Bug in Mathematica or my mistake?

• To: mathgroup at smc.vnet.net
• Subject: [mg10] Bug in Mathematica or my mistake?
• From: "ram.rachum at gmail.com" <ram.rachum at gmail.com>
• Date: Sun, 25 May 2008 02:01:10 -0400 (EDT)

```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?