I've been taking the Khan AP Calculus BC course, and I also have been following through with pretty extensive calculus notes found here. In neither of these (or when I learned Calc in high school) did they discuss limit inferior and superior, and yet I've seen it come up quite a few times on MSE and on Wiki.
Is this a High School vs College Calc distinction? The latter link is pretty rigorous (lots of proofs) and is for college.
Is it more covered in Analysis courses rather than Calculus? What is the typical pedagogy around this?