A) 1
B) 0
C) Does not exist
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\,\,\frac{\sin x}{x},\] let \[x=\frac{1}{y}\] or \[y=\frac{1}{x},\] so that \[x\to \infty \,\,\Rightarrow \,y\to 0\] \[\therefore \,\underset{x\to \infty }{\mathop{\lim }}\,\,\left( \frac{\sin x}{x} \right)=\underset{y\to 0}{\mathop{\lim }}\,\,\left( y.\sin \frac{1}{y} \right)=\underset{y\to 0}{\mathop{\lim }}\,\,y\times \underset{y\to 0}{\mathop{\lim }}\,\,\sin \frac{1}{y}=0\times ...=0\]
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