HW8 - Jolley Garrett – Homework 8 – Due 3:00 am –...

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Unformatted text preview: Jolley, Garrett – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: R Heitmann 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 4 x 2 + 5 y 2 = 3 . 1. dy dx =- 4 xy 2. dy dx =- 4 x y 3. dy dx =- 4 x 5 y correct 4. dy dx = 4 x 5 y 5. dy dx = 5 xy 6. dy dx = x 5 y Explanation: Diferentiating 4 x 2 + 5 y 2 = 3 implicitly with respect to x we see that 8 x + 10 y dy dx = 0 . Consequently, dy dx =- 8 x 10 y =- 4 x 5 y . keywords: implicit differentiation 002 (part 1 of 1) 10 points Find dy/dx when y + x = 2 √ xy . 1. dy dx = q y x + 1 1- q x y 2. dy dx = q y x + 1 2- q x y 3. dy dx = q y x- 1 2 + q x y 4. dy dx = q y x- 1 1- q x y correct 5. dy dx = q y x + 1 2 + q x y 6. dy dx = q y x- 1 1 + q x y Explanation: Differentiating implicitly with respect to x , we see that dy dx + 1 = µr y x + r x y dy dx ¶ , so dy dx µ 1- r x y ¶ = r y x- 1 . Consequently, dy dx = q y x- 1 1- q x y . keywords: implicit differentiation 003 (part 1 of 1) 10 points If y = y ( x ) is defined implicitly by 4 y 2- xy- 15 = 0 , Jolley, Garrett – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: R Heitmann 2 find the value of dy/dx at (7 , 3). 1. dy dx fl fl fl (7 , 3) = 4 17 2. dy dx fl fl fl (7 , 3) = 3 17 correct 3. dy dx fl fl fl (7 , 3) = 1 6 4. dy dx fl fl fl (7 , 3) =- 3 17 5. dy dx fl fl fl (7 , 3) =- 4 17 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 (7 , 3), therefore, dy dx fl fl fl (7 , 3) = 3 17 . 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 =- 10 qp 2 correct 4. dq dp =- 5 qp 2 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- 10 x ) 2 = 9( 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 = (4 , 4 √ 3). Jolley, Garrett – Homework 8 – Due: Oct 17 2007, 3:00 am – Inst: R Heitmann 3 1. y = 1 √ 3 · ‡ 13 7 x + 128 7 · 2. y = 1 √ 3 · ‡ 7 13 x + 128 13 · correct 3. y = 1 √ 3 · ‡ 7 13 x- 128 13 · 4. y = 1 √ 3 · ‡ 7 13 x + 24 13 · 5. y = 1 √ 3 · ‡ 13 7 x- 128 7 · Explanation: Differentiating ( x 2 + y 2- 10 x ) 2 = 9( x 2 + y 2 ) implicitly with respect to x we see that 2( x 2 + y 2- 10 x ) n 2 x + 2 y dy dx- 10 o = 18 n x + y dy dx o ....
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This note was uploaded on 10/29/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

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HW8 - Jolley Garrett – Homework 8 – Due 3:00 am –...

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