Limits and Cont...

$$\lim _{ x\rightarrow 0 }{ \frac { 1 }{ { x }^{ 8 } } [1-\cos { (\frac { { x }^{ 2 } }{ 2 } ) } ] } [1-\cos { (\frac { { x }^{ 2 } }{ 4 } ) } ]$$

$$\underset { x\rightarrow a }{ lim } \left( \sin { \dfrac { x-a }{ 2 } \tan { \dfrac { \pi x }{ 2a }  }  }  \right)$$

The value of $$\mathop {{\text{Limit}}}\limits_{x \to 0} \frac{{\cos \left( {\sin x} \right) - \cos x}}{{{x^4}}}$$ is equal to 

$$\displaystyle \lim _{ x\rightarrow 0 }{ \left[ \dfrac { 100\tan { x } .\sin { x }  }{ { x }^{ 2 } }  \right]  } $$ where $$[.]$$ represents greatest integer function is 

The value of $$ \lim _ { x \rightarrow 0 } \dfrac { \sin^3 ( \sqrt { x } ) \ln ( 1 + 3 x ) } { \left( \tan ^ { - 1 } \sqrt { x } \right) ^ { 2 } \left( e ^ { 5 ( \sqrt { x } ) } - 1 \right)x } $$ is equal to

The value of $$\lim _{ x\rightarrow \frac { \pi  }{ 2 }  }{ \tan ^{ 2 }{ \left( \sqrt { 2\sin ^{ 2 }{ x } +3\sin { x } +4 } -\sqrt { \sin ^{ 2 }{ x } +6\sin { x } +2 }  \right)  }  } $$ is equal to

$$ \lim _{x \rightarrow 0}\left(\frac{e^{x}+e^{-x}-2}{x^{2}}\right)^{1 / x^{2}} $$

$$\mathop {Lt}\limits_{x \to 1} {\left( {1 - x} \right)^{\tan \pi x}} = $$

$$\begin{matrix} lim \\ x\rightarrow a \end{matrix}(2-\frac { a }{ x } ){  }^{ tan(\frac { \pi x }{ 2a } ) }$$ is equal to 

The value of $$\displaystyle \lim _{ x\rightarrow 0 }\log_{\cos{2x}}{\cos{x}}+\log_{\cos{2x}}{\cos{2x}}$$ equals