Evaluate $\mathop {\lim }\limits_{x \to 0} \frac{{{y^2}}}{x}$,where ${y^2} = ax + b{x^2} + c{x^3}$.

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin ({x^{1/3}})\ln (1 + 3x)}}{{{{(\tan^{ - 1}\sqrt x )}^2}({e^{5{x^{1/3}}}} - 1)}} = $

Evaluate: $\cos \left[ \lim_{x \rightarrow \infty} \frac{2 \pi |x| + \pi x}{|x| - 3x} + \lim_{x \rightarrow 0} \frac{\cos \left( \frac{\pi}{2} \cos^2 x \right)}{x^2} \right]$

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}$,where $a+b+c \neq 0$.

$\lim _{x \rightarrow 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 2x)^2}$ is

$\mathop {\lim }\limits_{x \to \infty} \frac{2x^2 + 3x + 4}{3x^2 + 3x + 4}$ is equal to