Limits and Cont...

The value of $$\lim_{h\rightarrow 0}\left\{\dfrac {1}{h.(8+h)^{1/3}-\dfrac {1}{2h}}\right\}$$ equals

$$\underset { h\rightarrow 0 }{ lim } \quad \frac { (2+h)cos(2+h)-2cos2 }{ h } =$$

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

$$\displaystyle \lim _{ x\rightarrow \dfrac { \pi  }{ 2 }  }{ \dfrac { \sin { x }  }{ \cos ^{ -1 }{ \left[ \dfrac { 1 }{ 4 } \left( 3\sin { x } -\sin { 3x }  \right)  \right]  }  }  } $$, where [.] denotes greatest integer function is :

$$Im _{  }{ \left( \dfrac { 1 }{ 1-\cos { \theta  } +i\sin { \theta  }  }  \right)  } $$ is equal to

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

$$\lim _ { x \rightarrow 0 } \frac { \sqrt [ 3 ] { 1 + \sin x } - \sqrt [ 3 ] { 1 - \sin x } } { x } =$$

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