Chapter 6.3, Problem 170E

In the following exercises, use the fact that if $q(x)={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n{(n–c)}^n}$ converges in an interval containing c, then $\underset{x\to c}{\lim }q(x)=a_0$ to evaluate each limit using Taylor series.

170. $\underset{x\to 0}{\lim }\frac{\cos x-1}{x^2}$