Limits and Cont...

The value of $$\lim_{x \rightarrow 1} \sec \dfrac{\pi}{2x} \log x$$ is-

Evaluate: $$\underset { x\rightarrow 0 }{ \lim } \dfrac { x\tan2x-2x\tan x }{ \left( 1-\cos2x \right) ^{ 2 } } $$ 

Evaluate: $$\underset { x\rightarrow { 0 } }{ lim } \dfrac { x\tan 2x-2x \tan\ x\quad  }{ (1-\cos2x)^{ 2 } } $$

$$\lim _ { x \rightarrow \frac { \pi } { 2 } } \frac { \cot x - \cos x } { ( \pi - 2 x ) ^ { 3 } }$$ equals:

The function $$f\left( x \right) = \dfrac{{4 - {x^2}}}{{4x - {x^3}}}$$ is

If $$2f(\sin x)+\sqrt {2}f(\cos x)=\tan x,\ (x> 0)$$, then $$\displaystyle \lim _{ x\rightarrow 1 }{ \sqrt { 1-x } f\left( x \right) = }$$ 

$$\underset {x\rightarrow0}{ lim } \dfrac{x \tan 2 x - 2 x \tan x}{(1 - \cos 2 x)^2}$$ equals 

Solve:

Let $$f(x)=\begin{cases} { x }^{ 2 }+k,\quad \quad  when\quad x\ge 0 \\ -{ x }^{ 2 }-k,\quad \quad when \quad x<0 \end{cases}$$. If the function $$f(x)$$ be continous at $$x=0$$, then $$k=$$

Evaluate: $$\displaystyle\lim_{x\to 10}\dfrac{x^2-100}{x-10}$$