Tính giới hạn \(\lim\limits_{x\to-\infty}\left(|x|^3+2x^2+3|x|\right)\).
\(0\) | |
\(+\infty\) | |
\(1\) | |
\(-\infty\) |
Chọn phương án B.
\(\begin{aligned}
&\lim\limits_{x\to-\infty}\left(|x|^3+2x^2+3|x|\right)\\
=&\lim\limits_{x\to-\infty}\left((-x)^3+2x^2+3(-x)\right)\\
=&\lim\limits_{x\to-\infty}\left(-x^3+2x^2-3x\right)\\
=&\lim\limits_{x\to-\infty}x^3\left(-1+\dfrac{2}{x}-\dfrac{3}{x^2}\right)\\
=&+\infty.
\end{aligned}\)
Vì \(\begin{cases}
\lim\limits_{x\to-\infty}x^3&=-\infty\\
\lim\limits_{x\to-\infty}\left(-1+\dfrac{2}{x}-\dfrac{3}{x^2}\right)&=-1<0.
\end{cases}\)