Answer
diverges to $+\infty$
Work Step by Step
This is a limit at infinity. Use Theorem 10.2.
(use only the highest powers)
$\displaystyle \lim_{x\rightarrow+\infty}f(x)=\lim_{x\rightarrow+\infty}\frac{2x^{4}}{1000x^{3}}$=...reduce...
$=\displaystyle \lim_{x\rightarrow+\infty}\frac{x}{500}$,
which is of determinate form $\displaystyle \pm\frac{\infty}{k}=\pm\infty$
So, the limit diverges to $+\infty$ .
