Question

\(\lim\limits_{x\rightarrow2^+}\left(\dfrac{1}{x^2-4}-\dfrac{1}{x-2}\right)\)

Answer 1

\(\lim\limits_{x\rightarrow2^+}\left(\dfrac{1}{x^2-4}-\dfrac{1}{x-2}\right)\)

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

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

\(=\lim\limits_{x\rightarrow2^+}\left(\dfrac{-x-1}{x^2-4}\right)\)

\(=-\infty\) vì \(\left\{{}\begin{matrix}x^2-4>0\\\lim\limits_{x\rightarrow2^+}x^2-4=2^2-4=0\\\lim\limits_{x\rightarrow2^+}-x-1=-2-1=-3< 0\end{matrix}\right.\)