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Thomas D. Dean
Mar 28, 2013, 12:41:53 PM3/28/13
to
> restart;
> about(f(x));
f(x):
nothing known about this object
> g:=(x)->x^2*f(x);
> limit(g(x),x=0);
0
Maple has to be making some assumptions about f(x) to arrive at this
conclusion. What?
limit(f(x)*g(x),x=a) = limit(f(x),x=a) * limit(g(x),x=a);
consider imit(f(x),x=a) = inifinity and limit(g(x),x=a) = 0, then,
limit(f(x)*g(x),x=a) is undefined.
Correct?
Tom Dean
> about(f(x));
f(x):
nothing known about this object
> g:=(x)->x^2*f(x);
> limit(g(x),x=0);
0
Maple has to be making some assumptions about f(x) to arrive at this
conclusion. What?
limit(f(x)*g(x),x=a) = limit(f(x),x=a) * limit(g(x),x=a);
consider imit(f(x),x=a) = inifinity and limit(g(x),x=a) = 0, then,
limit(f(x)*g(x),x=a) is undefined.
Correct?
Tom Dean
Nasser M. Abbasi
Mar 28, 2013, 7:35:56 PM3/28/13
to
On 3/28/2013 11:41 AM, Thomas D. Dean wrote:
> > restart;
> > about(f(x));
> f(x):
> nothing known about this object
> > g:=(x)->x^2*f(x);
> > limit(g(x),x=0);
> 0
>
> Maple has to be making some assumptions about f(x) to arrive at this
> conclusion. What?
>
fyi, Mathematica v9.01, does not evaluate it
> > restart;
> > about(f(x));
> f(x):
> nothing known about this object
> > g:=(x)->x^2*f(x);
> > limit(g(x),x=0);
> 0
>
> Maple has to be making some assumptions about f(x) to arrive at this
> conclusion. What?
>
In[12]:= Limit[x*f[x], x -> 0]
Out[12]= Limit[x f[x], x -> 0]
and maxima 12.04 also does not evaluate this.
I think you are right, without knowing how the limit of f(x)
behaves as x->0 the answer seems strange. But Matlab 2013a,
which I tink uses mupad these days, gives zero also:
------------------------
EDU>> syms x f(x)
EDU>> limit(x*f(x),x,0)
ans =
0
----------------------
I think we need a math expert to come and sort out which
is correct and which is not. But I am voting for result
given by M and Maxima here and not Maple and Matlab.
> limit(f(x)*g(x),x=a) = limit(f(x),x=a) * limit(g(x),x=a);
>
> consider imit(f(x),x=a) = inifinity and limit(g(x),x=a) = 0, then,
> limit(f(x)*g(x),x=a) is undefined.
>
> Correct?
>
> Tom Dean
>
Joe Riel
Mar 29, 2013, 1:02:16 AM3/29/13
to
when f(x) = k/x^2.
--
Joe Riel
Nasser M. Abbasi
Mar 29, 2013, 1:16:26 AM3/29/13
to
On 3/29/2013 12:02 AM, Joe Riel wrote:
>
> It's clear the result should be undefined; consider the case
> when f(x) = k/x^2.
>
Yes. sure. That would depend on what value K has.
>
> It's clear the result should be undefined; consider the case
> when f(x) = k/x^2.
>
In[8]:= Limit[x*k/x^2, x -> 0]
Out[8]= k Infinity
In[9]:= % /. k -> 0
Out[9]= Indeterminate
May be someone should send a bug report to Maplesoft on this.
--Nasser
A N Niel
Mar 29, 2013, 9:29:43 AM3/29/13
to
In article <hO2dnU_SuLxJ78nM...@megapath.net>, Thomas D.
> restart;
> limit(f(x),x=0);
f(0)
Dean <tom...@speakeasy.org> wrote:
> > restart;
> > about(f(x));
> f(x):
> nothing known about this object
> > g:=(x)->x^2*f(x);
> > limit(g(x),x=0);
> 0
>
> Maple has to be making some assumptions about f(x) to arrive at this
> conclusion. What?
>
Maybe Maple is using this:
> > restart;
> > about(f(x));
> f(x):
> nothing known about this object
> > g:=(x)->x^2*f(x);
> > limit(g(x),x=0);
> 0
>
> Maple has to be making some assumptions about f(x) to arrive at this
> conclusion. What?
>
> restart;
> limit(f(x),x=0);
f(0)
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