Alright. Office hours with Dr. Doud went well. He writes his proofs a little different than we do in class, and I guess I needed that added dimension. I now know what's going on. I think. And now a play-by-play of section 12.3:
SO 12.3 is just taking what we've learned already about finding limits (from 12.1) and applying it as a limit at n--> a, where a is an integer value, rather than infinity. So we can find a limit for a divergent series. That makes sense, and the proofs appear to be largely the same as before as far as what we're proving. We're proving that if you go out a certain distance (delta...?) from a, then you will always be within epsilon of the value a. [[I really hope that is the definition of delta.. if it is, then I think I actually am starting to get this stuff!]]
We choose our distance delta the same way that we chose the value N. By solving for f(x)<epsilon. And our new assumption for this section is that 0<f(x)-L<delta. And since we define delta in terms of epsilon, we can basically say delta(epsilon). Things are going well.
For the quadratic (and other) proofs, the only thing was defining the trick that helped us find delta. I could follow it all, but I probably wouldn't have thought of any of that stuff with the lim as x-->3 of x^2 is 9. I hope that in the future the tricks are similar so I can actually find it. ok \qed for now.
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