20e_04s_fe

# 20e_04s_fe - Math 20E Final Exam 96 points 11:30AM Friday...

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Unformatted text preview: Math 20E Final Exam 96 points 11:30AM Friday June 11, 2004 • Print Name, ID number and Section on your blue book. • BOOKS and CALCULATORS are NOT allowed. Both sides of one page of NOTES is allowed. • You must show your work to receive credit. 1. (12 points) Given that A × B negationslash = , explain why the three vectors A | A | , A × B | A × B | and ( A × B ) × A | A × B | | A | are mutually orthogonal (i.e. mutually perpendicular) unit vectors. 2. (12 points) A surface is given by R = u cos v i − u sin v j + (4 − u 2 ) k for 0 ≤ u ≤ 2 and | v | ≤ π . (Note the minus sign on the j component.) Compute a unit normal to the surface such that the k component is positive. 3. (12 points) Find the value of the line integral integraldisplay C bracketleftbig (3 x + 4 y ) dx + (2 x + 3 y 2 ) dy bracketrightbig where C is the circle x 2 + y 2 = 4 traversed counterclockwise, that is, in the usual direction....
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## This note was uploaded on 06/18/2009 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.

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20e_04s_fe - Math 20E Final Exam 96 points 11:30AM Friday...

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