True or False: Choose True False If $f(x)$ is a function with the property that $\displaystyle \lim_{x \to a} f(x) = 0$ and $g(x)$ is another function also defined near $x = a$, then $\displaystyle \lim_{x \to a} \lbrack f(x) g(x) \rbrack = 0$.

In the answer box below, explain your reasoning for the choice of true or false you made above. Use complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if you were explaining the answer to someone else in class.