If the function $f(x) = \frac{2x - \sin^{-1}x}{2x + \tan^{-1}x}, (x \neq 0)$ is continuous at each point of its domain,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:

Let $f(x) = \begin{cases} \frac{(x - 1)(6x - 1)}{2x - 1}, & \text{if } x \neq \frac{1}{2} \\ 0, & \text{if } x = \frac{1}{2} \end{cases}$. Then at $x = \frac{1}{2}$,

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$ for $x \neq \pi$ is continuous at $x = \pi$,then the value of $f(\pi)$ is

Let $f(x) = \frac{1-\tan x}{4x-\pi}$,where $x \neq \frac{\pi}{4}$ and $x \in [0, \frac{\pi}{2}]$. If $f(x)$ is continuous in $[0, \frac{\pi}{2}]$,then $f(\frac{\pi}{4})$ 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