A Taylor polynomial is a polynomial that approximates a function. It is defined as follows:
$$p_{n}(x)=f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+...+\frac{f^{(n)}(a)}{n!}(x-a)^{n}$$
where $f^{(n)}(a)$ is the nth derivative of the function evaluated at the point
Show more…