Given four statements below,
$S_1$ : The value $\underset{x\to 0}{\lim }\frac{\sqrt{(1-\cos 2x)}}{x}is\sqrt{2}$
$S_2$ : The value $\underset{x\to 0}{\lim }\frac{\sqrt{(1-\cos 2x)}}{\left|x\right|}is\sqrt{2}$
$S_3$ : Given function $f:R-\left\{0\right\}\to R,f\left(x\right)=\frac{\left(\sin 3x\right)(1-\cos 6x)(e^{2x}-1)}{x^4}$ , then the value of  $\underset{x\to 0}{\lim }\frac{\left(\sin 3x\right)(1-\cos 6x)(e^{2x}-1)}{x^4}$ is  $108$
$S_4$ : Given function  $f:R-\left\{0\right\}\to R,f\left(x\right)=\frac{\left(\sin ax\right)(1-\cos 2ax)(e^{2x}-1)}{x^4},a\in R$ ,  then the value of    $\underset{a\to 0}{\lim }\frac{\left(\sin ax\right)(1-\cos 2ax)(e^{2x}-1)}{x^4}is4a^3$
Number of the statements among the given statements is/are CORRECT?