The role of sequences in calculus What is the role of sequences in (undergraduate, engineering) calculus?
Is it just there for a more gentle introduction to limits, instead of starting with limits of functions (which is actually a core topic of calculus) and as introduction to (infinite) series?
In that case my other question is: Where do squences belong? (discrete math ?)
Or, are sequences a core topic of calculus?
note: I am aksing this question with disregard whether a topic is a prerequisite for a calculus course or is covered within.
eg: I would not classify trigonometric identities nor hyperbolic functions as part of calculus, even though they are needed in a calculus course for integration techniques.

In the first place you should use sequences where they genuinely occur: In the definition of new objects, like $\exp$, as a tool to represent arbitrary (and maybe unknown) functions in a uniform way, as sequences of arrival times, as solutions of difference equations or more general recursions, and on, and on.
In my view sequences should be abolished as a means of understanding continuity or limits. Why would anyone test a gogol of sequences in order to prove a single instance of $\lim_{x\to\xi}=a$ when looking at the proper inequality makes the statement obvious. The problem with understanding limits is the handling of nested quantors. Why should you unnecessarily add to more of these when explaining what a limit is?
