cmr các dãy số sau có giới hạn 0 a,Un= (căn(3n^2+1)+3n)/n^2+2 b,Un=(4.3^n+2^n)/5^(n+1)+3

$\begin{array}{l} a)\lim \frac{{\sqrt {3{n^2} + 1} + 3n}}{{{n^2} + 2}} = \lim \frac{{\frac{{\sqrt {3{n^2} + 1} + 3}}{{{n^2}}}}}{{\frac{{{n^2} + 2}}{{{n^2}}}}} = \lim \frac{{\sqrt {\frac{{3{n^2} + 1}}{{{n^4}}}} + \frac{3}{{{n^2}}}}}{{1 + \frac{2}{{{n^2}}}}} = \lim \frac{{\sqrt {\frac{3}{{{n^2}}} + \frac{1}{{{n^4}}}} + \frac{3}{{{n^2}}}}}{{1 + \frac{2}{{{n^2}}}}} = \frac{{0 + 0}}{{1 + 0}} = 0\\ d)\lim {u_n} = \lim \frac{{{{4.3}^n} + {2^n}}}{{{5^{n + 1}} + 3}} = \lim \frac{{4.{{\left( {\frac{3}{5}} \right)}^n} + {{\left( {\frac{2}{5}} \right)}^n}}}{{5 + \frac{3}{{{5^n}}}}} = \frac{{4.0 + 0}}{{5 + 0}} = 0 \end{array}$