Limits and Cont...

$$\displaystyle\lim_{x\rightarrow 0}\dfrac{x\tan 2x-2x\tan x}{(1-\cos 2x)^2}$$ is equal to?

If $$f(x)$$ is odd linear polynomial with $$f(1)=1$$, then $$\underset{x \to 0} {\lim} \dfrac{2^{f(\tan x)}-2^{f(\sin x)}}{x^{2}f(\sin x)}$$ is 

If $$\displaystyle\lim_{x\rightarrow 0}[1+x ln (1+b^2)]^{1/x}=2b\sin^2\theta, b > $$ s m f $$\theta\in (-\pi, \pi]$$, then the value of $$\theta$$ is?

 $$\lim _ { x \rightarrow \infty } \dfrac { \sin \left( \pi \cos ^ { -2 } x \right) } { x ^ { 2 } }$$  is equal to:

The value of $$\underset { x\rightarrow 0 }{ lim } \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ \sqrt { 5 } -\sqrt { 4+cosx }  } $$ is 

$$\lim _ { x \rightarrow 0 } \dfrac { | \cos ( \sin ( 3 x ) ) | - 1 } { x ^ { 2 } }$$   equals

$$\lim _ { x \rightarrow 0 } \left( \left[ \dfrac { - 5 \sin x } { x } \right] + \left[ \dfrac { 6 \sin x } { x } \right] \right)$$  (where  $$[ .]$$  denotes greatest integer function) is equal to

$$\displaystyle\lim_{x\rightarrow \dfrac{\pi}{4}}\dfrac{\cos x-\sin x}{\left(\dfrac{\pi}{4}-x\right)(\cos x+\sin x)}=?$$

$$\displaystyle\lim_{x\rightarrow 0}\left\{\dfrac{log_e(1+x)}{x^2}+\dfrac{x-1}{x}\right\}$$ is equal to?

 Consider  $$\lim _ { x \rightarrow 0 } \dfrac { a x + b e ^ { - x } + \sin x + 1 } { a x - b \sin x } = \ell ( \ell$$  is a finite number)