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.