Hi there

I'm doing a worked example in a Larson book. I don't understand some of it. I have scanned this excerpt from Larson.

So what I don't understand is "Thus, letting $\displaystyle \delta$ be the minimum of $\displaystyle \varepsilon/5$ and 1, it follows that ....."

I don't understand why he is saying letting delta be the minimum of epsilon/5 and 1, and where he is getting 1 from? I'm thinking 1 is related to the solution of |x - 2| in the interval (1,3). In that interval the largest number that |x-2| can evaluate to is 1, or almost 1 and when that happens |x+2| = 5 or almost 5 because it's an open interval.

Am I thinking correctly? And does anybody else have anything to add to enhance my understanding becauuse even if I'm thinking right there, I still don't feel fully understand what he is doing in this example.

Dave.