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Re: Limit[Sin[a*x]/(a*x), x -> Infinity]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35818] Re: Limit[Sin[a*x]/(a*x), x -> Infinity]
  • From: "Dana DeLouis" <delouis at bellsouth.net>
  • Date: Fri, 2 Aug 2002 02:42:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello.  I do not have an answer, as I am new also.
In Mathematica 4.2, Help says in part "...Limit therefore makes no
explicit assumptions about symbolic functions." Same for the Package
"NLimit."  Therefore, I think we're out of luck here.

As an newbe observation, the only option for Limit (For Mathematica 4.2)
is "Direction."  However, if you type ??Limit, there is another Option
listed that appears not to be documented. That option is "Analytic."  I
thought maybe this would solve this type of problem, but it does not. I
do not know for sure what this option does.  Anyone else??

Information["Limit", LongForm -> True]
"Limit[expr, x->x0] finds the limiting value of \
expr when x approaches x0...

Attributes[Limit] = {Listable, Protected}

Options[Limit] = {Analytic -> False, Direction -> Automatic}

As a possible workaround, would substituting many values for "a" work?
Here is what I am thinking...

v = Table[Random[Real, {0, 2*Pi}], {100}];

Union[(Limit[Sin[#1*x]/(#1*x), x -> Infinity] & ) /@ v]

I get all zero's like you predicted for many values of a.
{0}

If you try "Integers", then I get an "Indeterminate" because the limit
does not like "a" being 0.

v = Table[Random[Integer, {-4, 4}], {10}];

Union[(Limit[Sin[#1*x]/(#1*x), x -> Infinity] & ) /@ v]


{0, Indeterminate}

--
Dana
Windows XP  & Mathematica 4.1
= = = = = = = = = = = = = = = = =

"JM" <j_m_1967 at hotmail.com> wrote in message
news:<aiat23$5b0$1 at smc.vnet.net>...
> Sorry for 'refreshing' this message but does anyone know if I can 
> define the assumption below.
> 
> I don't want to write specific assumptions for each term in Limit 
> since I have many different variables and forms of a. Is it possible 
> to generalise the assumption?
> 
> it would really help me (and I really don't want to have to buy any 
> additional maths software).
> 
> 
> timreh719 at yahoo.com.tw (bryan) wrote in message 
> news:<ahdf97$i36$1 at smc.vnet.net>...
> > Hi All :
> >    I am also interesting in the solution of how to make an asumption

> > in Mathematica. I can't find any method in Mathematica. If anybody 
> > has the approch to do this , please send it to my e-mail too , Thank

> > you all ..
> > 
> > j_m_1967 at hotmail.com (JM) wrote in message 
> > news:<ah8otr$aut$1 at smc.vnet.net>...
> > > I know that this should be 0 but why can't I get mathematica to 
> > > think likewise.
> > > 
> > > 
> > > In[4]:= Limit[Sin[a*x]/(a*x),x->Infinity]
> > > 
> > >               Sin[a x]
> > > Out[4]= Limit[--------, x -> Infinity]
> > >                 a x
> > > 
> > > Is the problem a? How can I specify the properties of or 
> > > assumptions that may be made about a?
> 


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