\(lim\dfrac{x^5-5x^3+2x^2+6x-4}{x^3-x^2-x+1}\)
\(=lim\dfrac{1-\dfrac{5}{x^2}+\dfrac{2}{x^3}+\dfrac{6}{x^4}-\dfrac{4}{x^5}}{\dfrac{1}{x^2}-\dfrac{1}{x^3}-\dfrac{1}{x^4}+\dfrac{1}{x^5}}\)
\(=\dfrac{1}{0}=+\infty\)
\(\left\{{}\begin{matrix}lim\left(1-\dfrac{5}{x^2}+\dfrac{2}{x^3}+\dfrac{6}{x^4}-\dfrac{4}{x^5}\right)=1>0\\lim\left(\dfrac{1}{x^2}-\dfrac{1}{x^3}-\dfrac{1}{x^4}+\dfrac{1}{x^5}\right)=0\end{matrix}\right.\)
Suy ra:\(lim\dfrac{x^5-5x^3+2x^2+6x-4}{x^3-x^2-x+1}=lim\dfrac{1-\dfrac{5}{x^2}+\dfrac{2}{x^3}+\dfrac{6}{x^4}-\dfrac{4}{x^5}}{\dfrac{1}{x^2}-\dfrac{1}{x^3}-\dfrac{1}{x^4}+\dfrac{1}{x^5}}=+\infty\)
