http://www.bing.com:80/search?q=L%27Hopital%27s+RuleSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=L%27Hopital%27s+RuleCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/505535/proof-of-lh%c3%b4pitals-rule1 Typically when they teach L'Hopital's Rule in school they just teach it algorithmically, that is just how to apply it, without the proof. This is very similar to the way calculus in general is taught in most schools, i.e., just as a bunch of techniques, no proofs or justifications.Mon, 13 Apr 2026 01:44:00 GMThttps://math.stackexchange.com/questions/98082/why-does-lh%c3%b4pitals-rule-workAt the heart of it though, L'Hopital's rule just seems to be a marriage of the ideas that differentiable functions are pretty darn close to their linear approximations at some point as long as you don't stray too far from that point and that for a continuous function, a small movement in the domain means a small movement in the value of the ...Sat, 11 Apr 2026 05:13:00 GMThttps://math.stackexchange.com/questions/602650/is-lhopitals-rule-applicable-to-complex-functionsL'Hopital's rule is a local statement: it concerns the behavior of functions near a particular point. The global issues (multivaluedness, branch cuts) are irrelevant.Tue, 14 Apr 2026 18:17:00 GMThttps://math.stackexchange.com/questions/4745400/lhospitals-rule-of-infinity-over-infinitySpivak's Calculus text has a careful series of exercises to do all the variations of L'Hôpital's rule.Fri, 10 Apr 2026 00:35:00 GMThttps://math.stackexchange.com/questions/3767136/lhopitals-rule-fails-with-limits-to-infinityL'Hopital's rule fails with limits to infinity? Ask Question Asked 5 years, 8 months ago Modified 1 year, 6 months agoMon, 13 Apr 2026 10:55:00 GMThttps://math.stackexchange.com/questions/1499731/when-to-use-lh%C3%B4pitals-ruleIt should be used only when other simpler techniques (algebra of limits, Squeeze theorem) fail. And even when you really need to apply this rule, it is better to simplify the expression using algebra of limits and usual algebraic manipulation. Jumping to L'Hospital's Rule for any and every limit problem is a bad bad bad idea.Tue, 07 Apr 2026 14:51:00 GMThttps://math.stackexchange.com/questions/1397736/lh%C3%B4pital-or-lhospitalHowever, though hôpital does mean hospital in English, isn't it totally ridiculous to translate Règle de L'Hôpital into L'Hospital's Rule (just because the corresponding English word hospital happens to make sense)? What's more, how are we supposed to pronounce L'Hospital? In an English way or in a French way?Sun, 05 Apr 2026 13:06:00 GMThttps://math.stackexchange.com/questions/2363181/understanding-the-proof-of-lhopitals-ruleUnderstanding the Proof of L'Hopital's Rule Ask Question Asked 8 years, 8 months ago Modified 8 years, 8 months agoThu, 02 Apr 2026 12:34:00 GMThttps://math.stackexchange.com/questions/461120/when-to-stop-using-lh%C3%B4pitals-rule16 A quick addition to Ra1nMaster's otherwise excellent answer: you can only apply L'Hopital's rule if you have an indeterminate form and if the limit, after applying L'Hopital's rule, exists.Thu, 09 Apr 2026 00:30:00 GMThttps://math.stackexchange.com/questions/2118581/lhopitals-rule-and-frac-sin-xxThe sine function fulfills the conditions of the L'Hopital's rule. Also, it is a fact that the derivative of sine is cosine, no matter how we proved it. Certainly there is a way to prove $\frac d {dx}\sin x=\cos x$ without using the said limit (if someone knows how, they can post it) so we don't even have any circular logic.Fri, 10 Apr 2026 02:30:00 GMT