## Calculus (3rd Edition)

$$\lim\limits_{t \to 3}g(t)=4.$$
Since $\lim\limits_{t \to 3}tg(t)$ exists, then we can apply the product law as follows $$\lim\limits_{t \to 3}tg(t)=12\Longrightarrow \lim\limits_{t \to 3}t\lim\limits_{t \to 3}g(t)=12.$$ But, $\lim\limits_{t \to 3}t=3$, so we have $$3\lim\limits_{t \to 3}g(t)=12\Longrightarrow \lim\limits_{t \to 3}g(t)=4.$$