Limits and Cont...

$$ \underset { x\rightarrow 0 }{ lim } \left[ { x }^{ 2 }cosec\quad \left( { x }^{ 2 } \right)^0 \right]  $$is equal to :

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

If $$\lim_{x \rightarrow 0}\dfrac{a \sin x-bx+cx^{2}+x^{3}}{2x^{2} \log(1+x)-2x^{3}+x^{4}}$$ exists and is finite, then the value of $$a,b,c$$ are respectively 

$$ \underset { x\rightarrow a }{ lim } \cfrac { sin\quad x-sin\quad a }{ \sqrt [ 3 ]{ x } -\sqrt [ 3 ]{ a }  }  $$

The value of $$\displaystyle \lim_{x\rightarrow 0}\dfrac {1-\cos^{3}x}{x\sin x\cos x}$$ is

Integrate:
 $$lim_{x\rightarrow 0}\dfrac{(1-\cos{2x})^{2}}{2x\tan{x}-x\tan{2x}}$$

The value of $$\lim_{x \rightarrow 0} \left(\dfrac{\tan x}{x}\right)^{1/x^{3}}$$ is-

$$\displaystyle \lim_{x\rightarrow 0^{+}}{(\csc x)^{1/\log x}}$$=

$$ \underset { x\rightarrow \cfrac { \pi  }{ 2 }  }{ lim } \cfrac { cot \,  x-cos\, x }{ \left( \pi -{ 2x } \right)^ 3 } $$ equals

The value of $$ \underset { x\rightarrow \frac { x }{ 2 }  }{ lim } \frac { log\sin { x }  }{ { \left( \frac { \pi  }{ 2 } -x \right)  }^{ 2 } }$$ is