It seems to me that most commenters are missing the point, which is that results like these usually remain unproven until the end of 2-3 course sequences that a

It seems to me that most commenters are missing the point, which is that results like these usually remain unproven until the end of 2-3 course sequences that are mainly taken by math majors. What the authors are doing is to reduce each result to something that can be verified by a high school calculus student (even if it does not provide very much insight). These are not elegantly concise proofs; they are maximally elementary proofs that you can give to a curious kid. I think there’s value in that, even if that’s not what mathematicians do with their proofs.