Limits and Cont...

$$\lim_{x\rightarrow 0}\dfrac{2\left(\sqrt{3}\sin\left(\dfrac{\pi}{6}+x\right)-\cos\left(\dfrac{\pi}{6}+x\right)\right)}{x\sqrt{3}\left(\sqrt{3}\cos x-\sin x\right)}$$

$$\lim_{x\rightarrow \pi/4}\dfrac{2\sqrt{2}-\left(\cos x+\sin x\right)^{2}}{1-\sin 2x}$$ is equal to 

the value of $$\underset { x\rightarrow \infty  }{ lim } \frac { { x }^{ 5 } }{ { 5 }^{ x } } $$ is-

$$\lim _ { x \rightarrow 5 } \frac { \sin ^ { 2 } ( x - 5 ) \tan ( x - 5 ) } { \left( x ^ { 2 } - 25 \right) ( x - 5 ) } =$$

$$\underset { x\rightarrow \pi /4 }{ Lim } \dfrac { 2\sqrt { 2 } \left( cosx+sinx \right) ^{ 3 } }{ 1-sin2x } =2$$ is equal to

The value f $$\lim_{x\rightarrow \pi/4}\dfrac{\sqrt{1-\sqrt{\sin 2x}}}{\pi-4x}=$$

If $$\displaystyle \lim_{x\rightarrow 0}\dfrac {ae^{-x}-b\cos x-\dfrac {1}{2}cx}{x\cos x}=2$$ then the value of $$a+b+c$$ is-

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

If $$\underset { x\rightarrow 0 }{ Lim } \dfrac { \left( 1+{ a }^{ 3 } \right) +8{ e }^{ 1/x } }{ 1+\left( 1-{ b }^{ 3 } \right) +{ e }^{ 1/x } } =2$$ then

$$\underset{x \rightarrow n/2}{lim} \dfrac{\cot x - \cos x}{(\pi - 2x)^3}$$ equals