Limits and Cont...

$$ \lim _{x \rightarrow0}\left(\frac{e^{x}+e^{-x}-2}{x^{2}}\right)^{1 / x^{2}}  $$ is

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 

Let x be an irrational, then $$\underset { m\rightarrow \infty  }{ lim } \underset { n\rightarrow \infty  }{ lim } \left\{ cos(n!\pi x) \right\} ^{ 2m }$$ equals

$$ \lim _ { x \rightarrow 0 } \frac { \sin x } { x } = y $$

$$\underset { \rightarrow  }{ Lim } \frac { 1-{ cos }^{ 2 }x }{ xsin2x } $$

$$\lim_{x\rightarrow 0}\frac{1-cos^{3}x}{x sib x cos x }$$  is equal to 

$$\displaystyle x\xrightarrow { lim } 5\quad \left(\frac{\sqrt{1-\cos(2x-10)}}{\sin (x-5)}  \right) $$

$$\lim _ { x \rightarrow 0 } \int _ { 0 } ^ { x } \dfrac { \left( \tan ^ { - 1 } t \right) ^ { 2 } } { \sqrt { 1 + x ^ { 2 } } } d t$$  is equal to

$$\underset {x\rightarrow 0}{Lim} \frac {sin x}{x} = y $$

$$\underset { x\rightarrow 1 }{ lim } { \left[ cosec { \dfrac { \pi x }{ 2 }  }  \right]  }^{ { 1 }/{ \left( 1-x \right)  } }$$ (where $$[.]$$ represents the greatest integer function) is equal to