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

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

If a real valued function

$$ f(x)=\left\{\begin{array}{cc} \log (1+[x]), & x \geq 0 \\ \sin ^{-1}[x], & -1 \leq x<0 \\ k([x]+|x|), & x<-1 \end{array}\right. $$

is continuous at $x=-1$, then $k=$

$$\mathop {\lim }\limits_{n \to \infty } \frac{\pi}{2 n}\left[\sin \frac{\pi}{2 n}+\sin \frac{2 \pi}{2 n}+\sin \frac{3 \pi}{2 n}+\ldots+\sin \frac{\pi}{2}\right]= $$