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We all know l'hopital's rule ! But what is its proof ?!!

I guess that not all people know its proof ! Do they ?

Can any one give a proof for it ? Starting with the simplest one . L'hopital's rule is very important for calculating limits and was discovered by a french mathematician , M.l'hopital !

So I'm interested to know the proof of this great theorem. Isn't it a great theorem ? Thanks !

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6  
open up any textbook on calculus and you will find such a proof. –  Ittay Weiss Jan 27 '13 at 23:54
    
@IttayWeiss , i look for many proofs , simple ones and hard ones ! –  Maths Lover Jan 27 '13 at 23:58
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See e.g. en.wikipedia.org/wiki/… –  Robert Israel Jan 28 '13 at 0:00
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It is very likely that the Rule was discovered by Johann Bernoulli. –  André Nicolas Jan 28 '13 at 0:01
    
@AndréNicolas , and why was it called l'hopital rule ? –  Maths Lover Jan 28 '13 at 0:07
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closed as not a real question by Ittay Weiss, TMM, rschwieb, Clive Newstead, ncmathsadist Jan 28 '13 at 0:25

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1 Answer

MathsLover visit wikipedia for a good proof.

See this youtube clip for a clip of the proof.

This youtube clip is awesome.

Here is a math poster of the proof:
enter image description here



The link to the PDF can be found here

The PDF of this math poster was brought to you in part by Peter Jipsen, Associate Professor of Mathematics, from Chapman University.

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