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animation question


Consider the simple animation

fr[n_] := Show[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 -> {{0, 10}, {2, 6.5}}, Frame -> {True, True, False,
False}], Graphics[{Red, Line[{{0, 4.5}, {10, 4.5}}]}]]

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

How is possible to hold the red line (which has the meaning of the
limit as x->infinity; try
Limit[(Sqrt[7*x^4 + 6*x + 5] - Sqrt[7*x^4 + 3*x + 3])*Sqrt[63*x^2 - 5*x
+ 20], x -> Infinity])
fixed (i.e. not "animated")?

I think where I have inserted the graphic primitive I can't avoid this.
But I can't think something other.

Regards
Dimitris


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