$\mathop {\lim }\limits_{n \to \infty } \left\{ {\frac{1}{{{n^2}}} + \frac{2}{{{n^2}}} + \frac{3}{{{n^2}}} + \dots + \frac{n}{{{n^2}}}} \right\}$ is

If $\lim _{n \rightarrow \infty} x_n$ exists and is finite,$x_1=2$,$x_{n+1}=\frac{a+b x_n}{b+c x_n}$ for all $n \in N$,and $c > b > a > 0$,then $\lim _{n \rightarrow \infty} x_n =$

$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{{\sum_{k=1}^{n} {k^2}}}{{{n^3}}}} \right] = $

$\lim _{x \rightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ is equal to

If $\mathop {\lim }\limits_{n \to \infty } \frac{1}{{10 + {{\left( {2\cos x} \right)}^{2n}}}} = 0$,then the complete set of all possible values of $|\sin x|$ is:

$\lim _{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4} = $