Chapter 4 - Applications of the Derivative - 4.7 L'Hopital's Rule - 4.7 Exercises - Page 307: 9

This means that $$\lim_{x\to \infty}\frac{f(x)}{g(x)}=\infty.$$

This means that if we take the limit of the ratio of $f$ and $g$ as $x\to \infty$ goes to infinity by definition of the term of growing faster or, in other words, $$\lim_{x\to \infty}\frac{f(x)}{g(x)}=\infty.$$