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: 39


a) not true b) true

Work Step by Step

a) This is not true. For example $$ f(x)=\left\{ \begin{array}{ll} x & \mbox{if } x \neq 0 \\ 1 & \mbox{if } x= 0 \end{array} \right.$$ b) True, $$\lim\limits_{x \to 0}f(x)=\left(\lim\limits_{x \to 0}x\right) \left( \lim\limits_{x \to 0}\frac{f(x)}{x}\right)=(0)(1)=0.$$
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