Tính giới hạn \(\lim\dfrac{\sqrt{9n^2-n+1}}{4n-2}\).
\(\dfrac{2}{3}\) | |
\(\dfrac{3}{4}\) | |
\(0\) | |
\(3\) |
Chọn phương án B.
Dùng máy tính cầm tay:
Chọn phương án B.
\(\begin{aligned}
\lim\dfrac{\sqrt{9n^2-n+1}}{4n-2}&=\lim\dfrac{\sqrt{n^2\left(9-\dfrac{1}{n}+\dfrac{1}{n^2}\right)}}{n\left(4-\dfrac{2}{n}\right)}\\
&=\lim\dfrac{n\sqrt{9-\dfrac{1}{n}+\dfrac{1}{n^2}}}{n\left(4-\dfrac{2}{n}\right)}\\
&=\lim\dfrac{\sqrt{9-\dfrac{1}{n}+\dfrac{1}{n^2}}}{4-\dfrac{2}{n}}\\
&=\lim\dfrac{\sqrt{9-0+0}}{4-0}=\dfrac{3}{4}.
\end{aligned}\)