Re: [obm-l] LIMITES

["Marcelo Salhab Brogliato" <k4ss@xxxxxxxxxx>]

b)

aplicando L'Hopital, temos:

 

nx^(n-1)/[n(lnx)^n . (1/x)] = (x/lnx)^n -> (a/lna)^n, qdo x->a, para "a" finito a diferente de 0.

se a = 0, (x/lnx)^n -> 0

se a = +inf, (x/lnx)^n -> +inf

 

abraços,

Salhab

 

----- Original Message -----

From: Ojesed Mirror

To: obm-l@mat.puc-rio.br

Sent: Tuesday, May 02, 2006 12:50 AM

Subject: Re: [obm-l] LIMITES

a) Fazendo x=1/y quando x->0+ y->+inf.

x^x = (1/y)^(1/y) = exp(-ln(y)/y)

Observe que y cresce mais rápido que ln(y), logo o expoente tende a zero e o limite de x^x tende a 1

 

Ojesed.

----- Original Message -----

From: Klaus Ferraz

To: obm-l@mat.puc-rio.br

Sent: Friday, April 28, 2006 2:42 PM

Subject: [obm-l] LIMITES

a) lim(x->0+) x^x

b)lim(x->a) (x^n-a^n)/((lnx)^n-(lna)^n)

 

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