CALCULUS Understanding Its Concepts and Methods
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Guillaume François Antoine Marquis de l'Hôpital (1661--1704) --- Historical Sketch
You might see the name "l'Hôpital" spelled "l'Hospital", which is how the Marquis himself spelled it. When the French decided to change their spelling a bit, his name got changed too.
L'Hôpital served in the military for a while before he turned to mathematics. He studied under Johann Bernoulli and became a very able mathematician. In 1696 he wrote the very first textbook on differential calculus. In this book, he included the now famous rule that he had learned from Bernoulli about calculating limits of functions of the form where the numerator and denominator both have limit . Although he acknowledged his indebtedness to Bernoulli for this technique, the rule nevertheless became known as l'Hôpital's rule.
An interesting excursion is to go to http://mathworld.wolfram.com/LHospitalsRule.html to see functions where the rule fails to be useful.
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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.