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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.