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Exam3Review - Math 2500 Fall 2009 Exam 3 - Practice...

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Unformatted text preview: Math 2500 Fall 2009 Exam 3 - Practice Questions 1. Evaluate the given line integral. (a) Z C yz 2 ds , where C is the line segment from (- 1 , 1 , 3) to (0 , 3 , 5) (b) Z C x 3 z ds , where C : x = 2sin t, y = t, z = 2cos t, t / 2 (c) Z C x 3 y dx- xdy , where C is the circle x 2 + y 2 = 1 with counterclockwise orientation (d) Z C x sin y dx + xyz dz , where C is given by r ( t ) = t i + t 2 j + t 3 k , 0 t 1 (e) Z C F d r , where F ( x,y ) = x 2 y i + e y j and C is given by r ( t ) = t 2 i- t 3 j , 0 t 1 (f) Z C F d r , where F ( x,y,z ) = h x + y,z,x 2 y i and C is given by r ( t ) = h 2 t,t 2 ,t 4 i , 0 t 1 2. Find the work done by the force field F ( x,y,z ) = z i + x j + y k in moving a particle from the point (3 , , 0) to the point (0 ,/ 2 , 3) (a) along a straight line (b) along the helix x = 3cos t , y = t , z = 3sin t 3. Show that F is a conservative vector field and find a potential function f such that F = f ....
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This note was uploaded on 03/13/2010 for the course MATH 0314 taught by Professor Ivoklemes during the Spring '10 term at McGill.

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Exam3Review - Math 2500 Fall 2009 Exam 3 - Practice...

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