Limits and Deri...

The value of $$\displaystyle \lim _{ x\rightarrow \frac { x }{ 4 }  }{ \dfrac { 4\sqrt { 2 } -{ \left( \cos { x } +\sin { x }  \right)  }^{ 5 } }{ 1-\sin { 2x }  }  } $$ is

The values of $$\displaystyle\lim_{n\rightarrow \infty}\dfrac{\sqrt[4]{n^5+2}-\sqrt[3]{n^2+1}}{\sqrt[5]{n^4+2}-\sqrt[2]{n^3+1}}$$ is?

$$\displaystyle\lim _{ x\rightarrow 0 }{ \dfrac { x\tan { 2x } -2x\tan { x }  }{ \left( 1-\cos { 2x }  \right) ^{ 2 } }  }$$ equal to 

Let $$f(x)=\displaystyle\lim _{ n\rightarrow \infty  }{ \dfrac { { 2x }^{ 2n }\sin { \frac { 1 }{ x } +x }  }{ 1+{ x }^{ 2x } }  } $$ then find 

$$lim_{x\to \dfrac{\pi}{2}} tan^2x(\sqrt{2sin^2x + 3 sin x +4} - \sqrt{sin^2x + 6 sin x+2})$$ is equal to

Evaluate $$\displaystyle \lim _{ x\rightarrow 0 }{ \dfrac { \sin { \left[ \cos { x }  \right]  }  }{ 1+\left[ \cos { x }  \right]  }  } $$ ($$[.]$$ denotes the greatest integer function)

$$\displaystyle \lim _{ x\rightarrow 0 }{ \frac { x\left( { e }^{ \sin { x }  }-1 \right)  }{ 1-\cos { x }  }  } $$

The value of $$\displaystyle\lim_{\theta \rightarrow 0^+}\dfrac{\sin\sqrt{\theta}}{\sqrt{\sin\theta}}$$ is equal to?

The value of $$\displaystyle\int^{\pi/2}_0ln|\tan x+\cot x|dx$$ is equal to?

$$\displaystyle \lim _{ x\rightarrow 0 } \left(\dfrac{1^{1/x}+2^{1/x}+3^{1/x}+.....n^{1/x}}{n}\right)^{nx} ,\ n\ \epsilon \ N $$ is equal to