Tìm lim (( căn 4n^2 - n +1)-n)/(căn 9n^2 +3n

* Hướng dẫn giải

Ta có:

$$\begin{gathered} \lim \frac{\sqrt{4n^2-n+1}-n}{\sqrt{9n^2+3n}}=\lim \frac{n\sqrt{4-\frac{1}{n}+\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{n^2}}-n}{n\sqrt{9+\text{\hspace{0.17em}}\frac{3}{n}}} \\ =\lim \frac{\sqrt{4-\frac{1}{n}+\frac{1}{n^2}}-1}{\sqrt{9+\frac{3}{n}}}=\frac{2-1}{3}=\frac{1}{3} \end{gathered}$$

Chọn đáp án A