Question

If [.] denotes the greatest integer function,then $\underset{x\to \frac{\pi }{2}}{lim}\left[\frac{x-\frac{\pi }{2}}{cosx}\right]=$

• A. 1
• B. -1
• C. 2
• D. -2

Answer 1

The correct option is B -1

$\underset{x\to \pi /2}{lim}\left[\frac{x-\pi /2}{\cos x}\right]$

$=\underset{x\to \pi /2}{lim}\left[\frac{x-\pi /2}{-\sin (x-\pi /2)}\right]$

as $x\to \pi /2,x-\pi /2\to 0$

$=\underset{x\to \pi /2}{lim}[-1]=-1$