L'Hôpital's rule
type: Item
instance of: scholarly article
title: L'Hôpital's rule
zbMATH Open document ID: 1311.01013
DOI: 10.4171/EM/254
author: Horst Struve
author: Ingo Witzke
published in: Elemente der Mathematik
publication date: 2015-02-10T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: When \(f\) and \(g\) are differential real functions in an interval around a point \(\alpha\) and \(\lim_{x\to\alpha} {f'(x)\over g'(x)}\) exists, then \(\lim_{x\to\alpha} {f(x)\over g(x)}\) exists also and both these values coincide. This is L'Hôpital's rule. In this paper, interesting knowledge around it, due to Cauchy, Leibniz, Bernoulli, Lacroix, Lagrange in their work has been treated. Relatively new sources are mentioned. Connections over three centuries are elucidated, as well as in the educational vain around the mathematical objects of study, the notions, the methods. According to the authors, in respect to modern standards, the proofs of L'Hôpital's rule due to Lacroix and Cauchy are the most reliable ones.
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 26-03
Mathematics Subject Classification ID: 26A06
zbMATH DE Number: 6399898
zbMATH Keywords: history of limits
zbMATH Keywords: analysis
zbMATH Keywords: L'Hôpital's rule
zbMATH Keywords: differential and integral calculus
zbMATH Keywords: continuity
zbMATH Keywords: sequences
zbMATH Keywords: series
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
OpenAlex ID: W2049710323
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description: scientific article