Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
B2:\\
1.\lim \frac{{{{\left( {\frac{1}{7}} \right)}^n} + 49}}{{\frac{3}{{{7^n}}} - 1}} = - 49\\
2.\lim \frac{{7.{{\left( {\frac{2}{4}} \right)}^n} + 1}}{{2.{{\left( 3 \right)}^n} + 1}} = 1\\
3.\lim \frac{{5.{{\left( {\frac{2}{3}} \right)}^n} - 1}}{{2.{{\left( {\frac{2}{3}} \right)}^n} + 3}} = \frac{{ - 1}}{3}\\
4.\lim \frac{{{{\left( {\frac{3}{4}} \right)}^n} - 4}}{{1 + 10.{{\left( {\frac{3}{4}} \right)}^n} + \frac{7}{{{4^n}}}}} = - 4\\
B3:\\
1.\lim \frac{n}{{\sqrt {{n^2} + n} + n}} = \lim \frac{1}{{\sqrt {1 + \frac{1}{n}} + 1}} = \frac{1}{2}\\
2.\lim \frac{{\sqrt {3 + \frac{1}{{{n^2}}}} - \sqrt {1 - \frac{1}{{{n^2}}}} }}{1} = 3 - 1 = 2\\
3.\lim \frac{{\sqrt {2 + \frac{1}{{{n^2}}}} - \sqrt {1 + \frac{1}{{{n^2}}}} }}{{1 + \frac{1}{{{n^2}}}}} = \sqrt 2 - 1
\end{array}\)
