Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\lim \frac{{4{n^2} - n - 1}}{{3 + 2{n^2}}}\\
= \lim \frac{{\frac{{4{n^2} - n - 1}}{{{n^2}}}}}{{\frac{{3 + 2{n^2}}}{{{n^2}}}}}\\
= \lim \frac{{4 - \frac{1}{n} - \frac{1}{{{n^2}}}}}{{\frac{3}{{{n^2}}} + 2}}\\
= \frac{{4 - 0 - 0}}{{0 + 2}}\\
= \frac{4}{2} = 2\\
b,\\
\lim \frac{{\sqrt {3{n^2} + 1} + n}}{{1 - 2{n^2}}}\\
= \lim \frac{{\frac{{\sqrt {3{n^2} + 1} + n}}{n}}}{{\frac{{1 - 2{n^2}}}{n}}}\\
= \lim \frac{{\sqrt {3 + \frac{1}{{{n^2}}}} + 1}}{{\frac{1}{n} - 2n}}\\
= 0\\
\left( \begin{array}{l}
\lim \left( {\sqrt {3 + \frac{1}{{{n^2}}}} + 1} \right) = \sqrt 3 + 1\\
\lim \left( {\frac{1}{n} - 2n} \right) = - \infty
\end{array} \right)
\end{array}\)
