Question

lim x³ + 2x² + 3x - 9 / x² - 9

x -> 3

 

Answer 1

\(\lim\limits_{x\rightarrow3}\dfrac{x^3+2x^2+3x-9}{x^2-9}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{x^3-3x^2+5x^2-15x+18x-54+45}{\left(x-3\right)\left(x+3\right)}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{\left(x-3\right)\left(x^2+5x+18\right)+45}{\left(x-3\right)\left(x+3\right)}\)

\(=+\infty\) vì \(\left\{{}\begin{matrix}\lim\limits_{x\rightarrow3}\left(x-3\right)\left(x+3\right)=\left(3-3\right)\left(3+3\right)=0\\\lim\limits_{x\rightarrow3}x^3+2x^2+3x-9=3^3+2\cdot3^2+3\cdot3-9=27+2\cdot18=45>0\end{matrix}\right.\)