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 = (2C1 + C2)/(2(C1 + C2 - C3)) - Sqrt[C2^2 + 4C1C3]/(2*(C1 + C2 - C3)) + g;
VarianceF[n_]:= 16C0^2(p) - 16C0^2(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 -4C2^2np^4 + 8C2^2p^4 - 6C2^2np^2 + 12C2^2p^2 + 2C2^2np - 4C2^2p + 8C2^2np^3 - 16C2^2p^3;
Plot[VarianceF[n], {n, 2, 10^10}, PlotRange -> All]
Asymptotic[VarianceF[n],n->Infinity]
Limit[VarianceF[n],n->Infinity]
Here is the output:
