HW 7 Gagan Solutions

# HW 7 Gagan Solutions - Nanda, Gagan Homework 7 Due: Oct 7...

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Unformatted text preview: Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 1 This print-out should have 19 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 + 3 y = 1 . 1. dy dx = 4 3 1- 4 x 2. dy dx = 4 9 4- 1 x correct 3. dy dx = 4 9 1 + 4 x 4. dy dx = 1- 4 x 5. dy dx = 4 3 4- 1 x 6. dy dx = 4 + 1 x Explanation: Differentiating implicitly with respect to x we see that 1 2 4 x + 3 y dy dx = 0 . Thus dy dx =- 4 3 y x . But y = 1- 4 x 3 , so dy dx = 4 9 4 x- 1 x . Consequently, dy dx = 4 9 4- 1 x . 002 (part 1 of 1) 10 points If y = y ( x ) is defined implicitly by 2 y 2- xy- 16 = 0 , find the value of dy/dx at (4 , 4). 1. dy dx fl fl fl (4 , 4) = 1 3 correct 2. dy dx fl fl fl (4 , 4) =- 1 3 3. dy dx fl fl fl (4 , 4) =- 5 12 4. dy dx fl fl fl (4 , 4) = 5 12 5. dy dx fl fl fl (4 , 4) = 4 13 Explanation: Differentiating implicitly with respect to x we see that 4 y dy dx- y- x dy dx = 0 , so dy dx = y 4 y- x . At (4 , 4), therefore, dy dx fl fl fl (4 , 4) = 1 3 . 003 (part 1 of 1) 10 points Determine d 2 y/dx 2 when 3 x 2 + 3 y 2 = 4 . 1. d 2 y dx 2 = 4 3 y 2 2. d 2 y dx 2 =- 4 3 y 2 Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 2 3. d 2 y dx 2 =- 4 3 y 3 correct 4. d 2 y dx 2 = 4 3 y 3 5. d 2 y dx 2 =- 1 3 y 3 Explanation: Differentiating implicitly with respect to x we see that 6 x + 6 y dy dx = 0 , so dy dx =- x y . But then d 2 y dx 2 =- d dx x y =- 9 y- 9 x dy dx 9 y 2 =- 1 3 y 2 3 y + 3 x 2 y . Thus d 2 y dx 2 =- 1 3 y 3 3 x 2 + 3 y 2 =- 4 3 y 3 . 004 (part 1 of 1) 10 points Find dy dx when x 3 y 3- y = x. 1. dy dx = 1- 3 x 2 y 3 3 x 3 y 2- 1 correct 2. dy dx = 1- 2 x 3 y 3 2 x 3 y 2- 1 3. dy dx = 1- 3 x 3 y 3 3 x 3 y 2- 2 4. dy dx = 1- 3 x 3 y 2 3 x 2 y 2- 1 5. dy dx = 1 + 3 x 2 y 3 3 x 3 y 2- 2 Explanation: Differentiating x 3 y 3- y = x implicitly with respect to x we see that 3 x 3 y 2 dy dx + 3 y 3 x 2- dy dx = 1 . Thus 3 x 3 y 2 dy dx- dy dx = 1- 3 x 2 y 3 and so dy dx = 1- 3 x 2 y 3 3 x 3 y 2- 1 . 005 (part 1 of 1) 10 points Use implicit differentiation to determine y when 11cos x sin y = 8 . 1. y = tan x 2. y = tan x tan y correct 3. y = cot x cot y 4. y = cot x tan y 5. y = tan xy Explanation: d dx (11cos x sin y ) = d dx (8) 11 cos x cos y y + sin y (- sin x ) / = 0 y (11cos x cos y ) = 11sin x sin y y = 11sin x sin y 11cos x cos y = tan x tan y Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 3 006 (part 1 of 1) 10 points...
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## HW 7 Gagan Solutions - Nanda, Gagan Homework 7 Due: Oct 7...

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