Limits and Deri...

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

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

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

$$\underset { x\rightarrow 0 }{ lim } \dfrac { 1 }{ { e }^{ 2 } } tan\left( \dfrac { \pi  }{ 4 } +x \right) ^{ 1/x }$$

If $$cosy=xcos(a+y)and\quad \cfrac { dy }{ dx } =\cfrac { k }{ 1+{ x }^{ 2 }-2xcosa } $$ then find value of k?

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

$$\lim_{x\rightarrow 1}\dfrac {1+\sin \pi\left(\dfrac {3x}{1+x^{2}}\right)}{1+\cos \pi x}$$ is equal to

$$lim_{x \to 0^-} \dfrac{x([x]+ \mid x \mid )sin[x]}{\mid x \mid}$$ is equal to

$$\lim _ { x \rightarrow \frac { \pi } { 2 } } \left( \frac { 1 + \cos x } { 1 - \cos x } \right) ^ { \sec x } =$$

The value of $$\displaystyle \lim _{ x\rightarrow \infty } (|x^{2}|+x)\log{(x\cot^{-1}{x})}$$ is :