L'Hôpital's rule

• L'Hôpital's Rule, l'Hôpital's Rule, l'Hôpital's rule
• L'Hospital's rule
• rule of L'Hôpital, rule of l'Hôpital

Named after French mathematician Guillaume de l'Hôpital (1661–1704).

• IPA^(key): /ˌloʊpiːˈtɑːlz ˈɹuːl/^[1]

L'Hôpital's rule

1. (mathematics) The rule that the limit of the ratio of two functions equals the limit of the ratio of their derivatives, usable when the former limit is indeterminate and the latter limit exists.

In mathematical terms, ${\displaystyle \textstyle \lim _{x\to a}{\frac {f(x)}{g(x)}}=\lim _{x\to a}{\frac {f'(x)}{g'(x)}}}$. The rule is applicable if the former limit turns out to be ${\displaystyle \textstyle {\frac {0}{0}}}$ or ${\displaystyle \textstyle {\frac {\infty }{\infty }}}$ and requires that the latter limit exist (including that ${\displaystyle \textstyle g'(x)\neq 0}$ for all ${\displaystyle x\neq a}$ in some interval around ${\displaystyle a}$).