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: 38


$ f(x)=\frac{x^2}{x+x^{1/4}}$ is continuous on $(0,\infty)$.

Work Step by Step

Putting $ x+x^{1/4}=0$, then $ x=0$ and since $ x^{1/4}$ is defined only when $ x\geq 0$ then the domain of $ f(x)=\frac{x^2}{x+x^{1/4}}$ is $(0,\infty)$. Now, since both $ x^2$ and $ x+x^{1/4}$ are continuous, then by using the continuity laws, $ f(x)=\frac{x^2}{x+x^{1/4}}$ is continuous on $(0,\infty)$.
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