# exam1 - pages 12 34 56 78 9 10 11 12 total scores Exam#1...

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pages 1 - 2 3 - 4 5 - 6 7 - 8 9 - 10 11 12 total scores Exam #1, October 17, Calculus III, Fall, 2006, Eugene Ha and W. Stephen Wilson I agree to complete this exam without unauthorized assistance from any person, materials or device. Name: Date: TA Name and section: NO CALCULATORS, NO PAPERS, SHOW WORK . This exam may well be too long. Use your time wisely. (48 points total) (1) (2 points) Let f : R 3 R 3 be given by f ( x, y, z ) = ( x 2 - y, xy + z, y 2 - xz ). Compute the divergence of f . (2) (2 points) Compute the derivative of f in problem # 1. 1

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2 (3) (2 points) Compute the curl of f in problem # 1, f ( x, y, z ) = ( x 2 - y, xy + z, y 2 - xz ). (4) (2 points) Let c : R R 3 be the path given by c ( t ) = ( t 3 - 1 , t 3 + 1 , t 2 + 3). What is the velocity at t ?
3 (5) (2 points) Let c be the path in problem # 4, c ( t ) = ( t 3 - 1 , t 3 +1 , t 2 +3). What is the speed at t = 1? (6) (2 points) Let c be the path in problem # 4. What is the acceleration at t = 1?

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4 (7) (2 points) Let
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## This note was uploaded on 10/15/2008 for the course 110 202 taught by Professor Wilson during the Fall '08 term at Johns Hopkins.

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exam1 - pages 12 34 56 78 9 10 11 12 total scores Exam#1...

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