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 - Exercises - Page 86: 3


See the proof below.

Work Step by Step

Since the function $ g(t)=t^2\tan t $ is continuous on $[0,\frac{\pi}{4}]$ and $ g(0)=0\neq g(\frac{\pi}{4})=\frac{\pi^2}{16}$ and $\frac{1}{2}$ is between $ g(0)$ and $ g(\frac{\pi}{4})$, then by the Intermediate Value Theorem the function $ g(t)$ takes on the value $\frac{1}{2}$ for some $ t\in (0,\frac{\pi}{4})$.
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