fitch4 - F d r C along the curve C given by r t (29 = t , t...

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NAME__________________________________ Math 22 Fall 2000 Test 4 Work 7 of the 8 problems, and CROSS OUT the one you choose not to work. Each problem is worth 14 points, and you get 2 points for free, for a total of 100 points. You must show all work in order to receive full credit. 1. Evaluate the line integral F d r C where F x , y ( 29 = 2 xy i + x 2 j + k and the curve C is given by the vector function r t (29 = t 2 i + t 3 j + t k , 0 t 1. 2. Evaluate xyds C where C is the line segment from - 1,1 ( 29 to 2,3 ( 29 . 3. Find the work done by the vector field F x , y ( 29 = xy i + x 2 j in moving a particle along the curve r t (29 = t i + 2 t j , 0 t 1. 4. Find the curl and divergence of the vector field F x , y , z ( 29 = e xyz i + sin x - y ( 29 j - xy z k . 5. The vector field F x , y , z ( 29 = 2 xy 3 z 4 i + 3 x 2 y 2 z 4 j + 4 x 2 y 3 z 3 k is conservative. Use this fact to evaluate
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Unformatted text preview: F d r C along the curve C given by r t (29 = t , t 2 , t 3 for 0 t 2. 6. Evaluate the line integral x 2 dy C along the triangular path consisting of the line segments from 0,0 ( 29 to 2,3 ( 29 , 2,3 ( 29 to 1,0 ( 29 , and 1,0 ( 29 to 0,0 ( 29 . Hint: Dont try to make this too hard! 7. Find the equation of the plane tangent to the parametric surface x = u-v , y = u + v , z = u 2 at the point 0,2,1 ( 29 . 8. Evaluate the surface integral x + y ( 29 dS S where S is the part of the plane x = z that lies above the square with vertices with vertices 0,0 ( 29 , 1,0, ( 29 , 0,1, ( 29 ,and 1,1 ( 29 ....
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fitch4 - F d r C along the curve C given by r t (29 = t , t...

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