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

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,

$$ \lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)= $$

If the function $f$ defined by

$$ f(x)=\left\{\begin{array}{cc} \frac{1-\cos 4 x}{x^2}, & x<0 \\ a, & x=0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & x>0 \end{array}\right. $$

is continuous at $x=0$, then $a=$

The domain of the derivative of the function $f(x)=\frac{x}{1+|x|}$ is