MARKED PROBLEM (-1 )nan+lyn+1 In this problem, we investigate the power series M 8 3n+1(n + 1) (a) Show that E is the Taylor series for the function f(x) = In 4x 3n+1(n + 1) 3 +1) n=0 centred on r = 0. (b) For which values of a is the series equal to In 4.x 3 + 00 (c) If we multiply the series by a* we get a*) (-1)nantlyn+5 3n+1(n + 1) n=0 3n+1(n + 1) , a re- n=0 lated power series, which is equal to * In 4.x " + 1 on the same interval you identified in part b. Express x4 In 3 + 1) dx as a power series in c. (d) Let g(x) = x4 In + 1. Find g'(x), and the Maclaurin series for g'(I). Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)