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Solutions HW 7

Solutions HW 7 - mao(tm23477 Homework 7 gualdani(57180 This...

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mao (tm23477) – Homework 7 – gualdani – (57180) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points If y = y ( x ) is defined implicitly by 4 y 2 - xy - 12 = 0 , find the value of dy/dx at (8 , 3). 1. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 1 4 2. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 3 16 correct 3. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 3 17 4. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = - 1 4 5. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = - 3 16 Explanation: Differentiating implicitly with respect to x we see that 8 y dy dx - y - x dy dx = 0 . Thus dy dx = y 8 y - x . At (8 , 3), therefore, dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 3 16 . 002 10.0 points Find dy dx when tan( x + y ) = 2 x - y . 1. dy dx = 2 - sec 2 ( x + y ) sec 2 ( x + y ) + 1 correct 2. dy dx = 2 - sec 2 ( x + y ) sec 2 ( x + y ) - 1 3. dy dx = 1 - sec 2 ( x + y ) sec 2 ( x + y ) + 2 4. dy dx = 1 + sec 2 ( x + y ) sec 2 ( x + y ) - 2 5. dy dx = 1 - sec 2 ( x + y ) sec 2 ( x + y ) - 2 6. dy dx = 2 + sec 2 ( x + y ) sec 2 ( x + y ) + 1 Explanation: Differentiating implicitly with respect to x , we see that sec 2 ( x + y ) parenleftBig 1 + dy dx parenrightBig = 2 - dy dx . After rearranging, this becomes dy dx parenleftBig sec 2 ( x + y ) + 1 parenrightBig = 2 - sec 2 ( x + y ) . Consequently, dy dx = 2 - sec 2 ( x + y ) sec 2 ( x + y ) + 1 . keywords: 003 10.0 points Determine dy/dx when 5 cos x sin y = 7 . 1. dy dx = tan x 2. dy dx = tan xy 3. dy dx = tan x tan y correct 4. dy dx = cot x tan y 5. dy dx = cot x cot y

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mao (tm23477) – Homework 7 – gualdani – (57180) 2 Explanation: Differentiating implicitly with respect to x we see that 5 braceleftBig cos x cos y dy dx - sin y sin x bracerightBig = 0 . Thus dy dx cos x cos y = sin x sin y . Consequently, dy dx = sin x sin y cos x cos y = tan x tan y . 004 10.0 points Find the rate of change of q with respect to p when p = 20 q 2 + 5 . 1. dq dp = - 10 qp 2. None of these 3. dq dp = - 5 q 2 p 4. dq dp = - 5 qp 2 5. dq dp = - 10 qp 2 correct Explanation: Differentiating implicitly with respect to p we see that 1 = - 2 q parenleftBig 20 ( q 2 + 5) 2 parenrightBig dq dp , and so dq dp = - ( q 2 + 5) 2 40 q . But q 2 + 5 = 20 p . Consequently, dq dp = - 10 qp 2 . 005 10.0 points Find the slope of the tangent line to the graph of x 3 - 2 y 3 - xy = 0 at the point P ( - 1 , - 1). 1. slope = - 4 5 2. slope = 4 5 correct 3. slope = - 2 3 4. slope = - 5 4 5. slope = 5 4 6. slope = 3 2 Explanation: Differentiating implicitly with respect to x we see that 3 x 2 - 6 y 2 dy dx - y - x dy dx = 0 .
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Solutions HW 7 - mao(tm23477 Homework 7 gualdani(57180 This...

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