1:50 PM
Should these two questions be closed as duplicates or perhaps merged?
3

Any ideas on how to calculate the limit of $(e^x -1)/{x}$ as $x$ goes to zero without applying L'Hôpital's rule?

11

I was messing around with the definition of the derivative, trying to work out the formulas for the common functions using limits. I hit a roadblock, however, while trying to find the derivative of $e^x$. The process went something like this: \begin{align} (e^x)' &= \lim_{h \to 0} \frac{e^{x+h...

The first one specifically asks not to use L'H.
In the second one the OP wrote: I can show that $\lim_{h\to 0} \frac{e^h-1}{h} = 1$ using L'Hôpital's, but it kind of defeats the purpose of working out the derivative, so I want to prove it in some other way.