Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 66: 7

Answer

The sum of two continuous functions is continuous.

Work Step by Step

We are given the function $ f(x)=x+\sin x $. By Theorem 2 and 3, $ x $ and $\sin x $ are continuous functions. Using the basic laws of continuity, the sum of two continuous functions is continuous; that is $$ f(x)=x+\sin x $$ is continuous.
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