\(\lim \frac{{{2^n} - {3^n}}}{{{2^n} + 1}}\) bằng
A. 1 | B. | C. 0 | D. |
Ta có:
\(\lim \frac{{{2^n} - {3^n}}}{{{2^n} + 1}} = \lim \frac{{{{\left( {\frac{2}{3}} \right)}^n} - 1}}{{{{\left( {\frac{2}{3}} \right)}^n} + {{\left( {\frac{1}{3}} \right)}^n}}} = - \infty \)
Vì \(\lim \left[ {{{\left( {\frac{2}{3}} \right)}^n} - 1} \right] = - 1 < 0\) và \(\lim \left[ {{{\left( {\frac{2}{3}} \right)}^n} + {{\left( {\frac{1}{3}} \right)}^n}} \right] = 0\)
Chọn B
-- Mod Toán 11