# CalcHW8Answers - Villarreal Natalie – Homework 8 – Due...

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Unformatted text preview: Villarreal, Natalie – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: Louiza Fouli 1 This print-out should have 21 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 Find dy/dx when 5 x 2 + 3 y 2 = 1 . 1. dy dx =- 5 x y 2. dy dx = 3 xy 3. dy dx =- 5 x 3 y correct 4. dy dx = 5 x 3 y 5. dy dx =- 5 xy 6. dy dx = x 3 y Explanation: Diferentiating 5 x 2 + 3 y 2 = 1 implicitly with respect to x we see that 10 x + 6 y dy dx = 0 . Consequently, dy dx =- 10 x 6 y =- 5 x 3 y . keywords: implicit differentiation 002 (part 1 of 1) 10 points Find dy/dx when y + x = 6 √ xy . 1. dy dx = q y x + 3 6 + q x y 2. dy dx = 3 q y x- 1 1 + 3 q x y 3. dy dx = q y x- 3 6 + q x y 4. dy dx = q y x + 3 6- q x y 5. dy dx = 3 q y x- 1 1- 3 q x y correct 6. dy dx = 3 q y x + 1 1- 3 q x y Explanation: Differentiating implicitly with respect to x , we see that dy dx + 1 = 3 µr y x + r x y dy dx ¶ , so dy dx µ 1- 3 r x y ¶ = 3 r y x- 1 . Consequently, dy dx = 3 q y x- 1 1- 3 q x y . keywords: implicit differentiation 003 (part 1 of 1) 10 points If y = y ( x ) is defined implicitly by 2 y 2- xy- 6 = 0 , Villarreal, Natalie – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: Louiza Fouli 2 find the value of dy/dx at (11 , 6). 1. dy dx fl fl fl (11 , 6) = 6 13 correct 2. dy dx fl fl fl (11 , 6) =- 6 13 3. dy dx fl fl fl (11 , 6) =- 7 13 4. dy dx fl fl fl (11 , 6) = 3 7 5. dy dx fl fl fl (11 , 6) = 7 13 Explanation: Differentiating implicitly with respect to x we see that 4 y dy dx- y- x dy dx = 0 . Thus dy dx = y 4 y- x . At (11 , 6), therefore, dy dx fl fl fl (11 , 6) = 6 13 . 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. dq dp =- 5 qp 2 2. dq dp =- 10 qp 3. dq dp =- 5 q 2 p 4. None of these 5. dq dp =- 10 qp 2 correct 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). Villarreal, Natalie – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: Louiza Fouli 3 1. y = 1 √ 3 · ‡ 3 5 x + 36 5 · correct 2. y = 1 √ 3 · ‡ 5 3 x + 12 · 3. y = 1 √ 3 · ‡ 5 3 x- 12 · 4. y = 1 √ 3 · ‡ 3 5 x- 36 5 · 5. y = 1 √ 3 · ‡ 3 5 x + 6 5 · 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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CalcHW8Answers - Villarreal Natalie – Homework 8 – Due...

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