Calculus: Early Transcendentals 8th Edition

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

Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises - Page 705: 72

Answer

$a_n= cos(n)$ is bounded and not monotonic.

Work Step by Step

A sequence is monotonic if it is either increasing ($a_n >a_{n+1}$ for all $n\geq 1$) or decreasing ($a_n< a_{n+1}$ for all $n\geq 1$). We see that $ cos( 2) > cos (3) < cos (4)$ . Thus, the sequence is not monotonic. Since $-1 \leq cos(n) \leq1 $, $a_n$ is bounded both from above and from below, respectively by 1 and -1. Therefore, $a_n$ is bounded.
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