Question

$\underset{x\to \pi /2}{\lim }\frac{\left[\frac{x}{2}\right]}{\ln (\sin x)}$ (where [.] denotes the greatest integer function)

• A. Does not exist
• B. equals 1
• C. equals 0
• D. equals -1

Answer 1

Answer: (C)

$\because \frac{\pi }{4}<1$,
$\therefore \left(\frac{\pi }{4}\right)=0$
$\therefore \underset{x\to \pi /2}{\lim }\frac{\left(\frac{x}{2}\right)}{\ln (\sin x)}=0$