Chapter 9.3, Problem 64E

Any method

1. a. Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.
2. b. Determine the radius of convergence of the series.

64. $f(x)=\{\begin{array}{ll}\frac{\sin x}{x}\hfill & \text{if}x\ne 0\hfill \\ 1\hfill & \text{if}x=0\hfill \end{array}$