Answer
$0$
Work Step by Step
$x$ is "approaching $-\infty$" means that $x$ is assuming negative values of greater and greater magnitude.
See table below.
As $x$ assumes negative values of greater and greater magnitude,
the function value approaches the value $0.$
So, we write
$\displaystyle \lim_{x\rightarrow-\infty}xe^{x}=0$
