Limits and Deri...

$\underset { \rightarrow  }{ Lim } \frac { 1-{ cos }^{ 2 }x }{ xsin2x }$

$\displaystyle x\xrightarrow { lim } 5\quad \left(\frac{\sqrt{1-\cos(2x-10)}}{\sin (x-5)}  \right)$

$\lim _ { x \rightarrow 0 } \int _ { 0 } ^ { x } \dfrac { \left( \tan ^ { - 1 } t \right) ^ { 2 } } { \sqrt { 1 + x ^ { 2 } } } d t$  is equal to

$\underset {x\rightarrow 0}{Lim} \frac {sin x}{x} = y$

If $y=e^{\sin^{2}x +\sin^{4}x + \sin ^{6}x +....+\infty}$ , then $\dfrac {dy}{dx} =?$

The value of $\lim _{ x\rightarrow 0 }{ \left( { \left( \sin { x }  \right)  }^{ 1/x }+{ \left( \dfrac { 1 }{ x }  \right)  }^{ \sin { x }  } \right)  }$

Find:
$\underset { x\rightarrow 0 }{ lim } \quad \dfrac { 1-cos^{ 3 }x }{ xsin2x } =\quad$

$\displaystyle \lim_{x\rightarrow 0}\dfrac {\sin x - x}{x^{3}}$ is equal to

$\lim _{ x\rightarrow 0 }{ \dfrac { 1-\cos { x }  }{ { { x\log { (1+x) }  } } }  }$ =

The value of $\mathop {\lim }\limits_{x \to 0} \frac{{\sec 5x - \sec 3x}}{{\sec 3x - \sec x}}$