Answer
$\displaystyle \lim_{x\rightarrow\infty}f(x)=$0
Work Step by Step
Evaluating the function for some x's, letting x become greater and greater
we build a table
we see that
f(x)$\rightarrow 0$ as x$\rightarrow\infty$ .
So, it seems that a limit exists,
$\displaystyle \lim_{x\rightarrow\infty}f(x)=$0