# [Maxima] pw.mac

Rupert Swarbrick rswarbrick at gmail.com
Fri Jun 1 14:44:55 CDT 2012

```"Richard Hennessy" <rich.hennessy at verizon.net> writes:
> Appealing to limit was my first idea.
>
> continuousp(expr,x,a,b):=if
> simp_given(limit(expr,x,_c,'plus)-limit(expr,x,_c,'minus), _c<b,_c>a)
> = 0 then true else false\$
> continuousp(x^2*signum(x-4),x,-8,10);
> true
>
> You can't do it that way. I actually thought that might work. I am
> assuming nothing about _c except that it is in the interval (a,b).

I don't know what your simp_given function looks like, but

(%i27) ctsp(expr,x,c) := limit(expr, x, c, plus) - limit(expr, x, c, minus);
(%o27) ctsp(expr, x, c) := limit(expr, x, c, plus) - limit(expr, x, c, minus)
(%i28) ctsp(x^2*signum(x-4), x, c);
2                          2
(%o28)        limit   x  signum(x - 4) - limit   x  signum(x - 4)
x -> c+                    x -> c-

However, of course:

(%i29) ctsp(u^2*signum(u-4), x, c);
(%o29)                                 0

Could you have a problem with what the dummy variable is or something?

Rupert
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