"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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