Guillaume de L'Hôpital

Sophia Zhang

Introduction

Born: 1661, Paris France.

Died: 2 February 1704 (≈ aged 43) Paris, France.

Nationality: French

Fields: Mathematician

Institutions: French Academy of Mathematics.

Distributions

Calculus Textbook.

In 1696 L'Hôpital published his book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes ("Infinitesimal calculus with applications to curved lines"). This was the first textbook on infinitesimal and it presented the ideas of differential calculus and their applications to differential geometry of curves of in a lucid form and with numerous figures

L'Hôpital's rule

In calculus, l'Hôpital's rule also called Bernoulli's rule, uses derivatives to help evaluate limits involving indeterminate forms.

The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital, who published the rule in his textbook, the first textbook on differential calculus. However, it is believed that the rule was discovered by the Swiss mathematician Johann Bernoulli.

In its simplest form, l'Hôpital's rule states that for functions f and g which are differentiable on I \ {c} , where I is an open interval containing c:

If

, and

 

exists, and

for all x in I with x ≠ c,

Then

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