L’Hôpital’s rule:
for functions $f$ and $g$ which are differentiable on $I \backslash{c}$ , where $I$ is an open interval containing $c$, if

then

Stolz-Cesàro theorem:
for real-number sequences $(a_n) _{n \ge 1}$ and $(b_n)_{n \ge 1}$, assume $b_n$ is stictly increasing and unbounded, and

then