Specify the precision in mathparse calculus

Question

I have defined the function f(x) = (sqrt(x)-1)/(x-1) and I need to calculate several values for f(x).
I have developed the following code, but, I cannot to specify the precision for f(x), for example, with 5 decimal places.
Anyone can help me please?
documentclass[tikz, border=.5cm]{standalone}
usepackage[portuguese]{babel}
usepackage[utf8]{inputenc}
usepackage{tkz-fct}   
usepackage{multido}
usetikzlibrary{calc,math}
usepackage{float}
usepackage{amsmath}

newcommandf[1]{ pgfmathparse{((#1)^0.5 - 1)/(#1 -1)} pgfmathresult }

begin{document}

foreach x in {2,1.5,1.2,1.19,1.189,...,1.001}{
begin{tikzpicture}[scale=0.8]
clip (-3.5,-2) rectangle (4,2);
node[above] (2) at (0,0)  {Vamos avaliar o limite $displaystylelim_{x to 1} frac{sqrt{x}-1}{x-1}$:};
node[below] (2) at (0,0)  {O valor da função em $pgfmathprintnumber{x}$ é boxed{$f{x}$}};
end{tikzpicture}
}
end{document}

egreg · Answer

I'm afraid that the standard floating point engine in TikZ/PGF is not apt for this task.
You get much better results with the engine in expl3.
documentclass{article}
usepackage[portuguese]{babel}
usepackage[utf8]{inputenc}
usepackage{amsmath}
usepackage{xfp}

newcommandf[1]{%
  fpeval{round((sqrt(#1)-1)/(#1-1),5)}%
}

ExplSyntaxOn
NewDocumentCommand{fpforeach}{o mmm +m}
 {
  IfValueT{#1}
   {
    clist_map_inline:nn { #1 } { #5 }
   }
  fp_step_inline:nnnn { #2 } { #3 } { #4 } { #5 }
 }
ExplSyntaxOff

begin{document}

fpforeach[2,1.5,1.2]{1.19}{-0.001}{1.001}{%
  O valor da função em $#1$ é boxed{$f{#1}$}par
}

end{document}

The command f defines the function, with rounding to five decimal digits.
I added a “for each” cycle, where the optional argument is a list of “exceptional values” to be evaluated first, then you can specify the starting point, the step and the final point. The last argument is what every value in the loop is passed to, using #1 to denote the current value.
Here are the first lines of the result.

The last lines.

I'm personally against this way to present limits, because it is not a good explanation of how limits work (because one has to do backwards, not forward). Anyway, I acknowledge that's used in many books. Unfortunately. ;-)

Specify the precision in mathparse calculus

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