Limits and Cont...

The value of $$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}$$ $$[\frac{x}{sinx}],$$ where [.] represents the greatest inter function , is 

$$\underset { x\rightarrow 0 }{ lim } \left( \dfrac { 1+tanx }{ 1+sinx }  \right) ^{ cosecx }$$ is equal to

The value of $$\displaystyle \lim_{x\rightarrow 0}\left(\dfrac {1}{x^{2}}-\cot x\right)$$ equals

$$\underset { \theta \longrightarrow 0 }{ Lt } \dfrac { 3tan\theta -tan3\theta  }{ { 2\theta  }^{ 3 } } =$$

$$\underset { x\rightarrow 0 }{ Lt\quad  } \frac { sec\quad x-1 }{ { \left( sec\quad x+\quad 1 \right)  }^{ 2 } } =$$

Value of $$\underset { x\rightarrow 0 }{ lim } \dfrac { \sqrt [ 3 ]{ 1+\tan { x }  } -\sqrt [ 3 ]{ 1-\tan { x }  }  }{ x } $$ is

If $$\begin{matrix} lim\quad  \\ x\rightarrow 0 \end{matrix}\dfrac { x\left( 1+acosx \right) -bsinx }{ { x }^{ 3 } } =1$$ then value of a + b 

$$\underset { x\rightarrow 0 }{ Lt } (1+sin\quad x)^{ cot\quad x }=$$ 

Value of $$\underset { x\rightarrow \dfrac { \pi  }{ 2 }  }{ lim } \tan { x } .\ell nsin{ x }$$ is 

For $$a > 1$$ then $$\displaystyle\lim_{x\rightarrow \infty}\dfrac{a^x-a^{-x}}{a^x+a^{-x}}=?$$