Tính \(L=\lim\dfrac{\sqrt{9n^2-n}-\sqrt{n+2}}{3n-2}\).
\(1\) | |
\(0\) | |
\(3\) | |
\(+\infty\) |
Chọn phương án A.
Dùng máy tính cầm tay:
Chọn phương án A.
\(\begin{aligned}
L&=\lim\dfrac{\sqrt{9n^2-n}-\sqrt{n+2}}{3n-2}\\
&=\lim\dfrac{\sqrt{n^2\left(9-\dfrac{1}{n}\right)}-\sqrt{n^2\left(\dfrac{1}{n}+\dfrac{2}{n^2}\right)}}{n\left(3-\dfrac{2}{n}\right)}\\
&=\lim\dfrac{n\sqrt{9-\dfrac{1}{n}}-n\sqrt{\dfrac{1}{n}+\dfrac{2}{n^2}}}{n\left(3-\dfrac{2}{n}\right)}\\
&=\lim\dfrac{\sqrt{9-\dfrac{1}{n}}-\sqrt{\dfrac{1}{n}+\dfrac{2}{n^2}}}{3-\dfrac{2}{n}}\\
&=\dfrac{\sqrt{9-0}-\sqrt{0+0}}{3-0}=1.
\end{aligned}\)