Showing that if $\lim_{x\to\infty}f'(x)=L$ then $\lim_{x\to\infty}\frac{f(x)}{x} = L$.
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$