Cho \(A = \mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {2x + 1} - 1}}{x};C = \mathop {\lim }\limits_{x \to 1} \frac{{x - 1}}{{\sqrt x - 1}};N = \mathop {\lim }\limits_{x \to + \infty } \left( {\sqrt {{x^2} + 4x} - x} \right);O = \mathop {\lim }\limits_{x \to - \infty } \frac{{12}}{{{x^{2023}}}}\) 

Từ CONAN được mã hóa từ chuỗi số nào sau đây?

Chọn C

              \[\cos x = - \frac{1}{2} \Leftrightarrow \cos x = \cos \frac{{2\pi }}{3} \Leftrightarrow \left[ \begin{array}{l}x = \frac{{2\pi }}{3} + k2\pi \\x = - \frac{{2\pi }}{3} + k2\pi \end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right).\]

Chọn B

\[\lim \frac{{{3^n} - 1}}{{{2^n} - {{2.3}^n} + 1}} = \lim \frac{{{3^n}\left[ {1 - {{\left( {\frac{1}{3}} \right)}^n}} \right]}}{{{3^n}\left[ {{{\left( {\frac{2}{3}} \right)}^n} - 2 + {{\left( {\frac{1}{3}} \right)}^n}} \right]}} = \lim \frac{{1 - {{\left( {\frac{1}{3}} \right)}^n}}}{{{{\left( {\frac{2}{3}} \right)}^n} - 2 + {{\left( {\frac{1}{3}} \right)}^n}}} = - \frac{1}{2}\].