Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
12,\\
\lim \frac{{\sqrt {4{n^2} - 7n + 1} + 3n}}{{9 - 5n}}\\
= \lim \frac{{\frac{{\sqrt {4{n^2} - 7n + 1} + 3n}}{n}}}{{\frac{{9 - 5n}}{n}}}\\
= \lim \frac{{\sqrt {4 - \frac{7}{n} + \frac{1}{{{n^2}}}} + 3}}{{\frac{9}{n} - 5}}\\
= \frac{{\sqrt 4 + 3}}{{ - 5}} = - 1\\
13,\\
\lim \frac{{\sqrt {4{n^2} + 5} - \sqrt {n + 4} }}{{2n - 1}}\\
= \lim \frac{{\frac{{\sqrt {4{n^2} + 5} - \sqrt {n + 4} }}{n}}}{{\frac{{2n - 1}}{n}}}\\
= \lim \frac{{\sqrt {4 + \frac{5}{{{n^2}}}} - \sqrt {\frac{1}{n} + \frac{4}{{{n^2}}}} }}{{2 - \frac{1}{n}}}\\
= \frac{{\sqrt 4 - \sqrt 0 }}{2} = 1
\end{array}\)
