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Re: solving nonlinear equation with mathematica !!


On 3/27/04 at 1:35 AM, m004202002 at yahoo.com (why) wrote:

>I have system nonlinear equation

>x^2-y-1 = 0; 10x exp(-x)-y = 0 ;

>If you draw the graph you see two intersecting point .

>I have found a point [Using FindRoot function ] In (-0.1,-0.5) the
>point is (-0.0905897,-0.991794 )---it is OK

>But In (2.0,1.0) the point is (1.94463,2.7816) But the graph says
>the x->2.something ,y->1.somthing I have used same FindRoot
>function to find the root in (2.0,1.0 ).

Precisely, what are you plotting?

When I do 

Plot[{x^2 - 1, 10*x*Exp[-x]}, 
   {x, -1, 3}, PlotStyle -> 
    {Hue[0], Hue[0.3]}]; 
    
using Mathematica 5.0 on Mac OS 10.3.3 then select the resulting plot and position the cursor over the intersection point while holding down the command key, I see {1.95108, 2.84716}. (I got these by copying the values from the plot to the clipboard). As you can see, these are reasonably close to the values returned by FindRoot. The small difference is undoubtedly due to the my inability to precisely position the cursor over the intersecting point.
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