Bài tập 16 trang 226 SGK Toán 11 NC

a. \(\lim \frac{{{n^4} - 40{n^3} + 15n - 7}}{{{n^4} + n + 100}} = \lim \frac{{1 - \frac{{40}}{n} + \frac{{15}}{{{n^3}}} - \frac{7}{{{n^4}}}}}{{1 + \frac{1}{{{n^3}}} + \frac{{100}}{{{n^4}}}}} = 1\)

b. \(\lim \frac{{2{n^3} + 35{n^2} - 10n + 3}}{{5{n^5} - {n^3} + 2n}} = \lim \frac{{\frac{2}{{{n^2}}} + \frac{{35}}{{{n^3}}} - \frac{{10}}{{{n^4}}} + \frac{3}{{{n^5}}}}}{{5 - \frac{1}{{{n^2}}} + \frac{2}{{{n^4}}}}} = 0\)

c. \(\lim \frac{{\sqrt {6{n^4} + n + 1} }}{{2n + 1}} = \lim \frac{{{n^2}\sqrt {6 + \frac{1}{{{n^3}}} + \frac{1}{{{n^4}}}} }}{{n\left( {2 + \frac{1}{n}} \right)}}\)

\( = \lim \frac{{n.\sqrt {6 + \frac{1}{{{n^3}}} + \frac{1}{{{n^4}}}} }}{{2 + \frac{1}{n}}} =  + \infty \)

d. \(\lim \frac{{{{3.2}^n} - {{8.7}^n}}}{{{{4.3}^n} + {{5.7}^n}}} = \lim \frac{{3.{{\left( {\frac{2}{7}} \right)}^n} - 8}}{{4{{\left( {\frac{3}{7}} \right)}^n} + 5}} =  - \frac{8}{5}\)

-- Mod Toán 11 HỌC247