Further Meditation on Taylor Series

I have spent a lot of time trying to think intuitively about calculus, Taylor series, divergent series, and things like that. Here are a couple things I realized at some point which I would like to have written down. (This is sort of a sequel to a much more elementary post some years ago . I know a lot more now, and have also apparently gotten a lot more verbose.) Maybe they are well-known to some people, or maybe not, but they were at least interesting to me. As usual: don’t expect anything even resembling