Tính giới hạn L = lim n → + ∞ ( 3 n 2 + 5 n − 3 )
Giải thích
D
\[{\rm{L = }}\mathop {\lim }\limits_{n \to + \infty } {\rm{(3}}{{\rm{n}}^{\rm{2}}}{\rm{ + 5n}} - 3) = \mathop {\lim }\limits_{n \to + \infty } {{\rm{n}}^{\rm{2}}}\left( {{\rm{3 + }}\frac{{\rm{5}}}{{\rm{n}}} - \frac{3}{{{{\rm{n}}^2}}}} \right)\]
\(\left\{ {\begin{array}{*{20}{c}}{\mathop {\lim }\limits_{n \to + \infty } {{\rm{n}}^{\rm{2}}} = + \infty }\\{\mathop {\lim }\limits_{n \to + \infty } \left( {{\rm{3 + }}\frac{{\rm{5}}}{{\rm{n}}} - \frac{3}{{{{\rm{n}}^2}}}} \right) = 3}\end{array}} \right. \Rightarrow \mathop {\lim }\limits_{n \to + \infty } {\rm{(3}}{{\rm{n}}^{\rm{2}}}{\rm{ + 5n}} - 3) = + \infty \).