Question $1.$ That dratted wizard is back again! This time, his spell causes you to forget that

$\underset{n}{lim}(1+\frac{1}{n}{)}^n=e$

Using L'Hopital's rule $($or otherwise$),$ prove that $\underset{x{0}^{+}}{lim}(1+x{)}^{\frac{1}{x}}=e.$

$($Hint $1$: The wizard's spell is extremely specific. Only the above information about this one sequence is missing from your mind. This time, you can use any information you like about exp and $ln.)$