HW07-solutions

# HW07-solutions - hinojosa(jah4698 – HW07 – seckin...

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Unformatted text preview: hinojosa (jah4698) – HW07 – seckin – (57195) 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- 32 = 0 , find the value of dy/dx at (28 , 8). 1. dy dx vextendsingle vextendsingle vextendsingle (28 , 8) = 2 9 correct 2. dy dx vextendsingle vextendsingle vextendsingle (28 , 8) =- 1 4 3. dy dx vextendsingle vextendsingle vextendsingle (28 , 8) = 1 4 4. dy dx vextendsingle vextendsingle vextendsingle (28 , 8) = 8 37 5. dy dx vextendsingle vextendsingle vextendsingle (28 , 8) =- 2 9 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 (28 , 8), therefore, dy dx vextendsingle vextendsingle vextendsingle (28 , 8) = 2 9 . 002 10.0 points Find dy dx when tan( x + y ) = x + 2 y . 1. dy dx = 1- sec 2 ( x + y ) sec 2 ( x + y ) + 2 2. dy dx = 1 + sec 2 ( x + y ) sec 2 ( x + y )- 2 3. dy dx = 2- sec 2 ( x + y ) sec 2 ( x + y )- 1 4. dy dx = 1- sec 2 ( x + y ) sec 2 ( x + y )- 2 correct 5. dy dx = 2 + sec 2 ( x + y ) sec 2 ( x + y ) + 1 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 = 1 + 2 dy dx . After rearranging, this becomes dy dx parenleftBig sec 2 ( x + y )- 2 parenrightBig = 1- sec 2 ( x + y ) . Consequently, dy dx = 1- sec 2 ( x + y ) sec 2 ( x + y )- 2 . keywords: 003 10.0 points Determine dy/dx when 3 cos x sin y = 2 . 1. dy dx = tan x 2. dy dx = cot x tan y 3. dy dx = tan xy 4. dy dx = cot x cot y 5. dy dx = tan x tan y correct hinojosa (jah4698) – HW07 – seckin – (57195) 2 Explanation: Differentiating implicitly with respect to x we see that 3 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. None of these 2. dq dp =- 5 q 2 p 3. dq dp =- 10 qp 2 correct 4. dq dp =- 10 qp 5. dq dp =- 5 qp 2 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)....
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HW07-solutions - hinojosa(jah4698 – HW07 – seckin...

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