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There are two separate problems here.
- Sage appears to calculate the wrong symbolic limit.
- Plotting expressions of this kind has inherent numerical instability, which Sage could make easier to control.
You seem to have almost purposely chosen a formula which would have high numerical instability! Any time you have denominators and numerators both going to zero and you start plugging in for tiny changes Δx you have the chance at running into trouble.
Unfortunately, limit(V(a,w), a=+oo, algorithm='sympy') doesn't seem to produce a result (perhaps Sympy doesn't handle these sorts of limits). If there is independent confirmation of this error, a ticket should be opened.
However, the issue is symbolics, not numerical precision. You may find some luck with adapting some plot refinement parameters, or possibly inputting numbers of higher precision - something like M = [(x,V(x,1)) for x in [RealField(1000)(y) for y in [0,0.001..8]]]; points(M) but I have to admit I was unable to get that to avoid the instability either.
