Let $f(x)=\frac{x}{\left(1+x^{n}\right)^{\frac{1}{n}}}, x \in \mathbb{R}-\{-1\}, n \in \mathbb{N}, n > 2$.

If $f^{n}(x)=\left(f \circ f \circ f \ldots .\right.$. upto $n$ times) $(x)$, then
$\lim_{n \to \infty} \int_{0}^{1} x^{n-2} \left( f^{n}(x) \right) dx$ is equal to ____________.