Finding limit of $\left(1 +\frac1x\right)^x$ without using L'Hôpital's rule. Is there a way to find this limit without using L'Hôpital's rule. Just by using some basic limit properties.
$$\lim_{x\to\infty}\left(1+\frac1x\right)^x=e$$

Here are two of my questions
which, combined,
answer your question:
Is this proof that $\lim_{n \to \infty} (1+1/n)^n$ exists (1) new, (2) interesting?
Is showing $\lim_{z \to \infty} (1+\frac{1}{z})^z$ exists the same as $\lim_{n \to \infty} (1+1/n)^n$ exists
