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If the function f defined on (pi/6,pi/3)...

If the function f defined on `(pi/6,pi/3)` by `{{:((sqrt2 cos x -1)/(cot x -1)" , " x ne pi/4),(" is continuous,"),(" k , "x=pi/4 ):}`
then k is equal to

A

`(1)/(sqrt(2))`

B

1

C

2

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`k=underset(x rarr pi/4)lim (sqrt(2)cos x-1)/(cot x-1)= underset(x rarr pi/4) lim (1-sqrt(2) cos x)/(cosec^(2)x)= underset(x rarr pi/4)lim sqrt(2) sin^(3)x=sqrt(2)xx(1/sqrt(2))^(3)=1/2`
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