Question

Giúp mình với thanks

Lim\(\frac{2\sqrt{x+2}-4}{x^2+x-6}\)(x=>2)

Answer 1

\(\lim\limits_{x\rightarrow2}\frac{2\left(\sqrt{x+2}-2\right)}{x^2+x-6}=\lim\limits_{x\rightarrow2}\frac{2\left(\sqrt{x+2}-2\right)\left(\sqrt{x+2}+2\right)}{\left(x-2\right)\left(x+3\right)\left(\sqrt{x+2}+2\right)}\)

\(=\lim\limits_{x\rightarrow2}\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)\left(\sqrt{x+2}+2\right)}=\lim\limits_{x\rightarrow2}\frac{2}{\left(x+3\right)\left(\sqrt{x+2}+2\right)}=\frac{2}{5.4}=\frac{1}{10}\)