If $\tan^{-1}ax + \tan^{-1}3x = \dfrac{\pi}{4}$, where $3ax^2 < 1$, then value of $a$ for $x = \dfrac{1}{6}$ is $\ldots$

$\sec^2(\tan^{-1}3) - \tan^2(\sec^{-1}3) = $

The domain of the function $f(x) = \sqrt{\dfrac{x}{1+x}}$ is $\ldots$

If $f(x) = \dfrac{3^x + 3^{-x} - 2}{\tan x \cdot \log(1+x)}$ for $x \neq 0$, is continuous at $x = 0$, then the value of $f(0)$ is equal to $\ldots$