Mathematics 317 T2Assignment#5

Mathematics 317 T2Assignment#5 - where C is the circle 2 2...

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Mathematics 317 T2 Assignment #5 due Friday, February 12, 2010 1. If - + + = C d y x y x r F j i F evaluate , ) 2 3 ( ) 2 ( where C is: (a) The straight line path from (0,0) to (1,1). (b) The parabolic path 2 x y = from (0,0) to (1,1). 2. Let . k j i F z y xy + - = Evaluate 1 0 P P d r F along the straight line path from 0 P to 1 P in each of the following cases. (a) ). 0 , 0 , 1 ( ), 0 , 0 , 0 ( 1 0 = = P P (b) ). 0 , 2 , 1 ( ), 0 , 0 , 1 ( 1 0 = = P P (c) ). 3 , 2 , 1 ( ), 0 , 2 , 1 ( 1 0 = = P P (d) ). 3 , 2 , 1 ( ), 0 , 0 , 0 ( 1 0 = = P P (e) ). 3 , 2 , 1 ( ), 0 , 0 , 1 ( 1 0 = = P P (f) ). 0 , 2 , 1 ( ), 0 , 0 , 0 ( 1 0 = = P P Can one deduce the answers for cases (d) to (f) from knowing the answers for cases (a) to (c)? Explain your answer. 3. Evaluate the integral , 2 2 + - C y x ydx xdy
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Unformatted text preview: where C is the circle 2 2 2 a y x = + taken in the counterclockwise sense. What is the answer if C is the same circle taken in the clockwise sense? How does the answer depend on the radius of the circle? 4. Suppose a particle moves counterclockwise around the square , 1 , 1 y x z = 0 under the action of the force . ) 2 ( ) ( 2 2 k j i F x x y y x + + +-= Calculate the work done....
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