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: 16


See the details below.

Work Step by Step

We are given the function $ f(x)=\tan \left(\frac{1}{x^2+1}\right)$. Since $\frac{1}{x^2+1}$ is a quotient of polynomials, and $1+x^2$ can not be zero for any $ x\in R $, then by Theorem 2, the function $\frac{1}{x^2+1}$ is continuous. Now, by Theorem 3, the function $$ f(x)=\tan \left(\frac{1}{x^2+1}\right)$$ is continuous.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.