$\displaystyle \lim_{x \rightarrow 0}\dfrac {1}{x\sqrt {x}}\left(a\ arc\ tan \dfrac {\sqrt {x}}{a}-b\ arc\ \tan \dfrac {\sqrt {x}}{b}\right)$ has the value equal to

Let $a \in \left( 0 , \frac { \pi } { 2 } \right)$, then the value of
$\lim _ { a \rightarrow 0 } \frac { 1 } { a ^ { 3 } } \int _ { 0 } ^ { a } \ell n (1+tan a tan x)dx$ is equal to 

$\underset { x\rightarrow 0 }{ Lt } \cfrac {tanx-x}{x^2tanx}$ equals:

The value of $\lim_{x \rightarrow -1} \dfrac{\sqrt{\pi}-\sqrt{\cos^{-1}x}}{\sqrt{x+1}}$ is given by