L'Hôpital's rule

English

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L'Hôpital's rule

Wikipedia

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, ${\displaystyle \textstyle \lim _{x\to a}{\frac {f(x)}{g(x)}}=\lim _{x\to a}{\frac {f'(x)}{g'(x)}}}$. 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 ${\displaystyle a}$).

Translations

References