PHẦN II. TRẢ LỜI NGẮN

Tính \(\mathop {\lim }\limits_{n \to  + \infty } \left( {\sqrt {{n^2} + 3n}  - n} \right)\).

\(\mathop {\lim }\limits_{x \to 1} \left[ {f\left( x \right) + g\left( x \right)} \right]\)\( = \mathop {\lim }\limits_{x \to 1} f\left( x \right) + \mathop {\lim }\limits_{x \to 1} g\left( x \right) = - 3 + 5 = 2\).

\(\mathop {\lim }\limits_{n \to + \infty } \frac{{\left( {a - 1} \right)n + 2}}{{2n + 9}} = 1\)\( \Leftrightarrow \mathop {\lim }\limits_{n \to + \infty } \frac{{\left( {a - 1} \right) + \frac{2}{n}}}{{2 + \frac{9}{n}}} = 1\)\( \Leftrightarrow \frac{{a - 1}}{2} = 1\)\( \Leftrightarrow a = 3\).