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Re: Bug in Mathematica or my mistake?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89110] Re: Bug in Mathematica or my mistake?
  • From: "ram.rachum at gmail.com" <ram.rachum at gmail.com>
  • Date: Mon, 26 May 2008 01:29:11 -0400 (EDT)
  • References: <g1avld$fb5$1@smc.vnet.net>

On May 25, 9:06 am, "ram.rac... at gmail.com" <ram.rac... at gmail.com>
wrote:
> I am trying to find the limit of this expression:
>
> (a t Sqrt[1 - (a^2 t^2)/c^2] +
>    c ArcSin[(a t)/
>      c])/(2 a (-(v Sqrt[(c^2 - v^2)/c^2] + c ArcSin[v/c])/(2
> \!\(\*OverscriptBox["a", "0"]\)) + 1/(2
> \!\(\*OverscriptBox["a",
>        "0"]\))(c ArcSin[(
>          v + (c^2 - a t v -
>            Sqrt[(c^2 - a t v)^2 + a t^2 (-2 (c^2 + a d) + a^2 =
t^2)
> \!\(\*OverscriptBox["a", "0"]\)] Sign[a t
> \!\(\*OverscriptBox["a", "0"]\)])/(a t))/
>          c] + (v + (
>           c^2 - a t v -
>            Sqrt[(c^2 - a t v)^2 + a t^2 (-2 (c^2 + a d) + a^2 =
t^2)
> \!\(\*OverscriptBox["a", "0"]\)] Sign[a t
> \!\(\*OverscriptBox["a", "0"]\)])/(a t)) Sqrt[(
>         c^2 - (v + (
>            c^2 - a t v -
>             Sqrt[(c^2 - a t v)^2 + a t^2 (-2 (c^2 + a d) + a^2=
 t^2)
> \!\(\*OverscriptBox["a", "0"]\)] Sign[a t
> \!\(\*OverscriptBox["a", "0"]\)])/(a t))^2)/c^2])))
>
> The limit calculation takes a lot of time, and then it says zero. But
> when I put in some numbers with "/.", and plot it, it converges not to
> zero but to other values, like 1 or 1.5, depending on the numbers I
> put in. So what's going on? How can Mathematica tell me that the limit
> is zero in the general case, but not zero in a specific case?
>
> Thanks for your time,
> Ram Rachum.

I apologize: I forgot to include some vital information. The limit I'm
taking is with t->0.

Also, you might want to know the values I assigned to the other
variables when I did the numeric computation. They are these:

{c -> 300000, a -> 10,
\!\(\*OverscriptBox["a", "0"]\) -> 1, v -> 7, d -> 10}

Although other values will work too, this is just an example.

Another thing is when you plot it, you need to pump up the
WorkingPrecision. A hundred was enough for my example. You can do the
plot as t goes from 0 to 10, for example, and see how it converges to
a non-zero value.

All the Best,
Ram.


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