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I'm doing some research for an algorithm, and I have a lot of curiosity, too. I'd like to learn how limits are calculated by mathematicians and mathematical software. I understand calculus somewhat, but I'm a litty rusty on it and I sometimes get perplexed by calculations involving limits. What's my best bet for learning about how limits are calculated? Should I review my calculus, or is there more science to limits (like numerical methods?!?)?

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closed as too broad by ᴡᴏʀᴅs, 91500, Claude Leibovici, Servaes, N. F. Taussig Oct 27 '15 at 9:32

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

On the numerical front, things get a little hazy... you'll want to look into the use of sequence transformation methods. Briefly, you construct an appropriate sequence for your limit; e.g. for something like $\lim\limits_{x\to 0} f(x)$, you might consider the sequence $f(x_k)$ where $x_k$ is a sequence that tends to 0 like $k^-n,\quad n>0$ or $c^k,\quad 0 < c < 1$, and then apply a transformation that accelerates the convergence. If that's what you're interested in, I'll write up something. – J. M. Aug 25 '11 at 2:51
@J.M. Yes-I'm very interested in sequence transformation methods. Anything relating to limits is good, and this seems prime territory to explore! I'd like to thank you in advance for bringing this up. :-) – Matt Groff Aug 25 '11 at 3:27
I've already given a short introduction in this answer (and also linked to one example where I used them here); if there's anything you still need that isn't there on sequence transformations, I'll post an elaboration. – J. M. Aug 25 '11 at 3:29