Limits and Cont...

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

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

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

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

If $$\alpha$$ and $$\beta$$ be the roots of the equation $$ax^{2} + bx + c = 0$$ then $$\displaystyle \lim_{x\rightarrow \dfrac {1}{\alpha}} \sqrt {\dfrac {1 - \cos^{2} (cx^{2} + bx + a)}{4(1 - \alpha x)^{2}}}$$

The value of $$\begin{matrix} lim \\ x\rightarrow \frac { 1 }{ \sqrt { 2 }  }  \end{matrix}\dfrac { x-cos\left( { sin }^{ -1 }x \right)  }{ 1-tan\left( { sin }^{ -1 }x \right)  } is$$

$$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}\frac { xcot(4x) }{ { sin }^{ 2 }x{ cot }^{ 2 }\left( 2x \right)  } $$ is equal to 

the value of $$\underset { x\longrightarrow \infty  }{ lim } \frac { { X }^{ 4 }sin\left( \frac { 1 }{ x }  \right) +{ x }^{ 3 } }{ 1+\left| x \right| ^{ 3 } } $$

$$\underset { x\rightarrow 0 }{ lim } \dfrac { sec4x-sec2x }{ sec3x-secx } =$$

$$\displaystyle \lim_{x\rightarrow 0} \dfrac {\sin 2x + 3x}{2x + \sin 3x}$$ is equal to