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HW_10_Key

# HW_10_Key - Miller Kierste Homework 10 Due Nov 1 2007 3:00...

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Miller, Kierste – Homework 10 – Due: Nov 1 2007, 3:00 am – Inst: JEGilbert 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Determine f x - f y when f ( x, y ) = 2 x 2 - 3 xy + y 2 + x + 2 y . 1. f x - f y = 7 x - y - 1 2. f x - f y = x - y + 3 3. f x - f y = 7 x - 5 y - 1 correct 4. f x - f y = 7 x - 5 y + 3 5. f x - f y = x - 5 y + 3 6. f x - f y = x - y - 1 Explanation: After differentiation we see that f x = 4 x - 3 y + 1 , f y = - 3 x + 2 y + 2 . Consequently, f x - f y = 7 x - 5 y - 1 . keywords: partial derivative, first order par- tial derivative, polynomial 002 (part 1 of 1) 10 points Determine f x when f ( x, y ) = x sin( y - x ) - cos( y - x ) . 1. f x = - x sin( y - x ) 2. f x = x cos( y - x ) - sin( y - x ) 3. f x = 2 sin( y - x ) - x cos( y - x ) 4. f x = x sin( y - x ) 5. f x = - x cos( y - x ) correct 6. f x = - 2 sin( y - x ) - x cos( y - x ) 7. f x = - cos( y - x ) - x sin( y - x ) 8. f x = x cos( y - x ) Explanation: From the Product Rule we see that f x = sin( y - x ) - x cos( y - x ) - sin( y - x ) . Consequently, f x = - x cos( y - x ) . partial derivative, first order partial deriva- tive, trig function, keywords: 003 (part 1 of 1) 10 points Determine f x when f ( x, y ) = (3 xy - 1) e - xy . 1. f x = x (2 - 3 xy ) e - xy 2. f x = x (2 - xy ) e - xy 3. f x = y (3 xy - 4) e - xy 4. f x = y (4 - 3 xy ) e - xy correct 5. f x = y (2 - 3 xy ) e - xy 6. f x = x ( xy - 4) e - xy 7. f x = x (4 - xy ) e - xy 8. f x = y (2 + 3 xy ) e - xy Explanation: From the Product Rule we see that f x = 3 ye - xy - y (3 xy - 1) e - xy .

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Miller, Kierste – Homework 10 – Due: Nov 1 2007, 3:00 am – Inst: JEGilbert 2 Consequently, f x = y (4 - 3 xy ) e - xy . keywords: partial derivative, first order par- tial derivative, exp function, 004 (part 1 of 1) 10 points Determine h = h ( x, y ) so that ∂f ∂x = h ( x, y ) (5 x 2 + 3 y 2 ) 2 when f ( x, y ) = 3 x 2 y 5 x 2 + 3 y 2 . 1. h ( x, y ) = 9 xy 3 2. h ( x, y ) = 18 xy 3 correct 3. h ( x, y ) = 18 x 3 y 4. h ( x, y ) = 18 xy 2 5. h ( x, y ) = 9 x 3 y 6. h ( x, y ) = 9 xy 2 Explanation: Differentiating with respect to x using the quotient rule we obtain ∂f ∂x = 6 xy (5 x 2 + 3 y 2 ) - 30 x 3 y (5 x 2 + 3 y 2 ) 2 .
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