The points of discontinuity of the function `lim_(n->oo) (((2 sin x )^(2n))/(3^n- (2 cosx )^(2n)))`

Options

A. R
B. `{n pi pm (pi)/(3), n in I}`
C. `{n pi pm (pi)/(6), n in I}`
D. None of these

Answer

C

Explanation

We have,
`f(x) =lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2cosx)^(2n))=lim_(n to oo) ((2 sinx)^(2n))/((sqrt(3))^(2n)-(2 cos x)^(2n))`
f(x) is discontinuous, when `(sqrt(3))^(2n)-(2 cos x)^(2n)=0`
`rArr cosx =(sqrt( 3))/(2)`
`rArr cos x = "cos"(pi)/(6) rArr x = n pi pm (pi)/(6)`