every maclaurin series contains $$\frac{f^0(0)\cdot x^0}{0!}$$ well, at $x=0 \rightarrow x^0=0^0=0^1\cdot 0^{-1}=\frac{0}{0}$ which has no arithmetic meaning. I understand it is indeterminate, but we are not talking limits here because it is at a discrete integer $n=0$. I understand that we want the first term to evaluate to a constant but wouldn't this issue be avoided by rewriting it as?:
$$S=f(0)+\sum_{n=1}^{\infty}\frac{f^n(0)\cdot x^n}{n!}$$