Answer
FALSE
Work Step by Step
Since, $\lim\limits_{x \to 0}x=0$ and $\lim\limits_{x \to 0}e^{x}=1\ne 0$
We have that $\lim\limits_{x \to 0}\frac{x}{e^{x}}=\frac{\lim\limits_{x \to 0}x}{\lim\limits_{x \to 0}e^{x}}$
$=\frac{0}{1}$
$=0$
Thus, $\lim\limits_{x \to 0}\frac{x}{e^{x}}=0$
Hence, the given statement is FALSE