Re: Unevaluated limit
- To: mathgroup at smc.vnet.net
- Subject: [mg84509] Re: Unevaluated limit
- From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
- Date: Mon, 31 Dec 2007 21:15:23 -0500 (EST)
- References: <fla7gm$feu$1@smc.vnet.net>
"Liverpool" <x at y.z> wrote:
> I have to evaluate this limit (I know the answer is 4)
> Limit[2*x^2*Exp[6 x]*(1 - Cos[Exp[-3 x]*Tan[2/x]]), x -> Infinity]
>
> but the output is unevaluated:
>
> Limit[2 \[ExponentialE]^(6 x) x^2 (1 - Cos[\[ExponentialE]^(-3 x)
> Tan[2/x]]), x -> \[Infinity]]
>
> Is there any way to evaluate it symbolically?
Yes, although it's not "direct":
In[4]:= Simplify[Normal[Series[
2*x^2*Exp[6 x]*(1 - Cos[Exp[-3 x]*Tan[2/x]]), {x, Infinity, 0}]]]
Out[4]= 4*E^(6*x)*x^2*Sin[1/(E^(3*x)*x)]^2
In[5]:= Limit[%, x -> Infinity]
Out[5]= 4
Perhaps someone else will have a better way.
David