List of top Mathematics Questions on Continuity asked in KEAM

Let $f(x) = \begin{cases} \frac{1-\sec^2(\alpha x)}{\alpha x^2}, & \text{for } x \neq 0 \\ -3, & \text{for } x = 0 \end{cases}$ be continuous at $x = 0$. Then the value of $\alpha$ is equal to

If \[ f(x)= \begin{cases} x^2, & \text{if } x\leq 2,\\[4pt] 4x-\alpha, & \text{if } x>2, \end{cases} \] is continuous at $x=2$, then the value of $\alpha$ is equal to: