Answer
$$1$$
Work Step by Step
Given
$$\lim _{x \rightarrow \infty}x\sin\frac{1}{x}$$
Let $t= \frac{1}{x}$ , then
\begin{aligned}
\lim _{x \rightarrow \infty}x\sin\frac{1}{x}&=\lim _{t \rightarrow 0^+}\frac{\sin t}{t} \\
&=1
\end{aligned}
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 31
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