1. ## Taylor polynomial

Use taylor polynomial approximations to avoid loss of significance error.

(x - sin(x)) / x^3

2. Originally Posted by jzellt
Use taylor polynomial approximations to avoid loss of significance error.

(x - sin(x)) / x^3

Note that there is loss of significance at $x=0$.
$\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\dots$.
\begin{aligned}\frac{x-\sin x}{x^3}&=\frac{x-\left(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\dots\right)}{x^3}\\ &=\frac{1}{3!}-\frac{x^2}{5!}+\frac{x^4}{7!}-\dots\end{aligned}