Cho hình hộp\[\mathop {\lim }\limits_{x \to + \infty } \left[ {f\left( x \right) - g\left( x \right)} \right] = a - b\]. Tìm mệnh đề sai trong các mệnh đề sau:

Ta có: \(\mathop {\lim }\limits_{n \to + \infty } \frac{{2022{n^2} - 2023n}}{{2024 + 2025n - 2026{n^2}}} = \mathop {\lim }\limits_{n \to + \infty } \frac{{{n^2}\left( {2022 - \frac{{2023}}{n}} \right)}}{{{n^2}\left( {\frac{{2024}}{{{n^2}}} + \frac{{2025}}{n} - 2026} \right)}}\)

              \( = \mathop {\lim }\limits_{n \to + \infty } \frac{{2022 - \frac{{2023}}{n}}}{{\frac{{2024}}{{{n^2}}} + \frac{{2025}}{n} - 2026}}\)\( = \frac{{2022}}{{ - 2026}} = - \frac{{1011}}{{1013}}.\)

Gọi \(E\) là trung điểm của \(AD\).

Trong

Xét tam giác \(ESF\) ta có: \(\frac{{EG}}{{ES}} = \frac{1}{3}\;\)

Do \(AE//BF \Rightarrow \frac{{NE}}{{NF}} = \frac{{AN}}{{BN}} = \frac{1}{2} \Rightarrow \frac{{NE}}{{EF}} = \frac{1}{3}.\)

Suy ra \(\frac{{EG}}{{ES}} = \frac{{NE}}{{EF}} \Rightarrow NG//SF.\)

Mà \(SF \subset \left( {SBC} \right)\)\( \Rightarrow NG//\left( {SBC} \right).\)