Calculus: Early Transcendentals (2nd Edition)

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, $$\lim_{x\to \infty}\frac{f(x)}{g(x)}=\infty.$$