[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[SPAM] RES: [obm-l] e^pi vs. pi^e

To: <obm-l@xxxxxxxxxxxxxx>
Subject: [SPAM] RES: [obm-l] e^pi vs. pi^e
From: "Bouskela" <bouskela@xxxxxxxxx>
Date: Thu, 26 Jun 2008 22:11:17 -0300
Dkim-signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:reply-to:from:to:subject:date :mime-version:content-type:x-mailer:in-reply-to:thread-index :x-mimeole:message-id; bh=v7CFaJAWvoxsKZjUwVVw8K7CAS909NVvsgXzIlg+Dn0=; b=WupKZUs4WqYl3Xh4+Q1pAjmFL5R7ZHoPAxyLgv1PuTY6CfOFZKNAfVuvw6gXWCeh8P npV0pGBXZQxGD5yOZJ+9PcAkM1QdQJdsEGBX7E1jkok7e85SAhnaYNyFyUq9geQ7/p/i VLviLk5VgOsp+NXoDW6Ytym6E2nHIsQ5Dbr1o=
Domainkey-signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=reply-to:from:to:subject:date:mime-version:content-type:x-mailer :in-reply-to:thread-index:x-mimeole:message-id; b=iRHIGKhF+Jnv+kUKsMHGTrjXqvVwfuofWzc4oAYNoktJkh40tlroJHEy0ERb0bQugj 34hf9nvZqcSlxwkLfwJqe5JRQpGGIRHvo0LPzH9k10az+Nv7Wk7zme6kQGi4MjRAj7sR 6g6GkTwK6RDf9KzWOuA/gfb+QObeg6+HV9b1s=
In-reply-to: <789aac5a0806261429g51b4fa80w8c433d1a74c3d7ef@xxxxxxxxxxxxxx>
Reply-to: obm-l@xxxxxxxxxxxxxx
Sender: owner-obm-l@xxxxxxxxxxxxxx
Thread-index: AcjX1PQxEg2SDFlJShKFHlpnVHan6wAHC+qQ

SPAM: -------------------- Start SpamAssassin results ----------------------
SPAM: This mail is probably spam.  The original message has been altered
SPAM: so you can recognise or block similar unwanted mail in future.
SPAM: See http://spamassassin.org/tag/ for more details.
SPAM: 
SPAM: Content analysis details:   (5.00 hits, 5 required)
SPAM: IN_REP_TO          (-0.8 points) Found a In-Reply-To header
SPAM: X_MAILING_LIST     (-0.3 points) Found a X-Mailing-List header
SPAM: EMAIL_ATTRIBUTION  (-1.6 points) BODY: Contains what looks like an email attribution
SPAM: SPAM_PHRASE_00_01  (0.8 points)  BODY: Spam phrases score is 00 to 01 (low)
SPAM: HTML_50_70         (0.3 points)  BODY: Message is 50-70% HTML tags
SPAM: MAILTO_LINK        (0.2 points)  BODY: Includes a URL link to send an email
SPAM: RCVD_IN_ORBS       (2.2 points)  RBL: Received via a relay in orbs.dorkslayers.com
SPAM:                    [RBL check: found 151.160.19.201.orbs.dorkslayers.com., type: 68.178.232.99]
SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points)  RBL: Received via a relay in relays.osirusoft.com
SPAM:                    [RBL check: found 151.160.19.201.relays.osirusoft.com.]
SPAM: X_OSIRU_OPEN_RELAY (2.7 points)  RBL: DNSBL: sender is Confirmed Open Relay
SPAM: MISSING_OUTLOOK_NAME (1.1 points)  Message looks like Outlook, but isn't
SPAM: 
SPAM: -------------------- End of SpamAssassin results ---------------------

This is a multi-part message in MIME format.

------=_NextPart_000_00FF_01C8D7D9.8FF4CF80
Content-Type: text/plain;
	charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Ol=E1!

Sua solu=E7=E3o - =E9 claro - est=E1 correta! Entretanto, acho mais =
elucidativo
demonstrar que

e^pi > pi^e

Demonstrando que:

Se   a > b >=3D e   ent=E3o   b^a > a^b=20

E mais:

Se   e >=3D b > a >=3D 0   ent=E3o   b^a > a^b

Da=ED:

Se   a >=3D 0   e   "a" =E9 diferente de "e"   ent=E3o   e^a > a^e   =
(dentre os
n=FAmeros reais, apenas  "e"  tem esta propriedade).

