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

$$ \mathop {\lim }\limits_{x \to 0} \frac{x+2 \sin x+3 \tan x-\tan ^3 x}{\sqrt{x^2+2 \sin x+\tan x+3}-\sqrt{\sin ^2 x-2 \tan x-x+3}} $$

$$ \mathop {\lim }\limits_{x \to \infty } \frac{(3-x)^{25}(6+x)^{35}}{(12+x)^{38}(9-x)^{22}}= $$