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The value of lim(xrarr(pi)/(4)) (sqrt(1-...

The value of `lim_(xrarr(pi)/(4)) (sqrt(1-sqrt(sin2x)))/(pi-4x)` is

A

`(1)/(4)`

B

`-(1)/(4)`

C

1

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xrarr(pi)/(4))(lim)(sqrt(1-sqrt(sin2x)))/(pi-4x)xx(sqrt(1+sqrt(sin2x)))/(sqrt(1+sqrt(sin2x)))`
`=underset(xrarr(pi)/(4))(lim)(sqrt(1-sin2x))/((pi-4x))xxunderset(xrarr(pi)/(4))(lim)(1)/(sqrt(1+sqrt(sin2x)))`
`=underset(xrarr(pi)/(4))(lim)(sqrt(sin^(2)((pi)/(4)-x)))/(pi-4x).1`
`=underset(xrarr(pi)/(4))(lim)(|sin((pi)/(4)-x)|)/(4((pi)/(4)-x))`
which gives RHL `=-(1)/(4)"at x"=(pi)/(4)and "LHL"=(1)/(4)"at x"=(pi)/(4)`
So, limit does not exist.
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