Question

tìm giới hạn sau : \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{2x-x^2}-1}{x^2-x}\)

Answer 1

\(=lim_{x\rightarrow1}\dfrac{-x^2+2x-1}{x\left(x-1\right)\left(\sqrt{2x-x^2}+1\right)}=lim_{x\rightarrow1}\dfrac{-\left(x-1\right)^2}{x\left(x-1\right)\left(\sqrt{2x-x^2}+1\right)}\)

\(=lim_{x\rightarrow1}-\dfrac{\left(x-1\right)}{x\left(\sqrt{2x-x^2}+1\right)}\)=0