Let $f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x} + \sqrt{2}}{\sqrt{16 + \sqrt{x}}}, & x > 0 \end{cases}$
If $f(x)$ is continuous at $x = 0$,then the value of $a$ is

If $f(x) = \begin{cases} \frac{\log_{e} x}{x-1} & x \neq 1 \\ k & x=1 \end{cases}$ is continuous at $x=1$,then the value of $k$ is

For every integer $n$,let $a_n$ and $b_n$ be real numbers. Let function $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = \begin{cases} a_n + \sin \pi x, & \text{for } x \in [2n, 2n+1] \\ b_n + \cos \pi x, & \text{for } x \in (2n-1, 2n) \end{cases}$,for all integers $n$. If $f$ is continuous,then which of the following hold$(s)$ for all $n$?

If the function $f(x) = \begin{cases} -2 \sin x, & x \leq \frac{-\pi}{2} \\ A \sin x+B, & \frac{-\pi}{2} < x < \frac{\pi}{2} \\ \cos x, & x \geq \frac{\pi}{2} \end{cases}$ is continuous everywhere,then the values of $A$ and $B$ are respectively

Let $f(x) = \begin{cases} \frac{x^4-5x^2+4}{|(x-1)(x-2)|} & , x \neq 1,2 \\ 6 & , x=1 \\ 12 & , x=2 \end{cases}$. Then $f(x)$ is continuous on the set:

Let $f(x) = \min \{x, x^2\}$ for every real number $x$. Then: