I don't use textbooks. Well, let me rephrase, I don't let the kids use textbooks. I'd like to know when the authors of these things last spent time with a teenager. I keep them around as jumping off points for my lessons as sometimes I'll forget about detail x or special case y of a given concept. The college professors I had who didn't use the book were the ones I liked the most. It can be a useful bit of reference material, but a teacher and his/her students should not sit around waiting for direction from the almighty textbook, because of garbage like this:
I'm fine with the what, but the why is maddening. The whole reason I should learn about limits at infinity is so that I can do one of your example problems? Shouldn't you point out that producing an infinite number of products is a) impossible b) unlikely and oh yeah, c) impossible?