Precise Definition of a Limit, Example Clarification

[Chase.]

This isn't a homework problem. My textbook has an example for this subject and I'm having difficulty understanding it.

I follow the example up until the point at which it says, "Notice that 0 < | x - 3 | < (0.1)/2 = 0.05, then "

I don't understand why delta was substituted with (what seem to be) arbitrary numbers.

 

[vela]

It looks like the 0.05 came out of thin air because they didn't show you how they found it. You'll probably have practice doing that soon in your homework.

The point was, however, that if x is within 0.05 of 3, then f(x) will be within 0.1 of 5, which answers the question posed earlier.