Guillaume de l'Hôpital

File:Guillaume François Antoine, Marquis de l'Hôpital.jpg

Guillaume François Antoine, Marquis de l'Hôpital (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 both approach zero or infinity.

L'Hôpital is commonly spelled as both "L'Hospital" and "L'Hôpital." The Marquis spelt his name with an 's'; however, the French language has since dropped the 's' (it was silent anyway) and replaced its preceding vowel with a circumflex.

L'Hospital was born in Paris, France. He initially had planned a military career, but poor eyesight caused him to switch to mathematics. He solved the brachistochrone problem, independently of other contemporary mathematicians, such as Isaac Newton. He died in Paris.

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. It is the method for solving such indeterminate forms through repeated differentiation that bears his name.