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Unformatted text preview: Math 20C, Final Exam March 21, 2007 Name : PID : TA : Sec. No : Sec. Time : This exam consists of 11 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 two 4by6 index cards, both sides. 4. You have two hours for this exam. Score 1 10 2 10 3 6 4 10 5 12 6 10 7 10 8 10 9 10 10 12 Total 100 1 1. (a) Let f ( x,y ) = xe y 2 . What is f xy ? f x = e y 2 , and so f xy = 2 ye y 2 . (b) Compute the double integral Z π Z x sin y dy dx Z π Z x sin y dy dx = Z π cos y y = x y =0 dx = Z π ( cos x + 1) dx = ( sin x + x ) π = π. 2 2. (a) Let f ( x,y,z ) = cos x + e x y 2 z . Find a symmetric equation of the line which goes through the origin and which is parallel to ∇ f (0 , 2 , 1) Since ∇ f ( x,y,z ) = ( sin x + e x y 2 z ) i + 2 e x yz j + e x y 2 k . we have ∇ f (0 , 2 , 1) = 4 i 4 j + 4 k . Hence any vector which is parallel to 4 i 4 j + 4 k can be a direction vector of the line. So let us choose i + j k . Hence the symmetric equation of the line is x = y = z 1 . (b) Find the velocity vector of a particle that has the following acceleration and the initial velocity....
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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.
 Winter '08
 Helton
 Math

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