# Question #cf0d2

May 21, 2017

$- \infty$

#### Explanation:

Solve each limit separately:
${\lim}_{x \to - \infty} \left[\left({e}^{- x}\right) \left({x}^{- \frac{1}{3}}\right)\right]$

Transform:
${\lim}_{x \to \infty} \left[\left({e}^{x}\right) \left(- {x}^{- \frac{1}{3}}\right)\right]$
$= - {\lim}_{x \to \infty} \left[\frac{{e}^{x}}{{x}^{\frac{1}{3}}}\right]$
$= - \left(\infty\right) = - \infty$

The growth of the numerator as $x \to \infty$ is much faster than the denominator and so the limit
is $\infty$.