In order to solve this exercise, you have to know the limit that defines the constant [tex]e[/tex]:
[tex]\displaystyle \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n=e[/tex]
With this limit in mind, we can perform the following variable change:
[tex]y=\dfrac{1}{x}[/tex]
With this new variable, we have
[tex]x\to 0 \implies \frac{1}{x}=y\to\infty,\quad x = \dfrac{1}{y},\quad \dfrac{1}{x}=y[/tex]
Substituting these pieces one by one, we have
[tex]\displaystyle \lim_{x\to 0}\left(1+x\right)^\frac{1}{x} = \lim_{y\to\infty}\left(1+\frac{1}{y}\right)^y[/tex]
and this is the limit that defines e.
