If [ ] denotes the greatest integer function, $\underset{x→\frac{π}{2}}{\lim}\frac{5\sin[\cos x]}{[\cos x]+2}$ is:
Answer & explanation
Correct answer: option 4
LHL = $\underset{x→\frac{π^-}{2}}{\lim}\frac{5\sin[\cos x]}{[\cos x]+2}=\frac{5\sin(0)}{0+2}=0$; RHL = $\underset{x→\frac{π^+}{2}}{\lim}\frac{5\sin(-1)}{-1+2}=-5\sin (1)$