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MCQ

$\lim _{x \rightarrow \infty} \frac{\sin x}{x}=$

A
1
✓
$0$
C
does not exist
D
none of these

✓

Answer

Correct option: B.

$0$

(B)
Let $x=\frac{1}{y}$ or $y=\frac{1}{x}$,
so that $x \rightarrow \infty, y \rightarrow 0$
$\therefore \quad \lim _{x \rightarrow \infty}\left(\frac{\sin x}{x}\right)=\lim _{y \rightarrow 0}\left(y \cdot \sin \frac{1}{y}\right)$
$=\lim _{y \rightarrow 0} y \times \lim _{y \rightarrow 0} \sin \frac{1}{y}=0$

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