Vicipaedia

Quantum redactiones paginae "Hospitalii regula" differant

Browse history interactively
← Differentia superiorDifferentia proxima →
Content deleted Content added
VisualWikitext
SieBot (disputatio | conlationes)
66 241 edits
m robot Modifying: hu:L’Hospital-szabály
m progressus et {{in progressu}}
Linea 1:
{{in progressu}}
'''Hospitalii regula''' est regula abs [[Marchio Hospitalius|Marchione Hospitalio]] proposita, qua [[derivativus|derivativi]] usurpantur ad fines indeterminatas computandas.▼
 
▲'''Hospitalii regula''' est regula abs[[calculus infinitessimalis|calculi infinitessimalis]] pro [[Marchio Hospitalius|Marchione Hospitalio]] propositanominata, qua [[derivativus|derivativi]] usurpantur ad fines indeterminatas computandas.
 
Fertur [[Ioannes Bernoulli]] re vera regulam proposuisse, quia Marchio Ioannem conduxit pretio per annum 300 [[francus (pecunia)|francis]] ad auxilium in rebus aerumnisque solvendis mathematicis dandum.<ref>Finney, Ross L. and George B. Thomas, Jr. Calculus. 2nd Edition. P. 390. Addison Wesley, 1994.</ref>
 
<!--
 
In [[calculus]], '''l'Hôpital's rule''' (often incorrectly '''l'Hospital's rule''') uses [[derivative]]s to help compute [[limit (mathematics)|limit]]s with [[indeterminate form]]s. Application (or repeated application) of the rule often converts an indeterminate form to a [[indeterminate form|determinate form]], allowing easy computation of the limit. The rule is named after the [[17th century|17th-century]] French mathematician [[Guillaume de l'Hôpital]], who published the rule in his book ''Analyse des infiniment petits pour l'intelligence des lignes courbes'' (literally: Analysis of the infinitely small to understand curves) ([[1696]]), the first book to be written on [[differential calculus]].
-->
 
==Explicatio==
The rule is believed to be the work of [[Johann Bernoulli]] since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300 Francs per year to keep him updated on developments in calculus and to solve problems he had. Among these problems was that of limits of indeterminate forms. When l'Hôpital published his book, he gave due credit to Bernoulli and, not wishing to take credit for any of the mathematics in the book, he published the work anonymously. Bernoulli, who was known for being extremely jealous, claimed to be the author of the entire work, and until recently, it was believed to be so. Nevertheless, the rule was named for l'Hôpital, who never claimed to have invented it in the first place<ref>Finney, Ross L. and George B. Thomas, Jr. Calculus. 2nd Edition. P. 390. Addison Wesley, 1994.</ref>.
===Praefatio===
 
InSimplicissime simple casesdictum, l'Hôpital's rule statesregula thatdicit forin functionsfunctionibus ''f''(''x'') andet ''g''(''x''), ifsi ''f''(''c'')=''g''(''c'')=0 orvel ''f''(''c'')=''g''(''c'')=<math>\infty</math>, thendein:▼
==Overview==
===Introduction===
 
▲In simple cases, l'Hôpital's rule states that for functions ''f''(''x'') and ''g''(''x''), if ''f''(''c'')=''g''(''c'')=0 or ''f''(''c'')=''g''(''c'')=<math>\infty</math>, then:
 
:<math>\lim_{x\to c}\frac{f(x)}{g(x)} = \lim_{x\to c}\frac{f'(x)}{g'(x)}</math>
where the prime (') denotes the [[derivative]].
 
Among other requirements, for this rule to hold, the limit <math>\lim_{x\to c}\frac{f'(x)}{g'(x)}</math> must exist. Other requirements are detailed below, in the formal definition.
 
Necessitate, <math>\lim_{x\to c}\frac{f'(x)}{g'(x)}</math> exstet. Sunt aliae postulationes, quae subter notantur.
 
<!--
===Formal statement===
 
Receptum de "https://la.wikipedia.org/wiki/Hospitalii_regula"