7. . . 1 (a) In the lectures we found the Maclaurin series for f(:1:) = . Use this series and the unique- 1w ness theorem to find the Maclaurin series for g(a:) = 14122' (b) An alternative method to find this series is to note that g(a:) = 1 + x is the derivative of 1n(1 + x). The series for 1n(1 + x) (found in the lectures) is given by x2 3:3 0 \"1&1 1n(1+x)~$3++m =k;(k Differentiate this series term by term to obtain the series for g(:c) = Hx, and confirm that this is the same as the series found in part (a). 1 . . . 1 (c) Use the Maclaurin series for g(x) = to find the Maclaurin series for h(x) = . 1+x 1+2x