Para demonstrar as desigualdades acima, basta analisar os intervalos nos
quais a fun=E7=E3o

f(x) =3D [ln(x)]/x

=E9 crescente e, depois, decrescente.

Sds.,

AB


  _____ =20

De: owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx] Em =
nome
de Iuri
Enviada em: quinta-feira, 26 de junho de 2008 18:30
Para: obm-l@xxxxxxxxxxxxxx
Assunto: Re: [obm-l] e^pi vs. pi^e


e^x >=3D x+1 (demonstra=E7=E3o a partir da expans=E3o de e^x em torno do =
ponto zero)

Sabemos que a igualdade acontece somente para x=3D0, entao, supondo x
diferente de zero, temos: e^x > x+1

Para x=3Dpi/e -1, temos:

e^((pi/e) -1) > pi/e
e^(pi/e) > pi
e^pi > pi^e




On Thu, Jun 26, 2008 at 6:17 PM, Bouskela <bouskela@xxxxxxxxx> wrote:


Sem dispor de uma calculadora e, tamb=E9m, sem fazer contas, c=E1lculos =
etc.,
demonstre, ANALITICAMENTE, que:
e^pi > pi^e
=20
Sds.,
AB



------=_NextPart_000_00FF_01C8D7D9.8FF4CF80
Content-Type: text/html;
	charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.6000.16674" name=3DGENERATOR></HEAD>
<BODY>
<DIV dir=3Dltr align=3Dleft>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>Ol=E1!</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>Sua solu=E7=E3o - =E9 claro - est=E1 correta! =
Entretanto, acho=20
mais elucidativo demonstrar que</SPAN></FONT></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT><SPAN=20
class=3D953060001-27062008></SPAN><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>e^pi &gt;=20
pi^e</SPAN></FONT></FONT></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT><FONT><SPAN=20
class=3D953060001-27062008></SPAN><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>Demonstrando=20
que:</SPAN></FONT></FONT></FONT></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT><FONT><FONT><SPAN=20
class=3D953060001-27062008></SPAN><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>Se&nbsp; &nbsp;a &gt; b &gt;=3D e&nbsp;&nbsp; =
ent=E3o=20
&nbsp; b^a &gt; a^b =
</SPAN></FONT></FONT></FONT></FONT></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT><FONT><FONT><FONT><SPAN=20
class=3D953060001-27062008></SPAN><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>E=20
mais:</SPAN></FONT></FONT></FONT></FONT></FONT></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><FONT><FONT><FONT><FONT><FONT><SPAN=20
class=3D953060001-27062008></SPAN><FONT face=3DVerdana><FONT =
size=3D2><SPAN=20
class=3D953060001-27062008>Se&nbsp;&nbsp; e &gt;=3D b &gt; a &gt;=3D =
0&nbsp;=20
&nbsp;ent=E3o&nbsp; &nbsp;b^a &gt;=20
a^b</SPAN></FONT></FONT></FONT></FONT></FONT></FONT></FONT></FONT></SPAN>=
</P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt 72pt; TEXT-INDENT: -72pt; LINE-HEIGHT: =
150%; TEXT-ALIGN: justify; tab-stops: 72.0pt"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>Da=ED:</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt 72pt; TEXT-INDENT: -72pt; LINE-HEIGHT: =
150%; TEXT-ALIGN: justify; tab-stops: 72.0pt"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT><SPAN =
class=3D953060001-27062008></SPAN><FONT=20
face=3DVerdana><FONT size=3D2><SPAN =
class=3D953060001-27062008>Se&nbsp;&nbsp; a &gt;=3D=20
0&nbsp;&nbsp; e&nbsp;&nbsp; "a" =E9 diferente de "e"&nbsp;&nbsp; =
ent=E3o&nbsp;&nbsp;=20
e^a &gt; a^e&nbsp;&nbsp;&nbsp;</SPAN></FONT></FONT></FONT></SPAN><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2>(dentre =
os n=FAmeros=20
reais, apenas<SPAN style=3D"mso-spacerun: yes">&nbsp;&nbsp;<SPAN=20
class=3D953060001-27062008>"</SPAN></SPAN>e<SPAN=20
class=3D953060001-27062008>"</SPAN><SPAN style=3D"mso-spacerun: =
yes">&nbsp;=20
</SPAN>tem esta<SPAN class=3D953060001-27062008>=20
</SPAN>propriedade).<?xml:namespace prefix =3D o ns =3D=20
"urn:schemas-microsoft-com:office:office" =
/><o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>Para demonstrar as desigualdades acima, basta =
analisar=20
os intervalos nos quais a fun=E7=E3o</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>f(x) =3D =
[ln(x)]/x</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>=E9 crescente e, depois,=20
decrescente.</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>Sds.,</SPAN></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 5pt 0cm; LINE-HEIGHT: 150%; TEXT-ALIGN: justify; =
mso-layout-grid-align: none"><SPAN=20
style=3D"FONT-FAMILY: Arial"><FONT face=3DVerdana><FONT size=3D2><SPAN=20
class=3D953060001-27062008>AB</SPAN></FONT></FONT></SPAN></P></DIV><BR>
<BLOCKQUOTE=20
style=3D"PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px =
solid; MARGIN-RIGHT: 0px">
  <DIV class=3DOutlookMessageHeader lang=3Dpt-br dir=3Dltr align=3Dleft>
  <HR tabIndex=3D-1>
  <FONT face=3DTahoma size=3D2><B>De:</B> owner-obm-l@xxxxxxxxxxxxxx=20
  [mailto:owner-obm-l@xxxxxxxxxxxxxx] <B>Em nome de =
</B>Iuri<BR><B>Enviada=20
  em:</B> quinta-feira, 26 de junho de 2008 18:30<BR><B>Para:</B>=20
  obm-l@xxxxxxxxxxxxxx<BR><B>Assunto:</B> Re: [obm-l] e^pi vs.=20
  pi^e<BR></FONT><BR></DIV>
  <DIV></DIV>e^x &gt;=3D x+1 (demonstra=E7=E3o a partir da expans=E3o de =
e^x em torno do=20
  ponto zero)<BR><BR>Sabemos que a igualdade acontece somente para =
x=3D0, entao,=20
  supondo x diferente de zero, temos: e^x &gt; x+1<BR><BR>Para x=3Dpi/e =
-1,=20
  temos:<BR><BR>e^((pi/e) -1) &gt; pi/e<BR>e^(pi/e) &gt; pi<BR>e^pi &gt; =

