University of Texas M 408D Rusin HW 10

# University of Texas M 408D Rusin HW 10 - byrne (cmb3744)...

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Unformatted text preview: byrne (cmb3744) – HW 10 – rusin – (55565) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. A short assignment to help you study the newest material while preparing for the test on TUESDAY 4/19. As before, this HW is not due until a little later than usual (Friday 4/22). What we discuss on Thursday 4/21 will be included on the next HW set (due 4/27). 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 ) = 2(2 x + y ) e − xy . 1. slope =- 2 2. slope =- 6 3. slope =- 8 4. slope = 0 5. slope =- 4 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 = 4 e − xy- 2(2 xy + y 2 ) e − xy . Consequently, at P (0 , 2 , f (0 , 2)) slope =- 4 . 002 10.0 points Find u t when u = xe − 7 t sin θ . 1. u t =- 7 xe − 7 t sin θ correct 2. u t =- 7 e − 7 t sin θ 3. u t = e − 7 t sin θ 4. u t = xe − 7 t cos θ 5. u t = 7 xe − 7 t sin θ Explanation: Differentiating u = xe − 7 t sin θ with respect to t keeping x and θ fixed, we see that u t =- 7 xe − 7 t sin θ . 003 10.0 points Determine f xy when f ( x, y ) = (2 x + 3 y )ln( xy ) . 1. f xy = 3 x- 2 y x 2. f xy = 3 x- 2 y xy 3. f xy = 2 x + 3 y y 4. f xy = 2 x + 3 y xy correct 5. f xy = 3 x + 2 y xy 6. f xy = 2 x- 3 y xy Explanation: Since ln( xy ) = ln x + ln y , we see that f ( x, y ) = (2 x + 3 y )(ln x + ln y ) . byrne (cmb3744) – HW 10 – rusin – (55565) 2 Thus f x = 2(ln x + ln y ) + 2 x + 3 y x = 2(ln x + ln y ) + 2 + 3 y x . Consequently, after differentiating with re- spect to y we see that f xy = 2 y + 3 x = 2 x + 3 y xy . 004 (part 1 of 4) 10.0 points A function f is defined by f ( x, y ) = ( x + 1)( y- 9)( x + y- 3) . (i) Determine f x for the function f . 1. f x ( x, y ) = ( y- 9)(2 x + y- 2) correct 2. f x ( x, y ) = ( y + 1)(2 x + y + 4) 3. f x ( x, y ) = ( x + 1)( x- 2 y- 2) 4. f x ( x, y ) = ( x- 9)( x + 2 y- 12) 5. f x ( x, y ) = ( y- 9)(2 x- y + 4) Explanation: Using the product rule to differentiate f ( x, y ) = ( x + 1)( y- 9)( x + y- 3) with respect to x we obtain f x = ( y- 9)( x + y- 3) + ( x + 1)( y- 9) ....
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## This note was uploaded on 05/08/2011 for the course MATH 408D taught by Professor Chu during the Spring '09 term at University of Texas.

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University of Texas M 408D Rusin HW 10 - byrne (cmb3744)...

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