Winter 2007 - Takeda's Class - Exam 2 (Version 2)

Winter 2007 - Takeda's Class - Exam 2 (Version 2) - Math...

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Math 20C, Midterm 2 February 26, 2007 Name : PID : TA : Sec. No : Sec. Time : This exam consists of 6 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use one 4-by-6 index card, both sides. Score 1 10 2 10 3 10 4 10 5 10 Total 50 1
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1. (a) Let f ( x, y ) = x 2 sin( xy ) + 2 - ln x . Find f y . f y = - x 3 cos( xy ) (b) For z = y x 2 , sketch several level curves. 2
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(a) Find the arc length of the curve r ( t ) = 3 sin t i +2 t j +3 cos t k for 0 t 1 Since r 0 ( t ) = 3 cos t i + 2 j - 3 sin t k , we have | r 0 ( t ) | = p 9 cos 2 t + 4 + 9 sin 2 t = 13 . So the arc length is Z 1 0 13 dt = 13 . (b) Consider a particle moving in space with the following position vector. x ( t ) = e t i + t 2 j + 2 t k . Find the acceleration a ( t ). a ( t ) = x 00 ( t ) = e t i + 2 j . 3
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This note was uploaded on 04/29/2008 for the course MATH 20C taught by Professor Helton during the Winter '08 term at UCSD.

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Winter 2007 - Takeda's Class - Exam 2 (Version 2) - Math...

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