You don’t learn Big-O in Calculus because it requires CS algorithmic concepts.

But the core question of “how does this behave as N -> \infty?” is asymptotic behavior (ie: limits) which were developed for calculus and are very much part of the foundational calculus canon.

Big O notation predates Computational Complexity. It was originally used to guesstimate asymptotic behavior (limits as they approach infinity). The related Little o notation (even more specifically limits of already large values as they approach infinity) is directly related to early attempts at defining differentiation and differentiability and still sometimes show up in Calculus next to derivatives to explain how derivatives work.

The visual interpretation/intuition of Big O notation can be a useful way to build a visual intuition of what a function's derivative and integral "shapes" may look like, so some Calculus books teach Big O notation, too.

I should add that text to the rant at my last paragraph!