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Homework 10 - vu(tv2894 Homework 10(Quest miner(55096 This...

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vu (tv2894) – Homework 10 (Quest) – miner – (55096) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find dy/dx when 2 x 3 + y 3 - 9 xy - 1 = 0 . 1. dy dx = 2 x 2 + 3 y y 2 - 3 x 2. dy dx = 2 x 2 - 3 y y 2 + 3 x 3. dy dx = 3 y + 2 x 2 y 2 + 3 x 4. dy dx = 2 x 2 - 3 y y 2 - 3 x 5. dy dx = 3 y - 2 x 2 y 2 - 3 x correct Explanation: We use implicit differentiation. For then 6 x 2 + 3 y 2 dy dx - 9 y - 9 x dy dx = 0 , which after solving for dy/dx and taking out the common factor 3 gives 3 parenleftBig (2 x 2 - 3 y ) + dy dx ( y 2 - 3 x ) parenrightBig = 0 . Consequently, dy dx = 3 y - 2 x 2 y 2 - 3 x . keywords: implicit differentiation, Folium of Descartes, derivative, 002 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 1 - radicalBig x y 4. dy dx = radicalBig y x + 1 1 + radicalBig x y 5.
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