$\mathop {\lim }\limits_{m \to \infty } {\left( {\cos \frac{x}{m}} \right)^m} = $

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 0} \frac{ax+b}{cx+1}$

$\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

If $0 \leq x \leq \pi / 2$,then $\lim _{x \rightarrow a} \frac{|2 \cos x-1|}{2 \cos x-1}$

$\mathop {\lim }\limits_{x \to 0} \frac{{x\sqrt {{y^2} - {{(y - x)}^2}} }}{{{{(\sqrt {8xy - 4{x^2}} + \sqrt {8xy} )}^3}}}$ is equal to

The value of $\lim _{x}$ ${\rightarrow \frac{\pi}{2}} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan \left(\frac{x}{2}\right)\right)(\pi-2 x)^3}$ is