y 2- 3 x- 2 y . 1. f x- f y = 6 x + 10 y- 5 2. f x- f y = 6 x- 6 y- 1 3. f x- f y = 6 x- 6 y- 5 4. f x- f y = 2 x- 6 y- 1 5. f x- f y = 2 x + 10 y- 5 6. f x- f y = 2 x + 10 y- 1 correct Explanation: After differentiation we see that f x = 4 x + 2 y- 3 , f y = 2 x- 8 y- 2 . Consequently, f x- f y = 2 x + 10 y- 1 . keywords: partial derivative, first order par- tial derivative, polynomial 002 (part 1 of 1) 10 points Determine f x when f ( x, y ) = cos(2 y- x )- x sin(2 y- x ) . 1. f x =- cos(2 y- x )- x sin(2 y- x ) 2. f x =- 2 sin(2 y- x )- x cos(2 y- x ) 3. f x = x sin(2 y- x ) 4. f x =- x cos(2 y- x ) 5. f x = x cos(2 y- x )- sin(2 y- x ) 6. f x = 2 sin(2 y- x )- x cos(2 y- x ) 7. f x =- x sin(2 y- x ) 8. f x = x cos(2 y- x ) correct Explanation: From the Product Rule we see that f x = sin(2 y- x )- sin(2 y- x )+ x cos(2 y- x ) . Consequently, f x = x cos(2 y- x ) . partial derivative, first order partial deriva- tive, trig function, keywords: 003 (part 1 of 1) 10 points Determine f x when f ( x, y ) = ( xy- 3) e- xy . 1. f x =- y (2- xy ) e- xy 2. f x =- y (2 + xy ) e- xy 3. f x = y ( xy- 4) e- xy 4. f x = x (4- 3 xy ) e- xy 5. f x = y (4- xy ) e- xy correct 6. f x = x (3 xy- 4) e- xy 7. f x =- x (2 + 3 xy ) e- xy 8. f x =- x (2 + xy ) e- xy Explanation: From the Product Rule we see that f x = ye- xy- y ( xy- 3) e- xy . Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00 am Inst: JEGilbert 2 Consequently, f x = y (4- xy ) e- xy . keywords: partial derivative, first order par- tial derivative, exp function, 004 (part 1 of 1) 10 points Determine h = h ( x,y ) so that f x = h ( x,y ) ( x 2 + 5 y 2 ) 2 when f ( x,y ) = 4 x 2 y x 2 + 5 y 2 . 1. h ( x,y ) = 20 xy 3 2. h ( x,y ) = 40 xy 2 3. h ( x,y ) = 20 x 3 y 4. h ( x,y ) = 40 x 3 y 5. h ( x,y ) = 40 xy 3 correct 6. h ( x,y ) = 20 xy 2 Explanation: Differentiating with respect to x using the quotient rule we obtain...
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This homework help was uploaded on 03/19/2008 for the course M 408M taught by Professor Gilbert during the Fall '07 term at University of Texas at Austin.

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HW10S - Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00...

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