Homework #7 - jiwani (amj566) Homework07 Fouli (58395) 1...

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Unformatted text preview: jiwani (amj566) Homework07 Fouli (58395) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find y when xy + 5 x + 2 x 2 = 4 . 1. y = y + 5 + 2 x x 2. y = 5 + 2 x- y x 3. y =- ( y + 5 + 4 x ) 4. y =- y + 5 + 2 x x 5. y = y + 5 + 4 x x 6. y =- y + 5 + 4 x x correct Explanation: Differentiating implicitly with respect to x we see that d dx ( xy + 5 x + 2 x 2 ) = d dx (4) . Thus ( xy + y ) + 5 + 4 x = 0 , and so xy =- y- 5- 4 x . Consequently, y =- y + 5 + 4 x x . 002 10.0 points Find dy dx when 4 x + 1 y = 7 . 1. dy dx = 4 parenleftBig y x parenrightBig 3 / 2 2. dy dx = 4( xy ) 1 / 2 3. dy dx = 1 4 ( xy ) 1 / 2 4. dy dx = 1 4 parenleftBig x y parenrightBig 3 / 2 5. dy dx =- 1 4 parenleftBig x y parenrightBig 3 / 2 6. dy dx =- 4 parenleftBig y x parenrightBig 3 / 2 correct Explanation: Differentiating implicitly with respect to x , we see that- 1 2 parenleftBig 4 x x + 1 y y dy dx parenrightBig = 0 . Consequently, dy dx =- 4 parenleftBig y x parenrightBig 3 / 2 . 003 10.0 points Find dy dx when tan(2 x + y ) = 2 x . 1. dy dx =- 4 x 2 2 + y 2 2. dy dx = 8 x 2 1 + 4 x 2 3. dy dx = 4 y 2 2 + x 2 4. dy dx =- 8 x 2 1 + 4 x 2 correct 5. dy dx =- 8 y 2 2 + x 2 jiwani (amj566) Homework07 Fouli (58395) 2 6. dy dx = 8 x 2 1 + 4 y 2 Explanation: Differentiating tan(2 x + y ) = 2 x implicitly with respect to x we see that sec 2 (2 x + y ) parenleftbigg 2 + dy dx parenrightbigg = 2 . Thus sec 2 (2 x + y ) dy dx = 2(1- sec 2 (2 x + y )) , in which case dy dx = 2(1- sec 2 (2 x + y )) sec 2 (2 x + y ) . But sec 2 = 1 + tan 2 , so sec 2 (2 x + y ) = 1 + tan 2 (2 x + y ) = 1 + 4 x 2 , while 1- sec 2 (2 x + y ) =- tan 2 (2 x + y ) =- 4 x 2 . Consequently, dy dx =- 8 x 2 1 + 4 x 2 . 004 10.0 points Find the equation of the tangent line to the graph of y 2- xy- 20 = 0 , at the point P = (1 , 5). 1. y = 5 x 2. 9 y + 5 x = 40 3. 8 y + 5 x = 35 4. 9 y = 5 x + 40 correct 5. 8 y = 5 x + 35 Explanation: Differentiating implicitly with respect to x we see that 2 y dy dx- y- x dy dx = 0 , so dy dx = y 2 y- x . At P = (1 , 5), therefore, dy dx vextendsingle vextendsingle vextendsingle P = 5 9 . Thus by the point slope formula, the equation of the tangent line at P is given by y- 5 = 5 9 ( x- 1) . Consequently, 9 y = 5 x + 40 . 005 10.0 points Find the slope of the tangent line to the graph of 2 x 3 + y 3 + xy = 0 at the point P (1 ,- 1). 1. slope = 3 2 2. slope =- 2 3 3. slope = 4 5 4. slope =- 4 5 5. slope = 5 4 6. slope =- 5 4 correct jiwani (amj566) Homework07 Fouli (58395) 3 Explanation: Differentiating implicitly with respect to x we see that 6 x 2 + 3 y 2 dy dx + y + x dy dx = 0 ....
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This note was uploaded on 07/10/2011 for the course KIN 321M taught by Professor Jensen during the Spring '11 term at University of Texas at Austin.

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Homework #7 - jiwani (amj566) Homework07 Fouli (58395) 1...

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