Tính giới hạn \(L=\lim\dfrac{\left(2n-n^3\right)\left(3n^2+1\right)}{(2n-1)\left(n^4-7\right)}\).
\(L=-\dfrac{3}{2}\) | |
\(L=1\) | |
\(L=3\) | |
\(L=+\infty\) |
Chọn phương án A.
Dùng máy tính cầm tay:
Chọn phương án A.
\(\begin{aligned}
L&=\lim\dfrac{\left(2n-n^3\right)\left(3n^2+1\right)}{(2n-1)\left(n^4-7\right)}\\
&=\lim\dfrac{n^3\left(\dfrac{2}{n^2}-1\right)n^2\left(3+\dfrac{1}{n^2}\right)}{n(2-\dfrac{1}{n})n^4\left(1-\dfrac{7}{n^4}\right)}\\
&=\lim\dfrac{\left(\dfrac{2}{n^2}-1\right)\left(3+\dfrac{1}{n^2}\right)}{\left(2-\dfrac{1}{n}\right)\left(1-\dfrac{7}{n^4}\right)}\\
&=\dfrac{\left(0-1\right)\left(3+0\right)}{(2-0)\left(1-0\right)}\\
&=-\dfrac{3}{2}.
\end{aligned}\)