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Unformatted text preview: Tran, Tony Homework 8 Due: Oct 17 2007, 3:00 am Inst: Samuels 1 This printout should have 21 questions. Multiplechoice 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 Find dy/dx when 5 x 2 + 4 y 2 = 2 . 1. dy dx = 5 x 4 y correct 2. dy dx = 5 xy 3. dy dx = 5 x 4 y 4. dy dx = 4 xy 5. dy dx = 5 x y 6. dy dx = x 4 y Explanation: Diferentiating 5 x 2 + 4 y 2 = 2 implicitly with respect to x we see that 10 x + 8 y dy dx = 0 . Consequently, dy dx = 10 x 8 y = 5 x 4 y . keywords: implicit differentiation 002 (part 1 of 1) 10 points Find dy/dx when y x = 8 xy . 1. dy dx = q y x 4 8 + q x y 2. dy dx = q y x + 4 8 + q x y 3. dy dx = q y x 4 8 q x y 4. dy dx = 4 q y x + 1 1 4 q x y correct 5. dy dx = 4 q y x + 1 1 + 4 q x y 6. dy dx = 4 q y x 1 1 4 q x y Explanation: Differentiating implicitly with respect to x , we see that dy dx 1 = 4 r y x + r x y dy dx , so dy dx 1 4 r x y = 4 r y x + 1 . Consequently, dy dx = 4 q y x + 1 1 4 q x y . keywords: implicit differentiation 003 (part 1 of 1) 10 points If y = y ( x ) is defined implicitly by y 2 xy 10 = 0 , Tran, Tony Homework 8 Due: Oct 17 2007, 3:00 am Inst: Samuels 2 find the value of dy/dx at (3 , 5). 1. dy dx fl fl fl (3 , 5) = 5 8 2. dy dx fl fl fl (3 , 5) = 6 7 3. dy dx fl fl fl (3 , 5) = 6 7 4. dy dx fl fl fl (3 , 5) = 5 7 5. dy dx fl fl fl (3 , 5) = 5 7 correct Explanation: Differentiating implicitly with respect to x we see that 2 y dy dx y x dy dx = 0 . Thus dy dx = y 2 y x . At (3 , 5), therefore, dy dx fl fl fl (3 , 5) = 5 7 . keywords: implicit differentiation 004 (part 1 of 1) 10 points Find the rate of change of q with respect to p when p = 20 q 2 + 5 . 1. None of these 2. dq dp = 5 q 2 p 3. dq dp = 5 qp 2 4. dq dp = 10 qp 2 correct 5. dq dp = 10 qp Explanation: Differentiating implicitly with respect to p we see that 1 = 2 q 20 ( q 2 + 5) 2 dq dp , and so dq dp = ( q 2 + 5) 2 40 q . But q 2 + 5 = 20 p . Consequently, dq dp = 10 qp 2 . keywords: implicit differentiation 005 (part 1 of 1) 10 points The graph of the equation of the ( x 2 + y 2 8 x ) 2 = 4( x 2 + y 2 ) is shown in the figure 2 4 6 8 10 12 2 4 6 2 4 6 P Find the equation of the tangent line to the graph at the point P = (3 , 3 3). Tran, Tony Homework 8 Due: Oct 17 2007, 3:00 am Inst: Samuels 3 1. y = 1 3 3 5 x + 36 5 correct 2. y = 1 3 3 5 x + 6 5 3. y = 1 3 3 5 x 36 5 4. y = 1 3 5 3 x + 12 5. y = 1 3 5 3 x 12 Explanation: Differentiating ( x 2 + y 2 8 x ) 2 = 4( x 2 + y 2 ) implicitly with respect to x we see that 2( x 2 + y 2 8 x ) n 2 x + 2 y dy dx 8 o = 8 n x + y dy dx o ....
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 Fall '08
 schultz

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