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

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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 = 2 sin t, y = t, z = 2 cos t, 0 t π/ 2 (c) Z C x 3 y dx - x dy , 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 , 0) to the point (0 , π/ 2 , 3) (a) along a straight line (b) along the helix x = 3 cos t , y = t , z = 3 sin t 3. Show that F is a conservative vector field and find a potential function f such that F = f . (a) F ( x, y ) = sin y i + ( x cos y + sin y ) j (b) F ( x, y, z ) = (2 xy 3 + z 2 ) i + (3 x 2 y 2 + 2 yz ) j + ( y 2 + 2 xz ) k 4. Show that F is a conservative vector field and use this fact to evaluate Z C F ·
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