L'Hopital's rule


L'Ho·​pi·​tal's rule ˌlō-pē-ˈtälz- How to pronounce L'Hopital's rule (audio)
variants or L'Hospital's rule
: a theorem in calculus: if at a given point two functions have an infinite limit or zero as a limit and are both differentiable in a neighborhood of this point then the limit of the quotient of the functions is equal to the limit of the quotient of their derivatives provided that this limit exists

Word History


Guillaume de l'Hôpital †1704 French mathematician

First Known Use

1918, in the meaning defined above

Time Traveler
The first known use of L'Hopital's rule was in 1918

Dictionary Entries Near L'Hopital's rule

Cite this Entry

“L'Hopital's rule.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/L%27Hopital%27s%20rule. Accessed 24 May. 2024.

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