Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.8 Intermediate Value Theorem - Preliminary Questions - Page 86: 1


The result follows by the Intermediate Value Theorem.

Work Step by Step

Since the function $ x^2$ is continuous on $[0,1]$ and $ f(0)=0\neq f(1)=1$, thus $0.5 $ is between $ f(0)$ and $f(1)$. Then, by the Intermediate Value Theorem, the function $x^2$ takes the value $0.5$ for some $x\in (0,1)$.
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