$\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots .(2)\right]^{1 / n}=$

$$ \begin{array}{r} \lim _{x \rightarrow 0} \frac{2 \tan x+\cos x-1+x}{\sqrt{4 \sin ^2 x+2 \tan x+1}}= \\ -\sqrt{3 \tan ^2 x+\sin x+1} \end{array} $$

If a function $f$ is defined by $f(x)=\frac{\cot ^3 x-\tan x}{\cos (x+\pi / 4)},(x \neq \pi / 4)$, then $\lim _{x \rightarrow \pi / 4} f(x)=$

$$ \lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n\left(k^2 x\right)= $$