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: 45


$ f(x)$ is continuous on $ R $.

Work Step by Step

Since $ x^4+1\gt 0$ for all $ x\in R $, then the domain of the function $ f(x)=(x^4+1)^{3/2}$ is $ R $, and since $ x^4+1$ is a polynomial then it is continuous. Now by using the continuity laws, $ f(x)$ is continuous on $ R $.
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