# Plotting a function with large negative exponents

I am trying to plot the function:

f(x)=(1-exp(-Vx^m))/(1-(1-x^m)^V)-1

for various values of $$V$$ and $$m$$ ranging from 1 to 30, and from $$0\leq x\leq1$$. How can I avoid numerical evaluation errors near zero? I've tried:

LogLinearPlot[(1-Exp[-4*x^6])/(1-(1-x^6)^(4))-1,{x,10^-6,1},PlotRange->{-1,1}]


But get warnings and an oscillatory behavior of the plot which I am not sure is correct, because the limit of the function is 0 at $$x=0$$.

• Maybe: LogLinearPlot[ Piecewise[{{0, 0 < x < 10^-3}}, (1 - Exp[-4*x^6])/(1 - (1 - x^6)^(4)) - 1], {x, 0, 1}, PlotRange -> {-1/10, 1/10}, WorkingPrecision -> 15] Dec 29, 2020 at 10:28

f[x0_] := Limit[(1 - Exp[-4*xx^6])/(1 - (1 - xx^6)^(4)) - 1, xx -> x0]

• I can only guess. But if you call f[x,V] with symbolic parameters, the limit can fail. And Evaluate@Table[f[x, V], {V, 2, 10, 2}] calls f[x,V] with symbolic x. This happens also with Plot[f[x,4],...] because Plothas the attribute HoldAll and tries first to simplify the given function symbolically. Therefore, to be on the safe side, declare: f[x0_?NumericQ, V0_?NumericQ] :=... Dec 30, 2020 at 9:44