Re: [Maxima-discuss] How do I tell limit that a function f is continuous?

[Barton W. <wi...@un...>]

It would be a nice feature, but Maxima's limit code doesn't have a way to do this. There is an option variable limsubst that "prevents limit<https://maxima.sourceforge.io/docs/manual/maxima_singlepage.html#limit> from attempting substitutions on unknown forms." Here is an example of what this option variable does:


(%i7) limit(F(x),x,%pi);

(%o7) 'limit(F(x),x,%pi)
(%i8) limsubst : true;

(%o8) true
(%i9) limit(F(x),x,%pi);

(%o9) F(%pi)

I'd say that when limsubst is true, Maxima assumes that a function is continuous everywhere, unless it has some other understanding of the function—I think that is what the documentation calls an "unknown form."

But as far as I can tell, setting  limsubst is true it doesn't allow Maxima to find the limit you asked about.


--Barton
________________________________
From: Eduardo Ochs <edu...@gm...>
Sent: Friday, November 15, 2024 22:37
To: <max...@li...> <max...@li...>
Subject: [Maxima-discuss] How do I tell limit that a function f is continuous?

Caution: Non-NU Email

Hi list,

How do I tell "limit" that a function f is continuous, or smooth?
I was hoping that the first limit below would yield f_x(42), but it
doesn't without assumptions like continuity and differentiability...

  gradef(f(x), f_x(x))$
  limit((f(42+eps)-f(42))/eps, eps,0);
  limit((sin(42+eps)-sin(42))/eps, eps,0);

Thanks in advance!
  Eduardo Ochs
  http://anggtwu.net/eev-qdraw.html<https://urldefense.com/v3/__http://anggtwu.net/eev-qdraw.html__;!!PvXuogZ4sRB2p-tU!HknIFRxu4TeK6Wx5hLBiygnycBCFhzZNgYJJ7LZPt603kcpvVNvPlH7iXDL3AXjgKo7uMozKRJGGWqht4AU$>  <- (work in progress)