If the function $f(x) = \begin{cases} \frac{\tan 4x \times \cos 3x}{x} & , x \neq 0 \\ k & , x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is equal to . . . . . .

The number of points at which the function $f(x) = \frac{\sqrt{11+|x|-6\sqrt{2+|x|}}}{6-2\sqrt{2+|x|}}$ is discontinuous in $(-\infty, \infty)$ is

$f$ is continuous at $x=\frac{\pi}{2}$ where,
$f(x)=\begin{cases}\frac{2 k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 2024, & x=\frac{\pi}{2}\end{cases}$ then,the value of $k$ is . . . . . .

If $f(x) = \frac{10^x + 7^x - 14^x - 5^x}{1 - \cos x}$ for $x \neq 0$ is continuous at $x = 0$,then the value of $f(0)$ is:

Let $f: \left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow \mathbb{R}$ be defined as
$f(x) = \begin{cases} (1+|\sin x|)^{\frac{3a}{|\sin x|}}, & -\frac{\pi}{4} < x < 0 \\ b, & x = 0 \\ e^{\frac{\cot 4x}{\cot 2x}}, & 0 < x < \frac{\pi}{4} \end{cases}$
If $f$ is continuous at $x = 0$,then the value of $6a + b^2$ is equal to:

Find all points of discontinuity of $f,$ where $f$ is defined by $f(x) = \begin{cases} x^3 - 3, & \text{if } x \le 2 \\ x^2 + 1, & \text{if } x > 2 \end{cases}$