The set of points of discontinuity of the function $\text{⨍ (x)=}\underset{\mathrm{n}\to \infty }{\mathrm{Lt}}\frac{{(2\sin \mathrm{x})}^{2\mathrm{n}}}{3^{\mathrm{n}}-{(2\cos \mathrm{x})}^{2\mathrm{n}}}$ is

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=\underset{\mathrm{n}\to \infty }{\lim }\frac{{\left(2 \sin \mathrm{x}\right)}^{2\mathrm{n}}}{3^{\mathrm{n}}-{\left(2 \cos \mathrm{x}\right)}^{2\mathrm{n}}} \\ \mathrm{is} \mathrm{discontinuous} \\ \mathrm{if} 3^{\mathrm{n}}-{\left(2 \cos \mathrm{x}\right)}^{2\mathrm{n}}=0 \\ \Rightarrow {\left(4 {\cos }^2\mathrm{x}\right)}^{\mathrm{n}}=3^{\mathrm{n}} \\ \Rightarrow {\cos }^2\mathrm{x}=\frac{3}{4}={\cos }^2\frac{\mathrm{\pi }}{6} \\ \Rightarrow \mathrm{x}=\mathrm{n\pi }\pm \frac{\mathrm{\pi }}{6}; \mathrm{n}\in \mathrm{z} \end{gathered}$$