\( f(x)=\dfrac{x}{(1+x^n)^\dfrac{1}{n}}, \ x \in \mathbb{R}-\{-1\}, \ n \in \mathbb{N}, \ n>2. \) If \( f^{n}(x)=(f \circ f \circ \ldots f \ \text{upto } n \ \text{times})(x) \), then let \(\displaystyle \lim\limits_{n \to \infty}\int_{0}^{1} x^{\,n-2}\big(f^{n}(x)\big)\,dx \) is equal to ________.
