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 $\ldots$

If $\lim\limits_{x \to \infty}\left[\dfrac{x^2+x+1}{x+1} - ax - b\right] = 3$, then $a - b = $...

The number of point / points where the function $f(x) = \dfrac{1}{x^2-5|x|+6}$ is discontinuous is......

If the function $f(x) = \dfrac{4\sqrt{2}(\sin 3x + \sin x)}{2\sin 2x\sin\dfrac{3x}{2} + \cos\dfrac{5x}{2} - \cos\dfrac{3x}{2}}$ for $x \neq \dfrac{\pi}{2}$ is continuous at $x = \dfrac{\pi}{2}$, then the value of $f\left(\dfrac{\pi}{2}\right)$ is equal to