Toán giúp mình với lim n–>0+= √n ²+n – √n ÷n ² 10/07/2021 By Aaliyah giúp mình với lim n–>0+= √n ²+n – √n ÷n ²
Đáp án: $\begin{array}{l}\mathop {\lim }\limits_{n \to {0^ + }} \frac{{\sqrt {{n^2} + n} – \sqrt n }}{{{n^2}}}\\ = \mathop {\lim }\limits_{n \to {0^ + }} \frac{{{n^2} + n – n}}{{{n^2}\left( {\sqrt {{n^2} + n} + \sqrt n } \right)}}\\ = \mathop {\lim }\limits_{n \to {0^ + }} \frac{1}{{\sqrt {{n^2} + n} + \sqrt n }}\\ = + \infty \end{array}$ Trả lời
Đáp án:
$\begin{array}{l}
\mathop {\lim }\limits_{n \to {0^ + }} \frac{{\sqrt {{n^2} + n} – \sqrt n }}{{{n^2}}}\\
= \mathop {\lim }\limits_{n \to {0^ + }} \frac{{{n^2} + n – n}}{{{n^2}\left( {\sqrt {{n^2} + n} + \sqrt n } \right)}}\\
= \mathop {\lim }\limits_{n \to {0^ + }} \frac{1}{{\sqrt {{n^2} + n} + \sqrt n }}\\
= + \infty
\end{array}$