32B(W08)_PracticeFinal

# 32B(W08)_PracticeFinal - MATH 32B Lecture 4 Winter 2008...

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Unformatted text preview: MATH 32B - Lecture 4 - Winter 2008 Practice Final - March 12, 2008 NAME: STUDENT ID #: DISCUSSION SECTION: This is a closed-book and closed-note examination. Calculators are not allowed. Please show all your work. Use only the paper provided. You may write on the back if you need more space, but clearly indicate this on the front. There are 9 problems for a total of 200 points. POINTS: 1. 2. 3. 4. 5. 6. 7. 8. 9. TOTAL: 1 2 1. (25 points) Use Stokes’ theorem to calculate the line integral R C F d r where F ( x,y,z ) = x 2 y i + y 2 z j + xz k and C is the intersection of the plane x + 3 y + z = 4 with the cylinder x 2 + y 2 = 1 with orientation induced by the upward unit normal to the plane. 3 2. (25 points) Find the value of the surface integral RR S F d S where F ( x,y,z ) = x 2 y i + y 2 z j + xz k over the cube formed by the coordinate planes and the planes x = 1, y = 1, and z = 1. 4 3. (20 points) Find the work done by the force field F ( x,y,z ) = x 2 i + y 2 j + z 2 k in moving a particle along the path C given by r ( t ) = t i + 3 t 2 j- 2 t k , ≤ t ≤ 2. 5...
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32B(W08)_PracticeFinal - MATH 32B Lecture 4 Winter 2008...

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