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 67: 31


The function is continuous.

Work Step by Step

We know that $\tan x $ is continuous on the interval $(-\frac{\pi}{2},\frac{\pi}{2})$ and $\sin x $ is continuous everywhere. Moreover, the range of $\sin x $ is $[-1,1]\subset (-\frac{\pi}{2},\frac{\pi}{2})$. Then, by Theorem 5 of the composition functions, the function $$ f(x)=\tan (\sin x) $$ is continuous.
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