Question

\(\lim\limits_{x\rightarrow2}\dfrac{2x^3+5x^2-7x+2}{x^2-3x+2}\)

Answer 1

\(\lim\limits_{x\rightarrow2}\dfrac{2x^3+5x^2-7x+2}{x^2-3x+2}\)

\(=\lim\limits_{x\rightarrow2}\dfrac{2x^3-4x^2+9x^2-18x+11x-22+24}{\left(x-2\right)\left(x+1\right)}\)

\(=\lim\limits_{x\rightarrow2}\dfrac{\left(x-2\right)\left(2x^2+9x+11\right)+24}{\left(x-2\right)\left(x+1\right)}\)

\(=+\infty\) vì \(\left\{{}\begin{matrix}\lim\limits_{x\rightarrow2}\left(x-2\right)\left(2x^2+9x+11\right)+24=24>0\\\lim\limits_{x\rightarrow2}\left(x-2\right)=2-2=0\\\lim\limits_{x\rightarrow2}x+1=2+1=3>0\end{matrix}\right.\)