$\lim \left( {3 + {{{n^2}\sin 3n} \over {{n^3} + 1}}} \right)$     

$\lim \left( {{n \over {{n^2} + 1}} - 1} \right)$

$\lim {{2n} \over {2n + 1}}$      

$\lim {{n + 1} \over {2n + 1}}$

$\lim {{{{5.2}^n} - \cos 5n} \over {{2^n}}}$  

$\lim {{{n^2} + 2n + 3} \over {2{{\left( {n + 1} \right)}^2}}}$