Almost all calculus classes start with limits. The consensus seems to be that it is impossible to discuss derivatives or integrals without first discussing limits. But of course, calculus without limits is possible: it is just numerical calculus.
Instead of asking “how can you talk about calculus without limits,” this post will argue that we should instead ask “how can we expect students to engage thoughtfully with limits unless they first see a problem where they are needed?”
Sam Shah’s blog has many interesting posts, and this post is related to Sam’s post on getting rid* of limits. In brief, I don’t think that we should get rid of limits, but I do think that they are a terrible place to start a calculus class, and I also think that they are much less central to calculus than many people seem to think they are.
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