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Pe=E7o ajuda com esta quest=E3o:
=20
=93Seja h : R - R uma fun=E7=E3o real que satisfaz as seguintes =
condi=E7=F5es:
i) h(x) + h(y) =3D h(xy), para todo x; y pertencente ao conjunto R.
ii) h (Max([m/2^p.3^q],[n/2^p]) + min([m/2^p],[n/2^p.3^q]))=3D log(base =
2)(q +
1), para todos m; n pertencente a Z e para todos p; q pertencente a N.
Mostre que se x pertence a Q, ent=E3o h(x) =3D 0.=94
=20
OBS.: L=EA-se [m/2^p.3^q] como M sobre o produto de dois elevado a p e =
tr=EAs
elevado a q.
L=EA-se tamb=E9m log(base 2)(q + 1) como logaritmo de (q+1) na base 2.
=20
Desde J=E1 Agrade=E7o Muito pela ajuda.
=20
JG.
No virus found in this outgoing message.
Checked by AVG.=20
Version: 7.5.519 / Virus Database: 269.22.1/1348 - Release Date: =
28/03/2008
10:58
=20
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<p class=3DMsoNormal style=3D'text-autospace:none'><span =
style=3D'font-size:12.0pt;
font-family:CMBX12'>Pe=E7o ajuda com esta =
quest=E3o:<o:p></o:p></span></p>
<p class=3DMsoNormal style=3D'text-autospace:none'><span =
style=3D'font-size:12.0pt;
font-family:CMBX12'><o:p> </o:p></span></p>
<p class=3DMsoNormal style=3D'text-autospace:none'><span =
style=3D'font-size:12.0pt;
font-family:CMBX12'>“</span><span =
style=3D'font-size:12.0pt;font-family:
CMR12'>Seja </span><i><span =
style=3D'font-size:12.0pt;font-family:CMMI12'>h </span></i><span
style=3D'font-size:12.0pt;font-family:CMR12'>: </span><span =
style=3D'font-size:
12.0pt;font-family:MSBM10'>R -</span><i><span style=3D'font-size:12.0pt;
font-family:CMSY10'> </span></i><span =
style=3D'font-size:12.0pt;font-family:MSBM10'>R
</span><span style=3D'font-size:12.0pt;font-family:CMR12'>uma fun=E7=E3o =
real que
satisfaz as seguintes condi=E7=F5es:<o:p></o:p></span></p>
<p class=3DMsoNormal style=3D'text-autospace:none'><span =
style=3D'font-size:12.0pt;
font-family:CMR12'>i) </span><i><span =
style=3D'font-size:12.0pt;font-family:CMMI12'>h</span></i><span
style=3D'font-size:12.0pt;font-family:CMR12'>(</span><i><span =
style=3D'font-size:
12.0pt;font-family:CMMI12'>x</span></i><span style=3D'font-size:12.0pt;
font-family:CMR12'>) + </span><i><span =
style=3D'font-size:12.0pt;font-family:
CMMI12'>h</span></i><span =
style=3D'font-size:12.0pt;font-family:CMR12'>(</span><i><span
style=3D'font-size:12.0pt;font-family:CMMI12'>y</span></i><span =
style=3D'font-size:
12.0pt;font-family:CMR12'>) =3D </span><i><span =
style=3D'font-size:12.0pt;
font-family:CMMI12'>h</span></i><span =
style=3D'font-size:12.0pt;font-family:CMR12'>(</span><i><span
style=3D'font-size:12.0pt;font-family:CMMI12'>xy</span></i><span
style=3D'font-size:12.0pt;font-family:CMR12'>), </span><i><span =
style=3D'font-size:
12.0pt;font-family:CMSY10'>para todo </span></i><i><span =
style=3D'font-size:12.0pt;
font-family:CMMI12'>x; y pertencente ao conjunto</span></i><i><span
style=3D'font-size:12.0pt;font-family:CMSY10'> </span></i><span =
style=3D'font-size:
12.0pt;font-family:MSBM10'>R</span><span =
style=3D'font-size:12.0pt;font-family:
CMR12'>.<o:p></o:p></span></p>
<p class=3DMsoNormal style=3D'text-autospace:none'><span =
style=3D'font-size:12.0pt;
font-family:CMR12'>ii) </span><i><span =
style=3D'font-size:12.0pt;font-family:
CMMI12'>h (Max([m/2^p.3^q],[n/2^p]) + =
min([m/2^p],[n/2^p.3^q]))=3D</span></i><span
style=3D'font-size:12.0pt;font-family:CMR12'> </span><i><span =
style=3D'font-size:
12.0pt;font-family:CMMI12'>log(base 2)(q </span></i><span =
style=3D'font-size:
12.0pt;font-family:CMR12'>+ 1), </span><i><span =
style=3D'font-size:12.0pt;
font-family:CMSY10'>para todos </span></i><i><span =
style=3D'font-size:12.0pt;
font-family:CMMI12'>m; n pertencente a</span></i><i><span =
style=3D'font-size:
12.0pt;font-family:CMSY10'> </span></i><span style=3D'font-size:12.0pt;
font-family:MSBM10'>Z </span><span =
style=3D'font-size:12.0pt;font-family:CMR12'>e
para todos</span><i><span style=3D'font-size:12.0pt;font-family:CMSY10'> =
</span></i><i><span
style=3D'font-size:12.0pt;font-family:CMMI12'>p; q </span></i><i><span
style=3D'font-size:12.0pt;font-family:CMSY10'>pertencente a =
</span></i><span
style=3D'font-size:12.0pt;font-family:MSBM10'>N</span><span =
style=3D'font-size:
12.0pt;font-family:CMR12'>.<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'>Mostre que
se </span><i><span style=3D'font-size:12.0pt;font-family:CMMI12'>x =
</span></i><i><span
style=3D'font-size:12.0pt;font-family:CMSY10'>pertence a =
</span></i><span
style=3D'font-size:12.0pt;font-family:MSBM10'>Q</span><span =
style=3D'font-size:
12.0pt;font-family:CMR12'>, ent=E3o </span><i><span =
style=3D'font-size:12.0pt;
font-family:CMMI12'>h</span></i><span =
style=3D'font-size:12.0pt;font-family:CMR12'>(</span><i><span
style=3D'font-size:12.0pt;font-family:CMMI12'>x</span></i><span =
style=3D'font-size:
12.0pt;font-family:CMR12'>) =3D 0.”<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'><o:p> </o:p></span></p>=
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'>OBS.: L=EA-se
</span><i><span =
style=3D'font-size:12.0pt;font-family:CMMI12'>[m/2^p.3^q] como M
sobre o produto de dois elevado a p e tr=EAs elevado a =
q.<o:p></o:p></span></i></p>
<p class=3DMsoNormal><i><span =
style=3D'font-size:12.0pt;font-family:CMMI12'>L=EA-se
tamb=E9m log(base 2)(q </span></i><span =
style=3D'font-size:12.0pt;font-family:CMR12'>+
1) como logaritmo de (q+1) na base 2.<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'><o:p> </o:p></span></p>=
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'>Desde J=E1
Agrade=E7o Muito pela ajuda.<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'><o:p> </o:p></span></p>=
<p class=3DMsoNormal><span =
style=3D'font-size:12.0pt;font-family:CMR12'>JG.</span><o:p></o:p></p>
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<BR>
<P><FONT SIZE=3D2>No virus found in this outgoing message.<BR>
Checked by AVG.<BR>
Version: 7.5.519 / Virus Database: 269.22.1/1348 - Release Date: =
28/03/2008 10:58<BR>
</FONT> </P>
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