1. Tardigrade
  2. Question
  3. Mathematics
  4. displaystyle lim x arrow π / 2 ([(x/2)]/ ln ( sin x)) (where [.] denotes the greatest integer function)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Limits and Derivatives

Solution:

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