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Unformatted text preview: Version PREVIEW – HW 06 – hoffman – (57225) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. CalC3g01a 001 10.0 points Find y ′ when xy + 5 x + 3 x 2 = 4 . 1. y ′ = y + 5 + 3 x x 2. y ′ = 5 + 3 x y x 3. y ′ = y + 5 + 3 x x 4. y ′ = ( y + 5 + 6 x ) 5. y ′ = y + 5 + 6 x x 6. y ′ = y + 5 + 6 x x correct Explanation: Differentiating implicitly with respect to x we see that d dx ( xy + 5 x + 3 x 2 ) = d dx (4) . Thus ( xy ′ + y ) + 5 + 6 x = 0 , and so xy ′ = y 5 6 x . Consequently, y ′ = y + 5 + 6 x x . CalC3g03a 002 10.0 points Find dy dx when 5 √ x + 3 √ y = 8 . 1. dy dx = 3 5 parenleftBig x y parenrightBig 3 / 2 2. dy dx = 5 3 ( xy ) 1 / 2 3. dy dx = 5 3 parenleftBig y x parenrightBig 3 / 2 correct 4. dy dx = 3 5 ( xy ) 1 / 2 5. dy dx = 3 5 parenleftBig x y parenrightBig 3 / 2 6. dy dx = 5 3 parenleftBig y x parenrightBig 3 / 2 Explanation: Differentiating implicitly with respect to x , we see that 1 2 parenleftBig 5 x √ x + 3 y √ y dy dx parenrightBig = 0 . Consequently, dy dx = 5 3 parenleftBig y x parenrightBig 3 / 2 . CalC3g05a 003 10.0 points If y = y ( x ) is defined implicitly by y 2 xy 32 = 0 , find the value of dy/dx at (4 , 8). 1. dy dx vextendsingle vextendsingle vextendsingle (4 , 8) = 3 4 2. dy dx vextendsingle vextendsingle vextendsingle (4 , 8) = 8 13 3. dy dx vextendsingle vextendsingle vextendsingle (4 , 8) = 2 3 correct 4. dy dx vextendsingle vextendsingle vextendsingle (4 , 8) = 2 3 Version PREVIEW – HW 06 – hoffman – (57225) 2 5. dy dx vextendsingle vextendsingle vextendsingle (4 , 8) = 3 4 Explanation: Differentiating implicitly with respect to x we see that 2 y dy dx y x dy dx = 0 ....
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This note was uploaded on 06/14/2011 for the course MATH 305G taught by Professor Cathy during the Spring '11 term at University of Texas at Austin.
 Spring '11
 Cathy

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