  pi^e<BR><BR><BR><BR>
  <DIV class=3Dgmail_quote>On Thu, Jun 26, 2008 at 6:17 PM, Bouskela =
&lt;<A=20
  href=3D"mailto:bouskela@xxxxxxxxx";>bouskela@xxxxxxxxx</A>&gt; =
wrote:<BR>
  <BLOCKQUOTE class=3Dgmail_quote=20
  style=3D"PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: =
rgb(204,204,204) 1px solid">
    <DIV>Sem dispor de uma calculadora e, tamb=E9m, sem fazer contas, =
c=E1lculos=20
    etc., demonstre, ANALITICAMENTE, que:</DIV>
    <DIV>e^pi &gt; pi^e</DIV>
    <DIV>&nbsp;</DIV>
    <DIV>Sds.,</DIV>
    <DIV>AB</DIV></BLOCKQUOTE></DIV><BR></BLOCKQUOTE></BODY></HTML>

------=_NextPart_000_00FF_01C8D7D9.8FF4CF80--

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================

Follow-Ups:
- Re: [obm-l] e^pi vs. pi^e
  - From: Bruno França dos Reis

References:
- Re: [obm-l] e^pi vs. pi^e
  - From: Iuri

Prev by Date: [SPAM] [obm-l] x^2 - xy + y^2 = Cte
Next by Date: Re: [obm-l] e^pi vs. pi^e
Previous by thread: Re: [obm-l] e^pi vs. pi^e
Next by thread: Re: [obm-l] e^pi vs. pi^e
Index(es):
- Date
- Thread