Editing L'Hôpital's rule (section)

== History ==
[[Guillaume de l'Hôpital]] (also written l'Hospital{{efn|In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. Since then, French spellings have [[Reforms of French orthography|changed]]: the silent 's' has been [[Circumflex in French#Indication of a lost phoneme|removed and replaced]] with a [[circumflex]] over the preceding vowel.}}) published this rule in his 1696 book ''[[Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes]]'' (literal translation: ''Analysis of the Infinitely Small for the Understanding of Curved Lines''), the first textbook on [[differential calculus]].<ref>{{Cite web | url=https://mathshistory.st-andrews.ac.uk/Biographies/De_LHopital/|title=De L'Hopital biography|first=John J.|last=O'Connor|author2=Robertson, Edmund F |work=The MacTutor History of Mathematics archive|publisher=School of Mathematics and Statistics, University of St Andrews|location=Scotland|access-date=21 December 2008}}</ref>{{efn|1="Proposition I.  Problême.  Soit une ligne courbe AMD (AP = x, PM = y, AB = a [see Figure 130] ) telle que la valeur de l'appliquée y soit exprimée par une fraction, dont le numérateur & le dénominateur deviennent chacun zero lorsque x = a, c'est à dire lorsque le point P tombe sur le point donné B.  On demande quelle doit être alors la valeur de l'appliquée BD.  [Solution: ]...si l'on prend la difference du numérateur, & qu'on la divise par la difference du denominateur, apres avoir fait x = a = Ab ou AB, l'on aura la valeur cherchée de l'appliquée bd ou BD."  ''Translation'' :  "Let there be a curve AMD (where AP = X, PM = y, AB = a) such that the value of the ordinate y is expressed by a fraction whose numerator and denominator each become zero when x = a; that is, when the point P falls on the given point B.  One asks what shall then be the value of the ordinate BD.  [Solution: ]... if one takes the differential of the numerator and if one divides it by the differential of the denominator, after having set x = a = Ab or AB, one will have the value [that was] sought of the ordinate bd or BD."<ref>{{cite book |author=L'Hospital |year=1696 |title=Analyse des infiniment petits |url=http://gallica.bnf.fr/ark%3A/12148/bpt6k205444w/f000171.tableDesMatieres |pages=145–146}}</ref>}} However, it is believed that the rule was discovered by the Swiss mathematician [[Johann Bernoulli]].<ref>{{cite book |title=A History of Mathematics |edition=3rd illustrated |first1=Carl B. |last1=Boyer |first2=Uta C. |last2=Merzbach |author2-link= Uta Merzbach |publisher=John Wiley & Sons |year=2011 |isbn=978-0-470-63056-3 |page=321 |url=https://books.google.com/books?id=bR9HAAAAQBAJ}} [https://books.google.com/books?id=bR9HAAAAQBAJ&pg=RA2-PT321 Extract of page 321]</ref>