I"m doing some problems regarding limits of functions, and using the epsilon delta defnition, I really have no idea on what they do, and how they pick the delta. for example: lim as x to 3 of | 5-3/x+3| = 1/3. after some siimplication, this turns to 4/3|x-3 / x+3| < epsilon. and to find a bound for |x+3| we set delta to 1. and this makes -1 <x-3 < 1. then, they add 6 to both sides, and this becomes -5 <|x+3|<7. after that, it is pretty straight forward. first question, why did they pick delta as 1? and also, why did they add 6 to the left and right side? and then, there are other problems such as as limit of x to 2 of 1/ 1 - x = - 1. they pick delta as 1/2, and what do they do from there?