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: 40


$ f(x)=x^{1/3}+x^{3/4} $ is contiuous on $[0,\infty)$

Work Step by Step

Since $ x^{1/3}$ is defined for all $ x\in R $ and $ x^{3/4}$ is defined only on $[0,\infty)$, then the domain of $ f(x)=x^{1/3}+x^{3/4} $ is $[0,\infty)$. Now, since $ x^{1/3}$ and $ x^{3/4}$ are continuous, then by using the continuity laws $ f(x)=x^{1/3}+x^{3/4} $ is contiuous on $[0,\infty)$.
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