Taylor series

Taylor series, L'Hôpital and Leibniz

Expanding about $x=a$ instead of $0$ gives the Taylor series $f(x)=\sum\frac{f^{(r)}(a)}{r!}(x-a)^r$. Series also crack "$\frac00$" limits (as does L'Hôpital's rule), and Leibniz's theorem gives the $n$th derivative of a product like a binomial expansion.