ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 29 Aug 2018 09:17:24 -0500Conflicting Sage vs Wolfram evaluation of a limit?http://ask.sagemath.org/question/43517/conflicting-sage-vs-wolfram-evaluation-of-a-limit/<s> >Why are the following computed limits different (1 by Sage, 0 by Wolfram), and which (if either) is correct?
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**EDIT**: Increasing the numerical precision in Wolfram produces a plot that *strongly suggests* that the limit is indeed $0$, which it had already computed. Presumably, Sage is computing the wrong limit simply because of inadequate numerical precision, so the question is now ...
>How can I increase the numerical precision in Sage, so that `limit()` and `plot()` will produce the correct results (i.e., the limit should be $0$ and the plot should show a stable approach to $0$)?
**Sage**: (you can cut/paste/execute this code [here](http://sagecell.sagemath.org/))
#in()=
f(x) = exp(-x^2/2)/sqrt(2*pi)
F(x) = (1 + erf(x/sqrt(2)))/2
num1(a,w) = (a+w)*f(a+w) - a*f(a)
num2(a,w) = f(a+w) - f(a)
den(a,w) = F(a+w) - F(a)
V(a,w) = 1 - num1(a,w)/den(a,w) - (num2(a,w)/den(a,w))^2
assume(w>0); print(limit(V(a,w), a=oo))
plot(V(a,1),a,0,8)
#out()=
1 #<--------- computed limit = 1
[![enter image description here][1]][1]
**Wolfram**: (you can execute this code [here](https://sandbox.open.wolframcloud.com/app/objects/0e2860d3-6c86-4d61-a9cf-e97fcf88c3b5#sidebar=compute))
#in()=
f[x_]:=Exp[-x^2/2]/Sqrt[2*Pi]
F[x_]:=(1 + Erf[x/Sqrt[2]])/2
num1[a_,w_] := (a+w)*f[a+w] - a*f[a]
num2[a_,w_] := f[a+w] - f[a]
den[a_,w_] := F[a+w] - F[a]
V[a_,w_] := 1 - num1[a,w]/den[a,w] - (num2[a,w]/den[a,w])^2
Assuming[w>0, Limit[V[a,w], a -> Infinity]]
Plot[V[a, 10], {a, 0, 100}, WorkingPrecision -> 128]
#out()=
0 (* <--------- computed limit = 0 *)
[![enter image description here][2]][2]
(This is supposed to compute the limit, as a -> oo, of the [variance of a standard normal distribution when truncated to the interval (a,a+w)](https://en.wikipedia.org/wiki/Truncated_normal_distribution#Moments).)
[1]: https://i.stack.imgur.com/eRAjI.png
[2]: https://i.stack.imgur.com/WTSf9.pngres0001Wed, 29 Aug 2018 09:17:24 -0500http://ask.sagemath.org/question/43517/