Consider the power series f(x) =5(-1)* · 2* k +1 Problem 2: (x- 1)3k. k=0 For the duration of this problem, pn(x) will represent the n- th order Taylor polynomial centered at r = 1. A Do the following. Exhibit p3(x), P6(x), p9(x), and p12(x) in the space below. Graph all of the Taylor polynomials above on the same set of axes for -1 < x < 3. Include an mage of your graph below. ii. iii. Based on your graph, estimate a value for the radius of convergence for the power series f(x) = 3·(-1)* . 2k k + 1 -(x – 1)3k. k=0

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