apcalcL’Hopitals’+Rule

﻿ L'Hopitals rule uses derivatives to help evaluate limits involving indeterminate forms

PROFILE: The differentiation of the numerator and the denominator allow you to simplify the limit and/or convert it to a determinate form, allowing the limit to be evaluated more easily. [|Interactive Site]for Indeterminate Forms and L'Hopital's Rule



***CHECK OUT THE [|PROOF]***

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KNOW YOUR LIMITS! This graph demonstrates L'Hopital's rule for the 0/0 case. As you can see the derivative of the curve and the curve itself are approaching the same point (x(t),y(t)). []

Watch a virtual demonstration [|here]

**﻿HISTORY **
 * ﻿ ﻿ **L'Hopital's rule was named after the 17th-century

mathematician Guillaume de L'Hopital.Although the rule did

<span style="color: #ff6c00; font-family: 'Lucida Console',Monaco,monospace; font-size: 170%; line-height: 0px; overflow: hidden;"> <span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;">not with L'Hôpital, it first appeared in

<span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;"> his bookAnalyse des Infiniment Petits pour

<span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;">L <span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;">'Intelligence des Courbes

<span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;"> This book was the first systematic

<span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%; line-height: 0px; overflow: hidden;">exposition of differential calculus.

<span style="font-family: 'Lucida Console',Monaco,monospace; font-size: 130%;">At the time these concepts were argued. However they were not ostracized like many other mathematicians claims.

<span style="color: #3d7b4c; font-family: 'Lucida Console',Monaco,monospace; font-size: 160%; line-height: 0px; overflow: hidden;"> <span style="color: #3d7b4c; font-family: 'Lucida Console',Monaco,monospace; font-size: 160%;">** GUILLAUME DE L'HOPITAL **

<span style="color: #000000; font-family: 'Lucida Console',Monaco,monospace; font-size: 130%;">L'Hôpital abandoned a military career due to poor eyesight and at a young age he decided to pursue his talents in math. He was a member of [|Nicolas Malebranche] 's circle in Paris where he met many other famous mathmaticians of this time including [|Johann Bernoulli]. Besides L'Hopital's rule, some of his other accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the [|brachistochrone problem], and the discovery of a turning point <span style="background-color: #ffffff; color: #000000; font-family: 'Lucida Console',Monaco,monospace; text-decoration: none;">singularity on the involute of a plane curve near an inflection point.

<span style="color: #800080; font-family: 'Lucida Console',Monaco,monospace; font-size: 140%; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">

<span style="color: #800080; font-family: 'Lucida Console',Monaco,monospace; font-size: 120%;">﻿Try some [|practice] problems



References:  youtube.com (all videos) [] [] [] [|http://mathworld.wolfram.com/LHospitalsRule.]html [] [] []