Bài tập 17 trang 226 SGK Toán 11 NC

Bài tập 17 trang 226 SGK Toán 11 NC

a. \(\lim \sqrt {3{n^4} - 10n + 12} \)

\( = \lim {n^2}.\sqrt {3 - \frac{{10}}{{{n^3}}} + \frac{{12}}{{{n^4}}}}  =  + \infty \)

b. \(\lim \left( {{{2.3}^n} - {{5.4}^n}} \right) = \lim {4^n}\left[ {2{{\left( {\frac{3}{4}} \right)}^n} - 5} \right] =  - \infty \)

c.

\(\begin{array}{l}
\lim \left( {\sqrt {{n^4} + {n^2} + 1}  - {n^2}} \right)\\
 = \lim \frac{{{n^2} + 1}}{{\sqrt {{n^4} + {n^2} + 1}  + {n^2}}}\\
 = \lim \frac{{1 + \frac{1}{{{n^2}}}}}{{\sqrt {1 + \frac{1}{{{n^2}}} + \frac{1}{{{n^4}}}}  + 1}} = \frac{1}{2}
\end{array}\)

 d. \(\lim \frac{1}{{\sqrt {{n^2} + 2n}  - n}} = \lim \frac{{\sqrt {{n^2} + 2n}  + n}}{{2n}}\)

\( = \lim \frac{{\sqrt {1 + \frac{2}{n}}  + 1}}{2} = 1\)

-- Mod Toán 11