final04fall - McGILL UNIVERSITY FACULTY OF SCIENCE FINAL...

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McGILL UNIVERSITY FACULTY OF SCIENCE FINAL EXAMINATION MATHEMATICS 262 Examiner: Professor Jakobson Date: Thursday, December 9, 2004 Associate Examiner: Professor Jaksic Time: 14:00 A.M. - 17:00 INSTRUCTIONS Answer all seven questions. Each question is worth 10 points. Please give a detailed explanation for each answer. Non-programmable calculators are permitted. This is a closed-book exam This exam comprises the cover and two pages of questions.
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MATH 262: FINAL EXAM page 1 Problem 1. (10 points) Consider power series X n =2 ( - 1) n x n n ( n - 1) . a) [2 pts] Find the radius of the convergence of the power series. b) [2 pts] Find the interval of convergence of the power series. c) [2 pts] Find the second derivative of the power series. d) [4 pts] Find the sum of the original power series. Problem 2. (10 points) Consider the circular helix r ( t ) = 3 cos t i + 3sin t j + 4 t k . a) [3 pts] Parametrize r in terms of the arc length r ( s ) measured from the point (1 , 0 , 0) in the direction of increasing
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final04fall - McGILL UNIVERSITY FACULTY OF SCIENCE FINAL...

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