Limits and Cont...

The value of $$lim_{x\to 0} \dfrac{sin(\pi cos^2 x)}{x^2}$$ equals 

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

The value of $$\displaystyle\lim _ { x \rightarrow \infty } a ^ { x } \sin \left( \frac { b } { a ^ { x } } \right)$$ where $$a > 1$$ is 

The value of $$\displaystyle \lim _{ x\rightarrow 3 }{ \dfrac { \left( { x }^{ 3 }+27 \right) \log _{ e }{ \left( x-2 \right)  }  }{ { x }^{ 2 }-9 }  } $$ is

$$\underset { x\rightarrow 1 }{ lim } \frac { xtan(x-[x]) }{ x-1 } $$ is:

The value of $$\displaystyle \lim_{x \rightarrow 0} \left(\dfrac{\sin x}{x}\right)^{1/x^{2}}$$ is 

$$\lim_{x\rightarrow 0 }(\frac{p^{\frac{1}{x}}+q^{\frac{1}{x}}+r^{\frac{1}{x}}+s^{\frac{1}{x}}}{4})3x $$ where p,q,r,s$$> 0 $$ is equal to

The value of $$lim_{\theta \to \dfrac{\pi}{2}} (sec \theta - tan \theta)$$ equals 

$$\lim- {x\to 0}$$ $$\dfrac{1- cos(1 - cos4x)}{x^4}$$ is equal to : 

If $$\displaystyle \lim _{ x\rightarrow 0 }{ \dfrac { \left( \sin { nx }  \right) \left[ (a-n)nx-tanx \right]  }{ { x }^{ 2 } }  } =0$$, then the value of $$a$$