Question

Let $\\{x\\}$ denote the fractional part of $x$, and $f(x) = \frac{\cos^{-1}(1 - \\{x\\}^2) \sin^{-1}(1 - \\{x\\})}{\\{x\\} - \\{x\\}^3}, \quad x \neq 0$.If $L$ and $R$ respectively denote the left-hand limit and the right-hand limit of $f(x)$ at $x = 0$, then $\frac{32}{\pi^2} \left(L^2 + R^2\right)$ is equal to \\_\\_\\_\\_\\_\\_\\_\\_.

Answer 1

The correct answer is