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Default Precision isn't reached yet no warning about convergence are generated


I have some doubts about solutions found by FindRoot.  I solved some
equation f[x]=0 and found some x*.  Now, if I plug x* back into f[x] then I
should get zero or something close to zero based on MaxPrecision, which is,
I believe, is equal to 10^-50.  However, I get f[x*]=10^-9 which is a lot
less than 10^-50 yet while solving FindRoot does not give me any warnings
about failure to coverge.  This is true for both Newton and Secant method.
I increased precision to 200, MaxPrecision->200, but the results are the
same.  Shall I accept solutions found by Mathematica as true solutions?  I
have version 4.0. Thanks.


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