$\mathop {\lim }\limits_{x \to \infty } \sqrt {\frac{{x + \sin x}}{{x - \cos x}}} = $

If $\lim _{x \rightarrow 0} \frac{\left(e^{k x}-1\right) \sin k x}{x^{2}}=4$,then $k$ is equal to

$\lim _{n}$ ${\rightarrow \infty} \frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\ldots +\left((n-1)^2-(n-1)\right) \cdot 1}{\left(1^3+2^3+\ldots +n^3\right)-\left(1^2+2^2+\ldots +n^2\right)}$ is equal to:

$\lim _{\theta \rightarrow \frac{\pi}{2}^{-}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4} = $

The limit of the interior angle of a regular polygon of $n$ sides as $n \rightarrow \infty$ is

If $\mathop {\lim }\limits_{n \to \infty } \frac{1 - 10^n}{1 + 10^{n+1}} = \frac{-\alpha}{10}$,then find the value of $\alpha$.