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I am trying to see the asymptotics of the Var function as below, from the plot it seems it goes to $-\infty$, however, I also calculate its asymptotics which gives me a positive $+\infty$.. Why could this happen?

Here is my code:

ClearAll["Global`*"];

C0=1;C1 = 1; C2 = 1; C3 = Sqrt[2]; 
g=1/(Log[n])^(1/20);
p = (2*C1 + C2)/(2*(C1 + C2 - C3)) - Sqrt[C2^2 + 4*C1*C3]/(2*(C1 + C2 - C3)) + g;

VarianceF[n_]:= 16*C0^2*(p) - 16*C0^2*(p)^2 + ((C1^2 + C3^2)/2)*n*(p) - ((C1^2 + C3^2)/2)*n*(p)^2 - (C1^2 + C3^2)*(p) + (C1^2 + C3^2)*(p)^2 -4*C2^2*n*p^4 + 8*C2^2*p^4 - 6*C2^2*n*p^2 + 12*C2^2*p^2 + 2*C2^2*n*p - 4*C2^2*p + 8*C2^2*n*p^3 - 16*C2^2*p^3;

Plot[VarianceF[n], {n, 2, 10^10}, PlotRange -> All]
Asymptotic[VarianceF[n],n->Infinity]
Limit[VarianceF[n],n->Infinity]

Here is the output:

enter image description here

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  • $\begingroup$ you can raise a cross post at mathematica.stackexchange.com $\endgroup$
    – 138 Aspen
    Commented Mar 10 at 13:33
  • $\begingroup$ @138Aspen Ok! I didn't know there is a specific website for mathematica, thank you! $\endgroup$
    – chloe
    Commented Mar 10 at 13:51

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