Question

lim x->0\(\frac{\sqrt{1-2x}-1}{\sqrt{5x+4}-2}\) ( giúp em với ạ )

Answer 1

\(\lim\limits_{x\rightarrow0}\frac{\left(\sqrt{1-2x}-1\right)\left(\sqrt{1-2x}+1\right)\left(\sqrt{5x+4}+2\right)}{\left(\sqrt{5x+4}-2\right)\left(\sqrt{5x+4}+2\right)\left(\sqrt{1-2x}+1\right)}\)

\(=\lim\limits_{x\rightarrow0}\frac{\left(-2x\right)\left(\sqrt{5x+4}+2\right)}{5x\left(\sqrt{1-2x}+1\right)}=\lim\limits_{x\rightarrow0}\frac{-2\left(\sqrt{5x+4}+2\right)}{5\left(\sqrt{1-2x}+1\right)}=-\frac{4}{5}\)