$\mathop {\lim }\limits_{x \to a} \frac{{{x^2} - {a^2}}}{{x - a}} = $

The value of $\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} \right)$ is

If $\sum_{r=1}^{n}(2r-1) = x$,then find the value of $\lim_{n}$ ${\rightarrow \infty} \left[ \frac{1^3}{x^2} + \frac{2^3}{x^2} + \frac{3^3}{x^2} + \ldots + \frac{n^3}{x^2} \right]$.

$\mathop {\lim }\limits_{x \to 0} {(\cos mx)^{n/{x^2}}}$ equals

If the value of $\lim _{x \rightarrow 0}(2-\cos x \sqrt{\cos 2 x})^{\left(\frac{x+2}{x^{2}}\right)}$ is equal to $e^{a}$,then $a$ is equal to $.....$

$\mathop {\lim }\limits_{x \to \pi /2} \frac{{1 + \cos 2x}}{{{{(\pi - 2x)}^2}}} = $