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 $k=$

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

$[x]$ represents the greatest integer function. If $\mathop {\lim }\limits_{x \to 0 + } \frac{\cos [x]-\cos (k x-[x])}{x^2}=5$, then $k=$

$$ \mathop {\lim }\limits_{x \to 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^2}= $$