Question

`Let f(x)=lim_(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)`. Then the set of values of x for which `f(x)=0` is
A. 199
B. 198
C. 0
D. none of these

Answer 1

Correct Answer - A
Given `g(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)=0`
or`underset(ntooo)lim[((3)/(pi)tan^(-1)2x)^(2)]^(n)rarroo`
or`((3)/(pi)tan^(-1)2x)^(2)gt1`
or `|tan^(-1)2x|gt(pi)/(3)`
i.e., i.e.,`tan^(-1)2xlt-(pi)/(3)" or "tan^(-1)2xgt(pi)/(3)`
`2xlt1sqrt(3)" or "2xgtsqrt(3),i.e.,|2x|gtsqrt(3)`