A9 - Math 128 ASSIGNMENT 9: Power, Taylor Series Winter...

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Unformatted text preview: Math 128 ASSIGNMENT 9: Power, Taylor Series Winter 2011 Due at 8:25 am on Wednesday, March 30 th in the correct drop slot across from MC4066 or in class depending on your instructor's preference. Assignments put into the wrong drop slot will not be marked. Note: This is the last assignment. Don't be scared by the 5-page length: two pages are examp- les, one is a template, and one has problems not to be submitted. So it's really a one-page assignment. Part A (answer only): Submit your answers using the template provided on the last page of this assignment, which you can print or hand-copy. 1. Find the interval of convergence (including a check of the end-points) for each of the given power series: a) X n =0 2 n x n n ! b) X n =1 n ! x n 2 n c) X n =1 3 n x n n 2 d) X n =1 2 n ( x + 1) n n 2 2. Use the geometric series test ( GST ) to write the function f ( x ) = 1 2 x + 3 as a power series centred at x = 0 , and state for what values of x the series converges. Part B (full solution): All solutions must be clearly stated and fully justi ed. 1. 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 of the series derived....
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A9 - Math 128 ASSIGNMENT 9: Power, Taylor Series Winter...

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