$The function f : R\to R defined by f\left(x\right)=\underset{n\to \infty }{\lim }\frac{\cos \left(2\pi x\right)-x^{2n}\sin \left(x-1\right)}{1+x^{2n+1}-x^{2n}} is continuous for all x in$

$f\left(x\right)=$$$\begin{gathered} n should be given as a natural number. \\ \left\{\begin{array}{l}-\frac{\sin \left(x-1\right)}{x-1} x<-1\\ -\left(\sin 2+1\right) x=-1\\ \cos 2\pi x -1<x<1\\ 1 x=1\\ \frac{-\sin \left(x-1\right)}{x-1} x>1\end{array}\right. \end{gathered}$$
$f\left(x\right) is dscontinuous at x=-1 and x=1$