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Unformatted text preview: suleimenov (bs26835) – HW 10 – rusin – (55565) 1 This printout should have 14 questions. Multiplechoice 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 xdirection at the point P (0 , 2 , f (0 , 2)) on the graph of f when f ( x, y ) = 3(2 x + y ) e − xy . 1. slope = 6 correct 2. slope = 4 3. slope = 0 4. slope = 2 5. slope = 8 Explanation: The graph of f is a surface in 3space and the slope in the xdirection 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 = 6 e − xy 3(2 xy + y 2 ) e − xy . Consequently, at P (0 , 2 , f (0 , 2)) slope = 6 . 002 10.0 points Find u t when u = xe − 7 t sin θ . 1. u t = e − 7 t sin θ 2. u t = 7 xe − 7 t sin θ correct 3. u t = 7 xe − 7 t sin θ 4. u t = xe − 7 t cos θ 5. u t = 7 e − 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 ) = (3 x y )ln( xy ) . 1. f xy = 3 x y y 2. f xy = x + 3 y xy 3. f xy = x 3 y xy 4. f xy = 3 x + y xy 5. f xy = 3 x y xy correct 6. f xy = x + 3 y x Explanation: Since ln( xy ) = ln x + ln y , we see that f ( x, y ) = (3 x y )(ln x + ln y ) . suleimenov (bs26835) – HW 10 – rusin – (55565) 2 Thus f x = 3(ln x + ln y ) + 3 x y x = 3(ln x + ln y ) + 3 y x . Consequently, after differentiating with re spect to y we see that f xy = 3 y 1 x = 3 x y xy . 004 (part 1 of 4) 10.0 points A function f is defined by f ( x, y ) = ( x + 6)( y 4)( x + y 5) . (i) Determine f x for the function f . 1. f x ( x, y ) = ( y 4)(2 x y + 11) 2. f x ( x, y ) = ( y + 6)(2 x + y + 11) 3. f x ( x, y ) = ( y 4)(2 x + y + 1) correct 4. f x ( x, y ) = ( x 4)( x + 2 y 9) 5. f x ( x, y ) = ( x + 6)( x 2 y + 1) Explanation: Using the product rule to differentiate f ( x, y ) = ( x + 6)( y 4)( x + y 5) with respect to x we obtain f x = ( y 4)( x + y 5) + ( x + 6)( y 4) ....
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 Spring '11
 RUSIN
 Derivative, ∂x

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