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February 8th, 2018, 05:09 PM  #11 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
I'm talking about the given problem, not the definition of the derivative.

February 8th, 2018, 05:12 PM  #12 
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics 
The given problem is a derivative. Specifically, what is the derivative of $e^x$ at $x = 0$? Well its \[\lim_{h \to 0} \frac{e^h  1}{h} \] which is exactly the limit in the OP. 
February 8th, 2018, 05:17 PM  #13 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
That's a specific derivative, The example you gave in your previous post uses the general formula. There's absolutely no reason you can't apply L'Hopital's rule to the limit the OP gave and the result is 1. That result is all I intended to have the OP see. I'm done.


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