# HW7 Calc - garcia(jjg2564 – HW 07 – gualdani –(56410...

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Unformatted text preview: garcia (jjg2564) – HW 07 – gualdani – (56410) 1 This print-out should have 13 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 + 3 x + 2 x 2 = 4 . 1. y ′ = y + 3 + 4 x x 2. y ′ =- y + 3 + 2 x x 3. y ′ =- ( y + 3 + 4 x ) 4. y ′ = 3 + 2 x- y x 5. y ′ = y + 3 + 2 x x 6. y ′ =- y + 3 + 4 x x correct Explanation: Differentiating implicitly with respect to x we see that d dx ( xy + 3 x + 2 x 2 ) = d dx (4) . Thus ( xy ′ + y ) + 3 + 4 x = 0 , and so xy ′ =- y- 3- 4 x . Consequently, y ′ =- y + 3 + 4 x x . 002 10.0 points Find dy dx when 1 √ x + 3 √ y = 8 . 1. dy dx =- 1 3 parenleftBig y x parenrightBig 3 / 2 correct 2. dy dx =- 3 parenleftBig x y parenrightBig 3 / 2 3. dy dx = 1 3 parenleftBig y x parenrightBig 3 / 2 4. dy dx = 3 parenleftBig x y parenrightBig 3 / 2 5. dy dx = 1 3 ( xy ) 1 / 2 6. dy dx = 3( xy ) 1 / 2 Explanation: Differentiating implicitly with respect to x , we see that- 1 2 parenleftBig 1 x √ x + 3 y √ y dy dx parenrightBig = 0 . Consequently, dy dx =- 1 3 parenleftBig y x parenrightBig 3 / 2 . 003 10.0 points Find dy/dx when y + x = 8 √ xy . 1. dy dx = radicalBig y x- 4 8 + radicalBig x y 2. dy dx = radicalBig y x + 4 8 + radicalBig x y 3. dy dx = 4 radicalBig y x- 1 1 + 4 radicalBig x y 4. dy dx = radicalBig y x + 4 8- radicalBig x y garcia (jjg2564) – HW 07 – gualdani – (56410) 2 5. dy dx = 4 radicalBig y x- 1 1- 4 radicalBig x y correct 6....
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## This note was uploaded on 10/08/2010 for the course MATH 408K taught by Professor Gualdani during the Fall '09 term at University of Texas.

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HW7 Calc - garcia(jjg2564 – HW 07 – gualdani –(56410...

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