(         )

where ( . ) denoted gretest integer fraction.

.use the graph of sin^-1x

at x=1,sin^-1x tends to pi/2 ,roughly 1.57.

[pi/2]=1

hence,[sin^-1x] tends to 1 at x=1

[sin^-1x]=

LHL

[sin^-1(1-h)]=[sin^-1(1)]=[pi/2]=1

RHL

[sin^-1(1+h)]=[sin^-1(1)]=[pi/2]=1

hence RHL=LHL=f(1) hence continuous hence limit is 1