Answer
$1$
Work Step by Step
Lets assume $t=\dfrac {1}{x}$ then
$\lim _{x\rightarrow \infty }x\sin \dfrac {1}{x}=\lim _{t\rightarrow 0}\dfrac {1}{t}\sin t=\dfrac {1}{t}\times t=1$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 3 - Applications of Differentiation - 3.5 Exercises - Page 203: 43
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