$\mathop {\lim }\limits_{x \to 0} \frac{{\sin ax}}{{\sin bx}} = $

$\mathop {\lim }\limits_{x \to 2} \left( {\frac{{\sqrt {1 - \cos \{ 2(x - 2)\} } }}{{x - 2}}} \right) = $

$\lim _{x \rightarrow 0} \left( \frac{\sin ax}{\tan bx} \right)$ is equal to

The value of $\mathop {\lim }\limits_{x \to 0} \frac{(1 - \cos 2x)\sin 5x}{x^2 \sin 3x}$ is

$\lim _{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} = $

If $x = \log_e \left( \cot \left( \frac{\pi}{4} + \theta \right) \right)$,then $\lim_{\theta \rightarrow 0} \frac{\theta}{(\sinh x)(\cosh x)} = $