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The value of lim(xto pi//2)([x/2])/(log(...

The value of `lim(xto pi//2)([x/2])/(log(sinx))` is equal to

A

0

B

1

C

`-1`

D

does no exist

Text Solution

Verified by Experts

The correct Answer is:
A
`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`
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