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