Let the function $f(x)$ be defined as:
$f(x) = \begin{cases} \left[\tan\left(\dfrac{\pi}{4} + x\right)\right]^{\dfrac{1}{x}}, & x \neq 0 \\ k, & x = 0 \end{cases}$
If $f(x)$ is continuous at $x = 0$, then the value of $k$ is...

If $y = f\left(\dfrac{3 + 2x}{3 - 2x}\right)$, where $f(x) = \tan(\log x)$ and $\dfrac{dy}{dx} = \left(\dfrac{A}{B + C x^2}\right) \cdot \sec^2\left(\log\left(\dfrac{3 + 2x}{3 - 2x}\right)\right)$, then the respective values of A, B and C are ......

If $y = \sqrt{x^2 + 8x + 3}$, then the value of $\dfrac{d^2 y}{dx^2}$ at $x = 3$ is

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \cdots \cdots \cdots \infty}}}$, then $\left(\dfrac{dy}{dx}\right)^2$ at $x = \dfrac{\pi}{4}$ is