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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20C Final Examination (blue) June 9, 2008 Turn off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If necessary, write see other side and continue working on the back of the same sheet. If any question is not clear, ask for clarification. # Points Score 1 6 2 6 3 8 4 6 5 6 6 6 7 8 8 6 9 12 64 1. (6 points) Consider the two planes given by 2 x y + z = 5 and x + y z = 1. (a) Find the angle (in radians) between the two planes. You may leave your answer in the form of an inverse trigonometric function of a number. (b) Find a vector equation for the line of intersection of the two planes. 2. (6 points) Consider the function f ( x, y ) = 2 x 3 3 x 2 + y 2 12 x + 10. (a) Find the critical points of f . (b) Classify each critical point of f as a local minimum, local maximum or saddle point of f . 3. (8 points) Consider the iterated integral integraldisplay 2...
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This note was uploaded on 12/08/2011 for the course MATH 20C 20C taught by Professor Boonyeap during the Fall '07 term at UCSD.
 Fall '07
 BoonYeap

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