We are used to do limits by means of $\epsilon, \delta$. This is the first step an student encounters limits. Using $\epsilon$ and $\delta$ leads him to be familiar to Logic. I have taught limits and other basic similar concepts and I did that by using Maple instead of Mathematica. Because of that, writing a program in which we can probe a real function like sin$(x)$ has a limit has been my old wish. This needs a computer-assisted analytic approach in which we are able to define $\epsilon, \delta$ randomly in $\mathbb R$ and then verify if a certain well-behaved function has a limit. Here, I am not intended to use packages. Thanks.

  • $\begingroup$ Are you asking for a visual look at the behavior? Or a computer-assisted analytic proof of something (maybe the Intermediate Value Theorem?) $\endgroup$ Commented Jun 19, 2012 at 18:13
  • $\begingroup$ Welcome to Mathematica.SE. You will need to edit your question to provide a more solid description of your problem or it will be closed as "not a real question." If the community votes to close it you can still improve it and it may be reopened. Also, you have enough "reputation" to talk in Chat -- that may be helpful! $\endgroup$
    – Mr.Wizard
    Commented Jun 19, 2012 at 18:33
  • $\begingroup$ @DanielLichtblau: Thanks for the comment and for your time. Honestly, I should have edited my question in time but I couldn't. As you kindly noted, I'd like to have a computer-assisted analytic approach rather than just seeing what happenes. In fact, how can we define $\epsilon, \delta$ in which a program be able to probe a certain limit? $\endgroup$
    – Mikasa
    Commented Jun 19, 2012 at 19:56
  • $\begingroup$ If the edit to my answer goes in the direction you want, maybe you can add to your question some more details on what you mean by a "computer-assisted approach" - my interpretation of "enlivening" a theorem is not the same as "proving" a theorem. But one has to know more about how you want to illuminate the theorem. $\endgroup$
    – Jens
    Commented Jun 19, 2012 at 20:03

1 Answer 1


For visualizations, maybe the following Wolfram Demonstrations will give some genreal idea of what has been done:


For an analytical approach to derivatives using limits, you could just apply the technique I proposed in this more specialized answer:

It just uses the command Limit, as in this simple example:

Limit[(Sin[x + d] - Sin[x])/d, d -> 0]

(* ==> Cos[x] *)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.