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Guillaume Franšois Antoine, Marquis de l'H˘pital
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Guillaume Franšois Antoine, Marquis de l'H˘pital

Guillaume Franšois Antoine, Marquis de l'H˘pital (1661 - February 2, 1704) was a French mathematician. He is perhaps best known for the rule which bears his name for calculating the limiting value of a fraction whose numerator and denominator approach zero.

He is also the author of the first known book on differential calculus, L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. Published in 1696, the text includes the lectures of his teacher, Johann Bernoulli, in which Bernoulli discusses the indeterminate form 0/0.

His name is also spelled l'Hospital. The circumflex in "l'H˘pital" is an anachronism; it was not in use at the time l'H˘pital was alive.

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