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HW 7 - mandel(tgm245 HW07 Radin(56470 This print-out should...

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mandel (tgm245) – HW07 – Radin – (56470) 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 + 5 x + 4 x 2 = 3 . 1. y = y + 5 + 8 x x 2. y = - ( y + 5 + 8 x ) 3. y = 5 + 4 x - y x 4. y = - y + 5 + 8 x x correct 5. y = y + 5 + 4 x x 6. y = - y + 5 + 4 x x Explanation: Differentiating implicitly with respect to x we see that d dx ( xy + 5 x + 4 x 2 ) = d dx (3) . Thus ( xy + y ) + 5 + 8 x = 0 , and so xy = - y - 5 - 8 x. Consequently, y = - y + 5 + 8 x x . 002 10.0 points Find dy dx when 3 x + 1 y = 6 . 1. dy dx = 1 3 ( xy ) 1 / 2 2. dy dx = 3 parenleftBig y x parenrightBig 3 / 2 3. dy dx = 3( xy ) 1 / 2 4. dy dx = 1 3 parenleftBig x y parenrightBig 3 / 2 5. dy dx = - 3 parenleftBig y x parenrightBig 3 / 2 correct 6. dy dx = - 1 3 parenleftBig x y parenrightBig 3 / 2 Explanation: Differentiating implicitly with respect to x , we see that - 1 2 parenleftBig 3 x x + 1 y y dy dx parenrightBig = 0 . Consequently, dy dx = - 3 parenleftBig y x parenrightBig 3 / 2 . 003 10.0 points Find dy/dx when y + x = 2 xy . 1. dy dx = radicalBig y x + 1 2 - radicalBig x y 2. dy dx = radicalBig y x - 1 1 - radicalBig x y correct 3. dy dx = radicalBig y x - 1 2 + radicalBig x y 4. dy dx = radicalBig y x + 1 1 - radicalBig x y
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mandel (tgm245) – HW07 – Radin – (56470) 2 5. dy dx = radicalBig y x + 1 2 + radicalBig x y 6. dy dx = radicalBig y x - 1 1 + radicalBig x y Explanation: Differentiating implicitly with respect to x , we see that dy dx + 1 = parenleftbiggradicalbigg y x + radicalbigg x y dy dx parenrightbigg , so dy dx parenleftbigg 1 - radicalbigg x y parenrightbigg = radicalbigg y x - 1 .
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