Guillaume De l'Hôpital served as a cavalry officer but resigned because of nearsightedness. From that time on he directed his attention to mathematics. L'Hôpital was taught calculus by Johann Bernoulli from the end of 1691 to July 1692.
L'Hôpital was a very competent mathematician and solved the brachystochrone problem. The fact that this problem was solved independently by Newton, Leibniz and Jacob Bernoulli puts l'Hôpital in very good company.
L'Hôpital's fame is based on his book Analyse des infiniment petits pour l'intelligence des lignes courbes (1696) which was the first text-book to be written on the differential calculus. In the introduction L'Hôpital acknowledges his indebtedness to Leibniz, Jacob Bernoulli and Johann Bernoulli but L'Hôpital regarded the foundations provided by him as his own ideas.
In this book is found the rule, now known as L'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point.
Article by: J J O'Connor and E F Robertson