`limsqrt(n^2+2n)-n-1`
`=lim(n^2+2n-(n-1)^2)/(sqrt(n^2+2n)-sqrt(n^2-2n+1))`
`=lim(n^2+2n-n^2+2n-1)/(sqrt(n^2+2n)-sqrt(n^2-2n+1))`
`=lim(4n-1)/(sqrt(n^2+2n)-sqrt(n^2-2n+1))`
`=lim(4-1/n)/(sqrt(1+2/n)-sqrt(1-2/n+1/n^2))`
`=(4-0)/(sqrt(1+0)-sqrt(1-0+0))`
`=(4)/2`
`=2`