Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - True-False Quiz - Page 166: 18

Answer

The statement is correct.

Work Step by Step

1) The Intermediate Value Theorem states that - If $f(x)$ is continuous on interval $[a,b]$ and $f(a)\ne f(b)$ - and N is any number between $f(a)$ and $f(b)$ - then there exists a number $c$ in $(a,b)$ such that $f(c)=N$ 2) Here we have: - $f$ is continuous on $[-1, 1]$ and $f(-1)\ne f(1)$ - $\pi\approx3.142$, so it is in the range of $f(-1)$ and $f(1)$: $\pi\in(3,4)$ - there exists a number $r$ such that $|r|\lt1$, which means $-1\lt r\lt1$, so $r\in(-1,1)$. And $f(r)=\pi$ 3) Therefore, all the requirements and results of the Intermediate Value Theorem are satisfied. The statement is correct.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.