If $\lim _{x \rightarrow 0} \frac{\cos 2x - \cos 4x}{1 - \cos 2x} = k$,then $\lim _{x \rightarrow k} \frac{x^k - 27}{x^{k+1} - 81} = $

If $[x]$ is the greatest integer function,then $\lim _{x \rightarrow 3^{-}} \frac{(3-|x|+\sin |3-x|) \cos [9-3 x]}{|3-x|[3 x-9]} = $

$\mathop {\lim }\limits_{x \to \pi /2} \frac{\tan 3x}{x} = $

$\mathop {\lim }\limits_{x \to - 1} \frac{{\sqrt \pi - \sqrt {{{\cos }^{ - 1}}x} }}{{\sqrt {x + 1} }}$ is equal to

If $\lim_{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+\ldots+(nk+n)] = 33 \cdot \lim_{n \rightarrow \infty} \frac{1}{n^{k+1}} \cdot [1^k + 2^k + 3^k + \ldots + n^k]$,then the integral value of $k$ is equal to $....$

The set of all values of $a$ for which $\lim_{x \rightarrow a}(\lfloor x-5 \rfloor - \lfloor 2x+2 \rfloor) = 0$,where $\lfloor \alpha \rfloor$ denotes the greatest integer less than or equal to $\alpha$,is equal to