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If f(x)={:{((cot x-cos x)/((pi-2x)^(3))"...

If `f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):}` is continuous at `x= pi/2`, where , then `k=`

A

`1/4`

B

`(1)/(24)`

C

`(1)/(16)`

D

None of these

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Verified by Experts

The correct Answer is:
C
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