$\mathop {\lim }\limits_{x \to 0^+} {x^x} = $

$\mathop {\lim }\limits_{\theta \to {0^ + }} {(\sin \theta )^{(\sin \theta - {{\sin }^2}\theta )}}$ is

$\mathop {\lim }\limits_{\theta \to \frac{\pi }{2}} \frac{\frac{\pi }{2} - \theta}{\cot \theta} =$

Let $f(2) = 4$ and $f'(2) = 4$,then $\mathop {\lim }\limits_{x \to 2} \,\frac{{xf(2) - 2f(x)}}{{x - 2}}$ equals

If $\alpha, \beta$ are the distinct roots of $x^{2}+bx+c=0$,then $\lim _{x \rightarrow \beta} \frac{e^{2(x^{2}+bx+c)}-1-2(x^{2}+bx+c)}{(x-\beta)^{2}}$ is equal to:

$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right] = $