Đáp án:
3) 0
Giải thích các bước giải:
\(\begin{array}{l}
1)\lim \dfrac{{4 - \dfrac{3}{n} - \dfrac{2}{{{n^2}}} + \dfrac{7}{{{n^4}}} - \dfrac{9}{{{n^5}}}}}{{ - 5\left( {3 - \dfrac{2}{n} + \dfrac{1}{{{n^2}}}} \right)\left( {\dfrac{5}{n} - 2} \right)}}\\
= \lim \dfrac{4}{{ - 5.3.\left( { - 2} \right)}} = \dfrac{2}{{15}}\\
3)\lim \dfrac{{\left( {\dfrac{2}{n} + \dfrac{1}{{{n^2}}}} \right)\left( {1 - \dfrac{3}{n}} \right) + \dfrac{3}{n}}}{{ - 3 + \dfrac{2}{{{n^2}}} + \dfrac{7}{{{n^3}}}}}\\
= \lim \dfrac{{0.1 + 0}}{{ - 3}} = 0\\
2)\lim \dfrac{{\left( {2 + \dfrac{3}{{{n^2}}} - \dfrac{5}{{{n^3}}} + \dfrac{1}{{{n^4}}}} \right)\left( {\dfrac{2}{n} + \dfrac{3}{{{n^2}}}} \right)}}{{\left( {3 + \dfrac{2}{{{n^3}}}} \right){{\left( {\dfrac{1}{n} - 1} \right)}^2}\left( {5 + \dfrac{7}{n}} \right)}}\\
= \lim \dfrac{{2.0}}{{3.\left( { - 1} \right).5}} = 0\\
4)\lim \dfrac{{\left( { - 1 + \dfrac{3}{n} - \dfrac{9}{{{n^2}}} + \dfrac{8}{{{n^3}}}} \right){{\left( {2 - \dfrac{3}{n}} \right)}^{97}}}}{{{{\left( {3 + \dfrac{2}{{{n^3}}}} \right)}^5}\left( {2 + \dfrac{{11}}{{{n^{15}}}} - \dfrac{4}{{{n^{55}}}} + \dfrac{5}{{{n^{85}}}}} \right)}}\\
= \lim \dfrac{{ - {2^{97}}}}{{{3^5}.2}} = \dfrac{{ - {2^{96}}}}{{{3^5}}}
\end{array}\)
