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**Runty** Prove that

$\displaystyle \lim_{h \to 0}(1+h)^{1/h}=e$

Hints outlined for this question are as follows.

Since$\displaystyle \frac{d}{dx}\ln1=1$,

As $\displaystyle h \to 0$, $\displaystyle \frac{\ln(1+h)-\ln1}{h}=\frac{\ln(1+h)}{h} \to 1$

A second hint is that if $\displaystyle g$ is continuous at $\displaystyle c$ and $\displaystyle f$ is continuous at $\displaystyle g(c)$, then $\displaystyle f\circ g$ is continuous at $\displaystyle c$.

**You are not allowed to use L'Hospital's Rule to solve this question.** This is one of the requirements, I'm afraid.