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Re: [obm-l] Limite
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] Limite
- From: "saulo nilson" <saulo.nilson@xxxxxxxxx>
- Date: Mon, 26 Mar 2007 21:03:58 -0300
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z=lim [cos(k/x)]^x=limraiz(1-(senk/x)^2)^x
x-oo
fazendo uma mudança de variaveis, x=1/y
limraiz(1-senky^2)^1/y
y-0
cos y torna-swe pequeno, podemos fazer
senky~ky
limraiz(1-(ky)^2)^1/y=limraiz(1-ky)^1/y *(1+ky)^1/y)
y-0 y-0
os dois sao limites fundamentais bem conhecidos de todos de forma que
z= raize^-k*e^k=1
On 3/26/07, Leonardo Borges Avelino <topgun.lba@gmail.com> wrote:
Calcule o limite:
lim [cos(k/x)]^x x->infinito com k constante sem utilizar l'hospital ou série ou equivalência..... somente por limites fundamentais..
grato
Leonardo Borges Avelino