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: 43


$ f(x)=\tan^2 x $ is contiuous on its domain.

Work Step by Step

We know that $\tan^2 x=\frac{\sin^2x}{\cos^2x}$ is defined for all $ x\in R $ such that $ x\neq \frac{(2n+1)\pi}{2}$, $ n $ is integer. Since $\sin x $ and $\cos x $ are continuous then by using the continuity laws, $ f(x)=\tan^2 x $ is continuous on its domain.
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