Chapter 11.2, Problem 73E

Exponential function In Section 11.3, we show that the power series for the exponential function centered at 0 is

$e^x={\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\frac{x^k}{k!}}$, for −∞ < x <∞.

Use the methods of this section to find the power series centered at 0 for the following functions. Give the interval of convergence for the resuming series.

74. f(x) = x^−3x