`lim_(xto(pi)/(2)) ([(x)/(2)])/(log_(e)(sinx))([.]` denotes greatest integer function)

Options

A. 0
B. 1
C. `-1`
D. does no exist

Answer

A

Explanation

`L.H.L implies underset(xto(pi^(+))/(2))(lim)([(x)/(2)])/(log_(e)(sinx))=underset(hto0)(lim)([(pi)/(4)-(h)/(2)])/(log_(e)sin((pi)/(2)-h))=0`
`R.H.L. underset(xto(pi^(+))/(2))(lim)([(x)/(2)])/(log_(e)(sinx))=underset(hto0)(lim)([(pi)/(4)+(h)/(2)])/(log_(2)sin((pi)/(2)+h))=0`