If f(x)={{:((1-sqrt2sinx)/(pi-4x)",",ifx...

If `f(x)={{:((1-sqrt2sinx)/(pi-4x)",",ifxne(pi)/(4)),(a",",if x=(pi)/(4)):}` in continuous at `(pi)/(4)`, then a is equal to :

A

4

B

2

C

1

D

`(1)/(4)`

Text Solution

Verified by Experts

`underset( x rarr ( pi)/(4))("lim") f(x) =underset(x rarr ( pi)/( 4))("lim")(1-sqrt( 2) sin x )/( pi-4x)`
` underset(x rarr ( pi)/( 4))( "lim")( - sqrt(2) cos x )/( -4) = (1)/( 4) ` (by L' Hospital's rule )
Since f( x) is continuous at `x = ( pi)/( 4)` `: underset(x rarr ( pi)/(4))("lim") f(x) =f ((pi)/( 4)) rArr ( 1)/(4) =a`

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