Question

[Ân Tầm Nhi]

Tìm giới hạn sau:

Answer 1

[Khôi Bùi]

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