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discoveries as he pleased. L'Hpital authored the first textbook on calculus, "l'Analyse des

Infiniment Petits pour l'Intelligence des Lignes Courbes", which mainly consisted of the work

of Bernoulli, including what is now known asL'Hpital's rule.In calculus,l'Hpital's rule

(also calledBernoulli's rule) uses derivatives to help evaluate limits involving indeterminate

forms. Application (or repeated application) of the rule often converts an indeterminate form

to a determinate form, allowing easy evaluation of the limit. The rule is named after the 17th-

century French mathematician Guillaume de l'Hpital, who published the rule in his book

l'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes(literal translation:

Analysis of the Infinitely Small to Understand Curved Lines) (1696), the first textbook on

differential calculus. However, it is believed that the rule was discovered by the Swiss

mathematician Johann Bernoulli.

The Stolz-Cesro theorem is a similar result involving limits of sequences, but it uses finite

difference operators rather than derivatives.

In its simplest form, l'Hpital's rule states that for functions and g:

If or and exists,

then

The differentiation of the numerator and denominator often simplifies the quotient and/or

converts it to a determinate form, allowing the limit to be evaluated more easily

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