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Practice-Final-2010 - 18.02A Practice Ques tions The actual...

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Unformatted text preview: 18.02A Practice Ques tions The actual exam will be about 1/3 fir st two weeks, 2/3 last two weeks. Use the last two problem sets to supplement the questions below on the last two weeks. (The practice questions below are evenly divided in terms of numbers, but the last five are more involved and would get mOre pOints.) Problem 1. a) In the xy-p lane, let F = Pi + Q j. Give in terms of P and Q the line integral representing the flux of F across a simple closed curve C, with outward-pointing normal. b) Let F = ax j + by j . How should the constants a itnd b be related if the fiu.., of F over any simple closed curve C is equal to the area inside C7 Pro bleI11 2. A solid hemisphere of radius 1 has its lower flat b"-Se on the xy-plane and center at the origin . Its density function is 0 = z. Find the force of gravitational attraction it exerts on a unit point mass at tbe origin Problem 3. Evaluate fc (y -x)dx+(y-z)dz over the lioesegrnent C [rom P: (1,1,1) to Q: (2 ,4,8) ....
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