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Assignment 17-solutions

# Assignment 17-solutions - nanni(arn437 Assignment 17...

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nanni (arn437) – Assignment 17 – guntel – (54940) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Determine f x when f ( x, y ) = x sin( x + 2 y ) + cos( x + 2 y ) . 1. f x = 2 cos( x + 2 y ) - x sin( x + 2 y ) 2. f x = - 2 x sin( x + 2 y ) 3. f x = x cos( x + 2 y ) correct 4. f x = 2 sin( x + 2 y ) + x cos( x + 2 y ) 5. f x = - x sin( x + 2 y ) 6. f x = 2 cos( x + 2 y ) + x sin( x + 2 y ) 7. f x = 2 x cos( x + 2 y ) 8. f x = 2 sin( x + 2 y ) - x cos( x + 2 y ) Explanation: From the Product Rule we see that f x = sin( x +2 y )+ x cos( x +2 y ) - sin( x +2 y ) . Consequently, f x = x cos( x + 2 y ) . 002 10.0points Find the slope in the x -direction at the point (1, - 2, 2) on the graph of f when f ( x,y ) = xy 2 + x 2 y. Correct answer: 0. Explanation: The graph of f is a surface in 3-space and the slope in the x -direction at the point (1, - 2, 2) on that surface is the value of the partial derivative f x at (1 , - 2). Now f x = y 2 + 2 xy, so f x vextendsingle vextendsingle vextendsingle (1 , - 2) = 0 .

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Assignment 17-solutions - nanni(arn437 Assignment 17...

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