JEE PYQ: Continuity And Differentiability Question 2
Question 2 - 2021 (16 Mar Shift 2)
Let $\alpha \in \mathbb{R}$ be such that the function
$$f(x) = \begin{cases} \dfrac{\cos^{-1}(1 - {x}^2) \sin^{-1}(1 - {x})}{{x} - {x}^3}, & x \neq 0 \ \alpha, & x = 0 \end{cases}$$
is continuous at $x = 0$, where ${x} = x - [x]$, $[x]$ is the greatest integer less than or equal to $x$.
Then:
(1) $\alpha = \dfrac{\pi}{\sqrt{2}}$
(2) $\alpha = 0$
(3) no such $\alpha$ exists
(4) $\alpha = \dfrac{\pi}{4}$
BETA
