Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 43



Work Step by Step

Since \begin{align*} \lim _{x \rightarrow \infty} \frac{\sin x}{\lfloor x\rfloor}&\leq \lim _{x \rightarrow \infty} \frac{1}{\lfloor x\rfloor}\\ &=0 \end{align*} $\text { since }\lfloor x\rfloor \rightarrow \infty \text { as } x \rightarrow \infty \Rightarrow \lim _{x \rightarrow \infty} \frac{\sin x}{\lfloor x\rfloor}=0$
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