$\displaystyle \lim{x\to1}\frac{x+1}{x^2+x+1}=\frac{2}{3}$

apparently $\displaystyle Delta=\frac {3Epsilon}{5} $

you see I know how they got the 5

but for the 3 all they did was say $\displaystyle |x^2+x+1|>1 $

and for some reason that lead them to 3

MAT196F Midterm Test Solutions

it's kind of hard to read but it's the first question