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Ambiguity of "Plot"

Dear members;

I have been embarrassed about a function Plot.
I would like to plot a curve defined as follows:

 f(\[Alpha]) = (\[Rho] + \[Delta] - \[Delta] \[Alpha] - Sqrt[\[Delta] \[Rho] \
\[Alpha] (1 - \[Alpha]) + \[Rho]^2 \[Alpha]])/((\[Rho] + \[Delta]) (1 \
- \[Alpha])).
Here, 0 < \[Alpha] < 1.

And I programmed in this way;
Plot[f(\[Alpha]), { \[Alpha],  0 < \[Alpha] < 1}]

The curve I obtained from Mathematica is monotonously decreasing. AS a result, f(1) =0.
However, by using  l'H=F4pital7 theorem, f(1) = 1/2 is correct.
In this situation, I would like to obtain an accurate curve.

Fujio Takata
Kobe University, Japan.
I use Mathematica 8.040, Macintosh version.

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