Question

Find $\underset{x\to (2n+1){\pi }^{+}}{lim}\sin \left(\right[\sin x\left]\frac{\pi }{6}\right)$ , where [.] is a greatest integer function and $nϵI$.

• A. 0
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. none of these

Answer 1

The correct option is C $-\frac{1}{2}$

$\underset{x\to (2n+1){\pi }^{+}}{lim}sin\left(\right[sinx\left]\frac{\pi }{6}\right)$
Since,$\underset{x\to (2n+1){\pi }^{+}}{lim}\left[sinx\right]=-1$
$\therefore \underset{x\to (2n+1){\pi }^{+}}{lim}sin\left(\right[sinx\left]\frac{\pi }{6}\right)=-sin\frac{\pi }{6}=-\frac{1}{2}$