dùng định nghĩa giới hạn chứng minh : lim $\frac{2n^2}{1+n^2}$ = 2 giúp e với ạ pl

$\begin{array}{l}
\lim \dfrac{{2{n^2}}}{{1 + {n^2}}} = 2\\
\lim \left( {\dfrac{{2{n^2}}}{{1 + {n^2}}} - 2} \right) = \lim \dfrac{{2{n^2} - 2{n^2} - 2}}{{1 + {n^2}}}\\
 = \lim \dfrac{{ - 2}}{{1 + {n^2}}}\\
0 \le \left| {\dfrac{{ - 2}}{{1 + {n^2}}}} \right| \le \dfrac{{ - 2}}{{{n^2}}}\,\forall n \in N*\\
\lim \dfrac{{ - 2}}{{{n^2}}} = 0\\
 \Rightarrow \lim \dfrac{{ - 2}}{{1 + {n^2}}} = 0 \Rightarrow \lim \left( {\dfrac{{2{n^2}}}{{1 + {n^2}}} - 2} \right) = 0\\
 \Rightarrow \lim \dfrac{{2{n^2}}}{{1 + {n^2}}} = 2
\end{array}$