Taylor Approximation

Approximate a function at a value a

$$\begin{aligned} f(x)&=f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^2+\dots \\ &=\sum_{n=0}^\infty{\frac{f^{(n)}(a)}{n!}(x-a)^n} \end{aligned}$$ So??

Use it to simplify a function near a value (by not going to infinity).