L'Hôpital's rule

See also: L'Hôpital's Rule, l'Hôpital's Rule, and l'Hôpital's rule

English

Alternative forms

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

Etymology

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

Pronunciation

• IPA^(key): /ˌloʊpiːˈtɑːlz ˈɹuːl/

Proper noun

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.

Usage notes

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

Translations

a rule which uses derivatives to help evaluate limits involving indeterminate forms

• Catalan: regla de L'Hôpital f
• French: règle de L’Hôpital f
• Galician: regra de l'Hôpital f
• Italian: regola di De l'Hôpital f
• Polish: reguła de l'Hospitala f
• Portuguese: regra de L'Hôpital f, regra de L'Hospital f
• Romanian: regula lui l'Hôpital f
• Spanish: regla de l'Hôpital f
• Turkish: L'Hôpital kuralı, L'Hospital kuralı