Giới hạn \(\lim\dfrac{\sqrt[3]{8n^3+2n}}{3-n}\) bằng
\(2\sqrt{2}\) | |
\(-2\) | |
\(-8\) | |
\(-2\sqrt{2}\) |
Chọn phương án B.
\(\begin{aligned}
\lim\dfrac{\sqrt[3]{8n^3+2n}}{3-n}&=\lim\dfrac{\sqrt[3]{n^3\left(8+\dfrac{2}{n^2}\right)}}{n\left(\dfrac{3}{n}-1\right)}\\
&=\lim\dfrac{n\sqrt[3]{8+\dfrac{2}{n^2}}}{n\left(\dfrac{3}{n}-1\right)}\\
&=\lim\dfrac{\sqrt[3]{8+\dfrac{2}{n^2}}}{\dfrac{3}{n}-1}\\
&=\dfrac{\sqrt[3]{8+0}}{0-1}=-2.
\end{aligned}\)