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Let f(x)=underset(ntooo)lim(1)/(((3)/(pi...

`Let f(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)`. Then the set of values of x for which `f(x)=0` is

A

`|2x|gtsqrt(3)`

B

`|2x|ltsqrt(3)`

C

`|2x|gesqrt(3)`

D

`|2x|lesqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=0` if `(3/(pi)tan^(-1)2x)^(2)gt1`
`impliestan^(-1)2xgt(pi)/3` or `tan^(-1)2xlt-(pi)/3`
`implies2xgtsqrt(3)` or `2xlt-sqrt(3)`
`=|2x|gtsqrt(3)`
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