Guillaume de l'Hopital publishes publishes his textbook on calculus, "Analyse des infiniment petits pour l'intelligence des lignes courbes." In it is found the rule now known as "l'Hopital's rule."

L'Hopital's rule is a method for finding the limit of a function expressed as a rational function the numerator and denominator of which both approach 0.

While this rule made l'Hopital famous and he insisted the foundations of the ideas in his textbook were his own, most likely the rule was discoverd by l'Hopital's teacher, Johann Bernoulli. Bernoulli was paid extremely well to be the private math teacher of l'Hopital. After l'Hopital's death, Bernoulli began to claim the idea for the rule was his. The investigation of historical records justify Bernoulli's claim. L'Hopital's great wealth likely bought Bernoulli's silence while Bernoulli's silence while l'Hopital was alive.

Jack Bookman of Duke University is reported as saying "Giving l'Hopital's Rule to a calculus student is like handing a chainsaw to a three year old" (Puckette). The power and subtlety of the method leads to horrendous computation errors when misapplied.

Whoever authored the rule that now bears l'Hopital's name, we can be thankful that the rule is in the arsenal of tools of the mathematician.

Author: Paul Koenig

References:
O'Connor, John and Edmund Robertson. 1996. "De_L'Hopital". 4 December 1998 <http://www-groups.dcs.st-and.ac.uk/~history//Mathematicians/De_L'Hopital.html>.

--------. 1998. "Bernoulli_Johann". 4 December 1998. <http://www-groups.dcs.st-and.ac.uk/~history//Mathematicians/Bernoulli_Johann.html>.

Puckette, Emily. 1998. Letter to author, 30 November.