Re: Possible bug concerning a limit computation

• To: mathgroup at smc.vnet.net
• Subject: [mg71142] Re: Possible bug concerning a limit computation
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 9 Nov 2006 03:38:07 -0500 (EST)
• References: <eish78\$nrd\$1@smc.vnet.net>

```Geia Hara! (another poster from Greece!)

Mathematica 5.2 gives the right answer

Limit[(Sqrt[7*x^4 + 6*x + 5] - Sqrt[7*x^4 + 3*x + 3])*Sqrt[63*x^2 - 5*x
+ 20], x -> Infinity]
N[%]
9/2
4.5

You can verify this result as follows

Needs["NumericalMath`"]

NLimit[(Sqrt[7*x^4 + 6*x + 5] - Sqrt[7*x^4 + 3*x + 3])*Sqrt[63*x^2 -
5*x + 20], x -> Infinity, WorkingPrecision -> 40]
4.4999964199295674409523166372`15.67626782000026

Here is also a very nice animation

fr[n_]:=Plot[(Sqrt[7*x^4+6*x+5]-Sqrt[7*x^4+3*x+3])*Sqrt[63*x^2-5*x+20],{x,
0,n},PlotRange\[Rule]{{0,10},{2,6.5}},
Frame\[Rule]{True,True,False,False}]

Table[fr[n],{n,1,10,0.1}];
SelectionMove[EvaluationNotebook[],All,GeneratedCell];
FrontEndTokenExecute["CellGroup"]
FrontEndTokenExecute["OpenCloseGroup"]

Double click somewhere inside the graohics to get the animation

I don't have Mathematica v.4 now installed but try to use the following
setting
to see if it might work...

Limit[function,x->Infinity,Direction->1]

Best Regards

Dimitris Anagnostou

Researcher Associate
National Technological University of Athens

```

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