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: 12


The quotient of two continuous functions is continuous.

Work Step by Step

We are given the function $ f(x)=\frac{x^{2}-\cos x}{3+\cos x}$. By Theorem 2 and 3, $ x^2$ and $\cos x $ are continuous functions. We know that $3+\cos x $ can not be zero for any $ x\in R $, so by using the basic laws of continuity the quotient of two continuous functions is continuous; that is $$ f(x)=\frac{x^{2}-\cos x}{3+\cos x}$$ is continuous.
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