The set of points of discontinuity of the function f ( x )= displaystyle lim n arrow ∞ ((2 sin x )2 n /3 n -(2 cos x )2 n ) is given by

Question

The set of points of discontinuity of the function f ( x )= displaystyle lim n arrow ∞ ((2 sin x )2 n /3 n -(2 cos x )2 n ) is given by (A) R (B)  n π ± (π/3), n ∈ I  (C)  n π ± (π/6), n ∈ I  (D) None of these

Tardigrade Admin · Accepted Answer

We have, f(x)= displaystyle lim n arrow ∞ ((2 sin x)2 n/3n-(2 cos x)2 n) = displaystyle lim n arrow ∞ ((2 sin x)2 n/(√3)2 n-(2 cos x)2 n) f ( x ) is discontinuous when (√3)2 n -(2 cos x )2 n =0 i.e. cos x=± (√3/2) ⇒ x=n π ± (π/6)(n ∈ I )

Q. The set of points of discontinuity of the function $f (x) = n \to \infty lim \frac{( 2 sin x ) ^{2 n}}{3 ^{n} - ( 2 cos x ) ^{2 n}}$ is given by

$R$

${nπ \pm \frac{π}{3}, n \in I}$

${nπ \pm \frac{π}{6}, n \in I}$

None of these

Q. The set of points of discontinuity of the function f(x)=n→∞lim​3n−(2cosx)2n(2sinx)2n​ is given by

R

{nπ±3π​,n∈I}

{nπ±6π​,n∈I}

None of these

We have, f(x)=n→∞lim​3n−(2cosx)2n(2sinx)2n​ =n→∞lim​(3​)2n−(2cosx)2n(2sinx)2n​ f(x) is discontinuous when (3​)2n−(2cosx)2n=0 i.e. cosx=±23​​⇒x=nπ±6π​(n∈I)

Q. The set of points of discontinuity of the function $f (x) = n \to \infty lim \frac{( 2 sin x ) ^{2 n}}{3 ^{n} - ( 2 cos x ) ^{2 n}}$ is given by

$R$

${nπ \pm \frac{π}{3}, n \in I}$

${nπ \pm \frac{π}{6}, n \in I}$