Let $f(x) = \frac{x - 1}{2x^2 - 7x + 5}$. Then:

The value of $\lim _{x \rightarrow 0} \operatorname{cosec} x\left(\sqrt{2 \cos ^2 x+3 \cos x}-\sqrt{\cos ^2 x+\sin x+4}\right)$ is

If $\lim _{x \rightarrow \infty}\left(1+\frac{p}{x}\right)^{q x}=e^9$ where $p, q \in \mathbb{N}$,then $p+q=$

If $\lim_{x}$ ${\rightarrow 0} \left\{ \frac{1}{x^{8}} \left( 1 - \cos \frac{x^{2}}{2} - \cos \frac{x^{2}}{4} + \cos \frac{x^{2}}{2} \cos \frac{x^{2}}{4} \right) \right\} = 2^{-k}$,then the value of $k$ is

The value of $\lim_{x \rightarrow 1} \frac{(x^{2}-1) \sin^{2}(\pi x)}{x^{4}-2x^{3}+2x-1}$ is equal to

$\lim _{x \rightarrow 0} \frac{\tan 2x - 2\tan x}{(1 - \cos x)(2^x - 1)} = $