Taylor polynomial
For a suitably differentiable $f(x)$, the taylor polynomial for $T_n$ about $c$ is defined by:
$T_n(x) = f(c) + f^{(1)}(c) \frac{(x-c)}{1!} + f^{(2)}(c) \frac{(x-c)^2}{2!} + \cdots + f^{(n)}(c) \frac{(x-c)^n}{n!}$
This polynomial closely tracks $f$, a fact roughly quantified by $f(x) - T\_n(x)$ being $\mathcal{o}((x-c)^n)$. This animation shows $T_n$ for an adjustable value of $n$ for the function $f(x) = \sin(x^2/4 - x/2)$.
Show $T_n, n=$
Show $T_1, T_2, ..., T_n$