Calculus (3rd Edition)

Published by W. H. Freeman

Chapter 2 - Limits - 2.3 Basic Limit Laws - Exercises - Page 59: 37

Answer

$$\lim\limits_{t \to 3}g(t)=4.$$

Work Step by Step

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 $$3\lim\limits_{t \to 3}g(t)=12\Longrightarrow \lim\limits_{t \to 3}g(t)=4.$$

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