Question

\(\lim\limits_{x\rightarrow-\infty}\dfrac{\left(2-x^4\right)\left(3x^5-1\right)}{7+9x-x^6}\)

Answer 1

Lời giải:\(\lim\limits_{x\to -\infty}\frac{(2-x^4)(3x^5-1)}{7+9x-x^6}=\lim\limits_{x\to -\infty}\frac{(\frac{2}{x}-x^3)(3-\frac{1}{x^5})}{\frac{7}{x^6}+\frac{9}{x^5}-1}\)

Ta thấy:

\(\lim\limits_{x\to -\infty}(\frac{2}{x}-x^3)=+\infty \)

\(\lim\limits_{x\to -\infty}\frac{3-\frac{1}{x^5}}{\frac{7}{x^6}+\frac{9}{x^5}-1}=\frac{3}{-1}=-3<0\)

\(\Rightarrow \lim\limits_{x\to -\infty}\frac{(2-x^4)(3x^5-1)}{7+9x-x^6}=-\infty \)