Đáp án:
`lim(\sqrt{n^2-2n+3}-n)=-1`
Giải thích các bước giải:
`lim(\sqrt{n^2-2n+3}-n)`
`=lim((\sqrt{n^2-2n+3}-n)(\sqrt{n^2-2n+3}+n))/(\sqrt{n^2-2n+3}+n)`
`=lim(n^2-2n+3-n^2)/(\sqrt{n^2(1-2/n+3/n^2)}+n`
`=lim(-2n+3)/(n\sqrt{1-2/n+3/n^2}+n)`
`=lim(n(-2+3/n))/(n(\sqrt{1-2/n+3/n^2}+1)`
`=lim(-2+3/n)/(\sqrt{1-2/n+3/n^2}+1)`
`=(-2+0)/(\sqrt{1-0+0}+1}=-1`
