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If f(x)={((1-sin((3x)/2))/(pi-3x) , x ...

If `f(x)={((1-sin((3x)/2))/(pi-3x) , x != pi/2),(lambda , x=pi/2))` be continuous at `x=pi/3` , then value of `lamda` is (A) `-1` (B) `1` (C) `0` (D) `2`

A

`2`

B

`1/2`

C

`1/4`

D

`-1/4`

Text Solution

Verified by Experts

The correct Answer is:
C
`lamda=lim_(xrarrpi//2) (1-sinx)/(1+cos2x)=lim_(xrarrpi//2)(-cosx)/(-2sin2x)`
`implieslamda=lim_(xrarrpi//2)(-sinx)/(4cos2x)=1/4`
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