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Unformatted text preview: MATH 231, Calculus III, Section 1, Fall 2007 Final Exam Date: Dec. 11, Tuesday Time: 9:00 am 12:00 noon Please write clearly, reduce answers to their simplest form, and box your answers. To receive full credit you must show ALL your work. Student's Name (Please print): __________________________________________ Pledge: On my honor as a student at the University of Virginia I have neither given nor received aid on this test. Signature: _______________________________ Problem Points Score 1 15 2 15 3 20 4 20 5 25 6 25 7 20 8 20 9 10 10 15 11 15 12 25 13 25 14 25 15 25 16 (Bonus) 25 Total 325/300 Problem 1 (15 points) (a) (5 points) For what value(s) of t are a = h t + 2 , t, t i and b = h t 2 , t + 1 , 1 i orthogonal? (b) (10 points) Consider the surface S given by 2 2 cos = 3 in spherical coordinates. Convert the equation into an equation in rectangular coordinates and identify (describe) the surface....
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 Spring '09
 Stojanovic
 Calculus

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