$$ \lim\limits_{x \rightarrow \infty}[x-\log (\cosh x)]= $$

$$ \lim\limits_{x \rightarrow \infty}\left(\sqrt[3]{x^3+4 x^2}-\sqrt{x^2-3 x}\right)= $$

If a real valued function $f(x)=\left\{\begin{array}{cl}e^{\frac{\sin a(x-[x])}{x-[x]}} & , \text { if } x<1 \\ b+1 & , \text { if } x=1 \text { is } \\ \frac{\left|x^2+x-2\right|}{x-1} & , \text { if } x>1\end{array}\right.$ continuous at $x=1$, then $b \sin a=([x]$ denotes the greatest integer function)

$$\mathop {\lim }\limits_{x \to {\pi \over 4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x}= $$