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Unformatted text preview: Math 128 ASSIGNMENT 9 Winter 2010 Submit problems 1-4 by 8:20 am on Wednesday, March 31 st in the drop boxes across from MC4066, or in class depending on your instructors preference. All solutions must be clearly stated and fully justified . Comment: You are only required to hand in questions 1-4, although you ARE responsible for the rest of the questions for the exam. Plan to complete the assignment on your own well before the exam period starts, so that you have adequate time to review and prepare for exams. Solutions to this assignment will be posted at least a week before the exam. 1. Find the interval of convergence (including a check of the end-points) for each of the given power series: a) X n =1 n (2 x- 1) n 3 n b) X n =1 1 3 n ( x + 1) n c) X n =0 3 n ( x- 1) n n ! d) X n =0 cos( n ) x n 4 n 2. Use the geometric series test (GST) to write each of the given functions as a power series centred at x = a , and state for what values of x the series converges. a) f ( x ) = 3 x + 2 , a =- 1 b) f ( x ) = 1 1 + 8 x 3 , a = 0 3. Use known Maclaurin series for e x , 1 1- x , and sin x to derive Maclaurin series for the given functions. State the operations used, and the radius of convergence offor the given functions....
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