Methods from Taylor polynomials

To construct the degree-$n$ Taylor polynomial of $f$ about $a$:

1. choose the centre $a$ and degree $n$;
2. calculate $f(a),f'(a),\ldots,f^{(n)}(a)$;
3. substitute those values into $$P_n(x)=\sum_{k=0}^{n}\frac{f^{(k)}(a)}{k!}(x-a)^k;$$
4. use Taylor's theorem to quantify the error of the approximation.