View source for L'Hôpital's rule

{{also|L'Hôpital's Rule|l'Hôpital's Rule|l'Hôpital's rule}}
==English==
{{wikipedia}}

===Alternative forms===
* {{alter|en|L'Hôpital's Rule|l'Hôpital's Rule|l'Hôpital's rule}}
* {{alter|en|L'Hospital's rule}}
* {{alter|en|rule of L'Hôpital|rule of l'Hôpital}}

===Etymology===
Named after French mathematician {{w|Guillaume de l'Hôpital}} (1661–1704).

===Pronunciation===
* {{IPA|en|/ˌloʊpiːˈtɑːlz ˈɹuːl/}}<ref>{{R:Merriam-Webster Online|L'Hopital's rule|accessdate=30 April 2017}}</ref>

===Proper noun===
{{en-proper noun}}

# {{lb|en|mathematics}} The [[rule]] that the [[limit]] of the ratio of two functions equals the limit of the ratio of their [[derivative]]s, usable when the former limit is [[indeterminate]] and the latter limit exists.

====Usage notes====
In mathematical terms, <math>\textstyle\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}</math>. The rule is applicable if the former limit turns out to be <math>\textstyle\frac{0}{0}</math> or <math>\textstyle\frac{\infty}{\infty}</math> and requires that the latter limit exist (including that <math>\textstyle g'(x)\ne 0</math> for all <math>x \ne a</math> in some interval around <math>a</math>).

====Translations====
{{trans-top|a rule which uses derivatives to help evaluate limits involving indeterminate forms}}
* Catalan: {{t|ca|regla de L'Hôpital|f}}
* French: {{t|fr|règle de L'Hôpital|f}}
* Galician: {{t|gl|regra de l'Hôpital|f}}
* Italian: {{t|it|regola di De l'Hôpital|f}}
* Polish: {{t|pl|reguła de l'Hospitala|f}}
* Portuguese: {{t|pt|regra de L'Hôpital|f}}, {{t|pt|regra de L'Hospital|f}}
* Romanian: {{t|ro|regula lui l'Hôpital|f}}
* Spanish: {{t|es|regla de l'Hôpital|f}}
* Turkish: {{t|tr|L'Hôpital kuralı}}, {{t|tr|L'Hospital kuralı}}
{{trans-bottom}}

===References===
<references/>

{{cln|en|eponyms}}