Limits and Cont...

The value of $$\displaystyle\lim_{x\to 0} |x|^{sinx}$$ equals 

$$\lim _ { x \rightarrow 0 } \frac { 1 - \cos x \cos 2 x \cos 3 x } { \sin ^ { 2 } 2 x } =$$

Arrange the following limits in the ascending order :
(1)  $$\lim _ { x \rightarrow \infty } \left( \dfrac { 1 + x } { 2 + x } \right) ^ { x + 2 }$$

(2)  $$\lim _ { x \rightarrow 0 } ( 1 + 2 x ) ^ { 3 / x }$$

(3)  $$\lim _ { \theta \rightarrow 0 } \dfrac { \sin \theta } { 2 \theta }$$

(4)  $$\lim _ { x \rightarrow 0 } \dfrac { \log _ { e } ( 1 + x ) } { x }$$

The value of $$lim_{x \to 0} (\dfrac{1}{x^2} - cotx)$$ equals 

$$ \displaystyle \lim _{ x-\infty  }{ sgn\left( \cot{\dfrac { { \pi x }^{ 2019 } }{ { x }^{ 2019 }+7 }}  \right)  }$$

$$\displaystyle\lim_{x \to \pi/2} (sec x +tan x)$$ is equal to 

$$\mathop{\lim}\limits_{x \to 0} \left(\dfrac{3+x}{3-x}\right)^{\dfrac{x+1}{x}}$$ is equal to 

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

$$\displaystyle\lim_{x\to \pi/2} \dfrac{sinx-(sinx)^{sin x}}{1-sin x + In sin x}$$ is equal to

If $$\mathop {\lim }\limits_{x \to 0} \frac{{x\left( {1 + a\cos x} \right) - b\sin x}}{{{x^3}}} = 1,$$ then