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lim(x to (pi)/(6)) [(3sinx - sqrt(3)cos ...

`lim_(x to (pi)/(6)) [(3sinx - sqrt(3)cos x)/(6x -pi)]` is equal to

A

`sqrt(3)`

B

`(1)/sqrt(3)`

C

`-sqrt(3)`

D

`-(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(x to (pi)/(6))(lim)[(3sin x - sqrt(3)cos x)/(6x - pi)] " "[because (0)/(0) "form"]`
By L Hospital's rule
` =underset(x to (pi)/(6))(lim)[(3cos x + sqrt(3)sin)/(6)]`
` = (3sqrt(3)/(2) + sqrt(3)(1)/(2))/(6) = (1)/(sqrt(3))`
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