Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

Let $f(x) = \lim_{\theta \to 0} \left(\frac{\cos\pi x - x^{(2/\theta)}\sin(x-1)}{1 + x^{(2/\theta)}(x-1)}\right)$, $x \in \mathbb{R}$. Consider the following two statements : (I) $f(x)$ is discontinous at $x = 1$. (II) $f(x)$ is continous at $x = -1$. Then,