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If `f(x)` and `f'(x)` are continuous at `x=pi/6`, where `f(x)={:{(sin 2x", if " x lt pi/6),(ax+b", if " x gt pi/6):}`, then

A

`a=-2, b=(sqrt(3))/(2)+pi/3`

B

`a=2, b=(sqrt(3))/(2)- pi/3`

C

`a=-1, b=(sqrt(3))/(2)+ pi/6`

D

`a=1, b= (sqrt(3))/(2)- pi/6`

Text Solution

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The correct Answer is:
D
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