Let $T_{2}(x)$ be the Taylor polynomial of degree $2$ for the function $f(x) = \cos(x)$ at $a = 0$. Suppose you approximate $f(x)$ by $T_{2}(x)$. If $|x| \leq 1$, what is the bound for your error of your estimate?

Hint: use the alternating series approximation.

Answer: