$\text{ The number of points of discontinuity of }f\left(x\right)={\mathrm{Lt}}_{n\to \mathrm{\infty }}\left[\frac{x^{2n}-1}{x^{2n}+1}\right]\text{ is }$

$f\left(x\right)=\frac{1-\frac{1}{x^{2n}}}{1+\frac{1}{x^{2n}}}=\left\{\begin{array}{l}1,x<-1\\ 0,x=-1\\ -1,-1<x<1\\ 0\text{ , }x=1\\ \text{1 , }x>1\end{array}\right.$     $\therefore f\left(x\right)\text{ is discontinuous at X=±1}$