# Lagrange error bound. What is it?

Given a Taylor series with n terms, the Lagrange remainder is $R_n=\frac{f^{(n+1)}(\xi)}{(n+1)!}(x-x_0)^{n+1}$ for some $\xi$.
What you need to do is to find $f^{(n+1)}(x)$ and pick $|\xi|<0.5$ and $|x|<0.5$ so that $R_n$ is maximized. That tells you the maximum error when using the Taylor series with n terms as the approximation.