Suppose $f$ and $g$ are functions satisfying

• $\displaystyle{\lim_{x \to 6} f(x) = 0}$,
• $\displaystyle{\lim_{x \to 6} g(x) = 0}$, and
• $\displaystyle{\lim_{x \to 6} \frac{f(x)}{g(x)} = 3 }$.

What can be said about the relative sizes of $f(x)$ and $g(x)$ as $x$ approaches $6$? Select all that apply.

A. $g(x) \approx 3 f(x)$ for $x$ near $6$.
B. Values of $f(x)$ are about 3 times as large as values of $g(x)$ as $x$ approaches $6$.
C. Values of $g(x)$ are about 3 times as large as values of $f(x)$ as $x$ approaches $6$.
D. $f(x) \approx 3 g(x)$ for $x$ near $6$.
E. Nothing definitive can be said.