Proving L'Hospital's Rule with Mean Value Theorem

KLscilevothma · Jul 2, 2003

How to prove it? I've watched a tv program before and I vaguely remember the proof consists of 4 parts, which includes the mean value theorem, Cauchy's mean value theorem and the other 2 theorems. I haven't learned mean value theorem at that time and I didn't understand it, perhaps I can now.

Lonewolf · Jul 2, 2003

Check out http://mathforum.org/library/drmath/view/53340.html. It's a bit too large to type in the forum. The proof that uses Cauchy's mean value theorem begins

Code:

Date: 12/23/98 at 11:43:47
From: Doctor Rob
Subject: Re: Proof of L'hopital's rule

The first proof uses Taylor expansions. The second uses Cauchy's MVT.

Dx · Jul 2, 2003

Originally posted by KL Kam
How to prove it? I've watched a tv program before and I vaguely remember the proof consists of 4 parts, which includes the mean value theorem, Cauchy's mean value theorem and the other 2 theorems. I haven't learned mean value theorem at that time and I didn't understand it, perhaps I can now.

http://archives.math.utk.edu/visual.calculus/3/index.html

Proving L'Hospital's Rule with Mean Value Theorem

Similar threads

Undergrad Problem in understanding instantaneous velocity

Undergrad Unit Circle Confusion: A Self-Study Challenge?

Undergrad Proving that convexity implies second order derivative being positive

Undergrad Derive the orthonormality condition for Legendre polynomials

Undergrad Problem with calculating projections of curl using rotation of contour

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers