The value of limx→0 sin⁡xx, where [.] represents the greatest integer function is :

The value of $lim_{x \to 0} [\frac{\sin x}{x}]$ , where [.] represents the greatest integer function is :

A
B
C
D

Solution:

We have, $x > \sin x$ for al $x > 0$ and $x < \sin x$ for all $x < 0$

$\Rightarrow \frac{\sin x}{x} < 1$ for all $x \neq 0 \Rightarrow lim_{x \to 0} [\frac{\sin x}{x}] = 0$

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