Answer
diverges to $-\infty$
Work Step by Step
This is a limit at infinity. Use Theorem 10.2.
(use only the highest powers)
$\displaystyle \lim_{x\rightarrow-\infty}f(x)=\lim_{x\rightarrow-\infty}\frac{10x^{2}}{5x}$=...reduce...
$=\displaystyle \lim_{x\rightarrow-\infty}\frac{10x}{5}$,
which is of determinate form $\displaystyle \pm\frac{\infty}{k}=\pm\infty$.
(numerator negative, denominator positive)
So, the limit diverges to $-\infty$ .
