Limit of a function with e. I'm struggling with calculating the limit of the following function:
$$\lim_{x\to 0^-}\frac{e^{\frac{1}{x}}}{x}$$
I tried using L'Hopital's rule, but I'm still getting $\frac{0}{0}$ and the denominator keeps getting greater exponent.

Change $t=-1/x$, so the limit becomes
$$
\lim_{t\to\infty}\frac{e^{-t}}{-1/t}=
\lim_{t\to\infty}-\frac{t}{e^t}
$$
