L'hopital in english

Application of l hospital rule in real life
L'hospital rule proof
Guillaume de l'hôpital cause of death

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L’hospital(L

(b. Paris, France, 1661; d. Paris, 2 February 1704),

mathematics.

The son of Anne-Alexandre de L’Hospital and of Elizabeth Gobelin, L’Hospital served for a time as a cavalry officer but resigned from the army because of nearsightedness. From that time onwards he devoted his energies entirely to mathematics. He married Marie-Charlotte de Romilley de La Chesneiaye, who bore him one son and three daughters.

L’Hospital’s mathematical talents were recognized when he was still a boy. It is reported that when he was only fifteen years of age he solved, much to the surprise of his elders, a problem on the cycloid which had been put forward by Pascal. Later he contributed solutions to several problems posed by Jean (Johann) Bernoulli, among them the problem of the brachistochrone, which was solved at the same time by three others—Newton, Leibniz, and Jacques (Jakob) Bernoulli. His memory has survived in the name of the rule for finding the limiting value of a fraction whose numerator and denominator tend to zero. However, in his own time, and for several generations

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L'Hôpital's rule

Mathematical rule for evaluating some limits

L'Hôpital's rule (, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily evaluated by substitution. The rule is named after the 17th-century FrenchmathematicianGuillaume De l'Hôpital. Although the rule is often attributed to De l'Hôpital, the theorem was first introduced to him in 1694 by the Swiss mathematician Johann Bernoulli.

L'Hôpital's rule states that for functions f and g which are defined on an open intervalI and differentiable on for a (possibly infinite) accumulation pointc of I, if and for all x in , and exists, then

The differentiation of the numerator and denominator often simplifies the quotient or converts it to a limit that can be directly evaluated by continuity.

History

Guillaume de l'Hôpital (also written l'Hospital^[a]) publis

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Guillaume François Antoine Marquis de L'Hôpital

To give Guillaume de l'Hôpital's full name would take a whole paragraph so we give just a much shortened version: Guillaume-François-Antoine Marquis de l'Hôpital, Marquis de Sainte-Mesme, Comte d'Entremont and Seigneur d'Ouques-la-Chaise. The family had been a prominent one in France over many generations going back to around the 12th century. There are various spellings of the name Hôpital, the earlier versions being l'Hospital or Lhospital with l'Hôpital being a relatively modern form of the name. His father was Anne-Alexandre de l'Hôpital, a Lieutenant-general in the King's Army; he was Comte de Sainte-Mesme and Duc d'Orléans. Guillaume's mother was Elisabeth Gobelin, the daughter of Claude Gobelin who was an Intendant in the King's Army and a Councillor of State. Sturdy writes [5]:-

The prominent association which Anne-Alexandre de l'Hôpital had with the house of Orléans and the trust which Gaston d'Orléans placed in him conferred a brilliant lustre on the reputation of the l'Hôpitals; it also afforded them a protection