Final_Fall-2007-2008_3

# Final_Fall-2007-2008_3 - FINAL EXAMINATION MATH 201...

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FINAL EXAMINATION MATH 201 January 24, 2008, 11:30-1:30pm Name: Student number: Section number (Encircle): 21 22 23 Instructions: No calculators are allowed. There are two types of questions: Part I consists of ten multiple choice questions out of 5 points each with exactly one correct answer. Part II consists of ﬁve work-out problems out of 10 points each. Give a detailed solution for each of these problems.

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Part I: 1 - The series n =2 ( - 1) n nlnn : a. Converges absolutely b. Converges conditionally c. Diverges 2. The interval of convergence of the power series n =1 ( x + π ) n n is: a. ] - 1 - π, 1 - π [ b.] - 1 - π, 1 - π ] c. [ - 1 - π, 1 - π [ d. [ - 1 - π, 1 - π ] e. None of the above 3. The Maclaurin series of the function R x 1 ln (1 - t ) t dt is: a. - n =0 x n +1 ( n +1) 2 d. - n =1 x n +1 n ( n +1) b. - n =1 x n +1 ( n +1) 2 e. None of the above. c. - n =0 x n n ( n +1)
4. The function f ( x, y, z ) at a point P decreases most rapidly in the direction of v = i - 2 j + 3 k . In this direction the value of

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Final_Fall-2007-2008_3 - FINAL EXAMINATION MATH 201...

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