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Q.
A point where function $f (x) = [sin [x]]$ is not continuous in $(0, 2\pi)$, [.] denotes the greatest integer $\le\,x$, is
Continuity and Differentiability
Solution:
For
$0 \le\,x <\,1, f \left(x\right)=\left[sin\,0\right]=0$,
$1 \,\le x <\,2, f \left(x\right)=\left[sin\,1\right]=0$,
$2 \le\,x <\,3, f \left(x\right)=\left[sin\,2\right]=0$,
$3 \le\,x <\,4, f\left(x\right)=\left[sin\,3\right]=0$,
$4 \le\,x <\,5, f \left(x\right)=\left[sin\,4\right]=-1$
Hence, there is discontinuity at point $\left(4,-1\right)$