How can one find out $f^{(k)}(x)$ for $k \in \mathbb{N}$ and the n-th taylor series $P_n(x)$ for
$f(x) = \sinh(x)$ at $a = 0$
$f(x) = x^4$ at $a = 1$
$f(x) = \frac{1}{1+2x}$ at $a = 0$
And for which x does $R_n(x) \to 0$ for $n \to \infty$ hold? My guess is only the last one because $x^4$ just goes towards $\infty$while the last one goes to $0$ for lim x $\to \infty$. And lim $x \to \infty$ for $\sinh(x)$ is $\infty.$
With WolframAlpha I used the taylor series calculator and I get results, but how does with work for the n-th taylor series?