Spring 2007 - Takeda's Class - Practice Exam 2

Spring 2007 - Takeda's Class - Practice Exam 2 - Math 20E,...

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Unformatted text preview: Math 20E, Practice Midterm 2 May 21, 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. 4. Show your ID on your desk. Score 1 10 2 10 3 10 4 10 5 10 Total 50 1 1. (a) Find the arc length of the path given by x ( t ) = 7 i + t j + t 2 k , 1 ≤ t ≤ 3. Answer : Z 3 1 || x ( t ) || dt = Z 3 1 || j + 2 t k || dt = Z 3 1 √ 1 + 4 t 2 dt. Note : It seems to be extremely difficult to compute R √ 1 + 4 t 2 dt . In- deed, R √ 1 + 4 t 2 dt = t √ 1+4 t 2 2 + 1 4 sinh- 1 (2 t ). For the actual exam, I will carefully choose the problems so that this kind of situation will never happen. (b) Show that the vector field F = 2 x i + 2 y j- 3 k is a gradient field....
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This note was uploaded on 04/30/2008 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.

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Spring 2007 - Takeda's Class - Practice Exam 2 - Math 20E,...

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