Answer
indeterminate,
diverges to $-\infty$
Work Step by Step
See the table: "Some Determinate and lndeterminate Forms" and$, $after plugging in the value for x, recognize
that the limit is initially in the form $\displaystyle \frac{\infty}{\infty}$ (indeterminate)
Applying the "Strategy for Evaluating Limits Algebraically, case 2 of step 2"
after simplifying (reducing) with $x^{3},$ the limit becomes
$\displaystyle \lim_{x\rightarrow-\infty}\frac{-x^{3}}{3}.$
(when x$\rightarrow-\infty$,
$ x^{3}\rightarrow$+$\infty$,
$-\displaystyle \frac{1}{3}x^{3}\rightarrow-\infty $,
because it is of the determinate form $ k(\pm\infty)=\pm\infty$ )
so, the limit diverges to $-\infty$.
