If $\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}-a x\right)=b$,then the ordered pair $(a, b)$ is:

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

$\mathop {\lim }\limits_{x \to 0} {\left( {\frac{{1 + \tan x}}{{1 + \sin x}}} \right)^{\text{cosec } x}}$ is equal to

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

Let $L(m)$ be the $x$-coordinate of the left endpoint of the intersection of the graphs of $y = x^2 - 6$ and $y = m$,where $-6 < m < 6$. The value of $\mathop {\lim }\limits_{m \to 0} \left( {\frac{{L\left( { - m} \right) - L\left( m \right)}}{m}} \right)$ equals

The value of $\lim_{x \to 0} (\frac{8}{x^8}) [1 - \cos \frac{x^2}{2} - \cos \frac{x^2}{4} + \cos \frac{x^2}{2} \cdot \cos \frac{x^2}{4}]$ is equal to: