http://img34.imageshack.us/img34/198...s123523456.jpg

I'm trying to work through some examples, but im not sure where the following comes from:

1. circled in black -- how do i get the δ<1?

2. circled in red -- how do I get 0<x<2, i.e. x∈(0,2)?

3. cirlced in blue -- how do i get |x^2+x+3|<9

Thanks, most appreciated.