Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

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


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

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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