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: 41


$ f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.

Work Step by Step

Since $ x^{-4/3}$ is defined for all $ x\neq 0$ then the domain of $ f(x)=x^{-4/3}$ is $(-\infty,0)\cup(0,\infty)$. Now, since $ x^{-4/3}$ is continous for all $ x\neq 0$, then by using the continuity laws, $ f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.
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