Chapter 11.3, Problem 39E

Manipulating Taylor series Use the Taylor series in Table 11.5 to find the first four nonzero terms of the Taylor series for the following functions centered at 0.

39. $\{\begin{array}{cc}\frac{e^x-1}{x}& \text{if }x\ne \text{1}\\ 1& \text{if }x=\text{1}\end{array}$