Question

tính

\(\lim\limits_{x\rightarrow1}\frac{\sqrt{2x-1}+x^2-3x+1}{\sqrt[3]{x-2}+x^2-x+1}\)

Answer 1

\(=\lim\limits_{x\rightarrow1}\frac{\left(\sqrt{2x-1}-1\right)+x^2-3x+2}{\sqrt[3]{x-2}+1+x^2-x}\) \(=\lim\limits_{x\rightarrow1}\frac{\frac{2\left(x-1\right)}{\sqrt{2x-1}+1}+\left(x-1\right)\left(x-2\right)}{\frac{x-1}{\sqrt[3]{\left(x-2\right)^2}-\sqrt[3]{x-2}+1}+x\left(x-1\right)}\)

\(=\lim\limits_{x\rightarrow1}\frac{\left(x-1\right)\left(\frac{2}{\sqrt{2x-1}+1}+x-2\right)}{\left(x-1\right)\left[\frac{1}{\sqrt[3]{\left(x-2\right)^2}-\sqrt[3]{x-2}+1}+x\right]}\) \(=\lim\limits_{x\rightarrow1}\frac{\frac{2}{\sqrt{2x-1}+1}+x-2}{\frac{1}{\sqrt[3]{\left(x-2\right)^2}-\sqrt[3]{x-2}+1}+x}=0\)