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Re: Unevaluated limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84508] Re: Unevaluated limit
  • From: Norbert Marxer <marxer at mec.li>
  • Date: Mon, 31 Dec 2007 21:14:51 -0500 (EST)
  • References: <fla7gm$feu$1@smc.vnet.net>

On 31 Dez., 08:59, "Liverpool" <x... at y.z> wrote:
> I have to evaluate this limit (I know the answer is 4)
> =A0 =A0 =A0Limit[2*x^2*Exp[6 x]*(1 - Cos[Exp[-3 x]*Tan[2/x]]), x -> Infini=
ty]
>
> but the output is unevaluated:
>
> =A0 =A0 =A0Limit[2 \[ExponentialE]^(6 x) x^2 (1 - Cos[\[ExponentialE]^(-3 =
x)
> Tan[2/x]]), x -> \[Infinity]]
>
> Is there any way to evaluate it symbolically?
>
> Thanks, Liverpool

Hello

You could use a power series expansion around Infinity (or around 0
after substituting x->1/x). You get the answer 4 if you expand either
to the order 1 or order 2.

f[x_] = 2*x^2*E^(6*x)*(1 - Cos[Tan[2/x]/E^(3*x)]);

n = 1;
Limit[Normal[Series[f[x] /. x -> 1/x, {x, 0, n}]], x -> 0]
Limit[Normal[Series[f[x], {x, Infinity, n}]], x -> Infinity]

n = 2;
Limit[Normal[Series[f[x] /. x -> 1/x, {x, 0, n}]], x -> 0]
Limit[Normal[Series[f[x], {x, Infinity, n}]], x -> Infinity]

Best Regards
Norbert Marxer


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