Buscar

matematica aplicada exercicios resolvidos

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 3, do total de 39 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 6, do total de 39 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 9, do total de 39 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Prévia do material em texto

�
$SRVWLOD�GH�0DWHPiWLFD�$SOLFDGD
9ROXPH���±�(GLomR�����
3URI��'U��&HOVR�(GXDUGR�7XQD
�
&DStWXOR�����5HYLVmR
1HVWH�FDStWXOR�VHUi�IHLWD�XPD�UHYLVmR�DWUDYpV�GD�UHVROXomR�GH�DOJXQV�H[HUFtFLRV�
GRV�SULQFLSDLV�WySLFRV�Mi�HVWXGDGRV�
2V�WySLFRV�VHOHFLRQDGRV�SDUD�HVWD�UHYLVmR�VmR�
&iOFXOR�1XPpULFR�
&iOFXOR�FRP�1~PHURV�SHUFHQWXDLV�
&iOFXOR�DOJpEULFR�
(TXDo}HV�H�6LVWHPDV�GR��R JUDX�
(TXDo}HV�H�6LVWHPDV�GR��R JUDX�
��� &iOFXOR�1XPpULFR
2SHUDo}HV�FRP�IUDo}HV
$GLomR�H�6XEWUDomR��XVDPRV�R�PHQRU�P~OWLSOR�FRPXP�
��
��
��
��
��
�����
�
�
�
�
�
� ʝ� ʝ�
0XOWLSOLFDomR��2�SURGXWR�GH�GXDV�IUDo}HV�p�XPD�IUDomR�TXH�WHP�SRU�QXPHUGRU�R
SURGXWR�GRV�QXPHUDGRUHV�H�TXH�WHP�SRU�GHQRPLQDGRU�R�SURGXWR�GRV
GHQRPLQDGRUHV�
��
�
��
�
�
�
�
� Ø
'LYLVmR��2�TXRFLHQWH�GH�GXDV�IUDo}HV�p�XPD�IUDomR�UHVXOWDQWH�GR�SURGXWR�GD
SULPHLUD�IUDomR�SHOR�LQYHUVR�GD�VHJXQGD�IUDomR�
�
�
�
�
�
�
�
�
�
�
�
� Ø ¬
&iOFXOR�GR�YDORU�GH�H[SUHVV}HV�QXPpULFDV��GHYH�VH�REHGHFHU�j�SULRULGDGH�GRV
VLQDLV�LQGLFDWLYRV�H�GDV�RSHUDo}HV�PDWHPiWLFDV�
3ULRULGDGH�GRV�6LQDLV 3ULRULGDGH�GDV�2SHUDo}HV
� �� � � ([SRQHQFLDomR�H�/RJDULWPDomR
� >� @ � 3RWHQFLDomR�H�5DGLFLDomR
� ^���` � 0XOWLSOLFDomR�H�'LYLVmR
� $GLomR�H�6XEWUDomR
�
&DOFXOH�R�YDORU�QXPpULFR�GDV�H[SUHVV}HV�
D� �`�@�������>�^� ʝ��ʝʝ�
5����
E� �
�
�
�
�
�
�
�
�
� ʝЪ
Ы
ЩЧ
Ш
Ц ��
5���������RX�����
F� Ъ
Ы
ЩЧ
Ш
Ц ʝØЪ
Ы
ЩЧ
Ш
Ц �
�
�
�
��
��
�
��
��
5�������������RX�����
G�
�
�
�
�
�
�
�
�
ʝ
Ъ
Ы
ЩЧ
Ш
Ц ʝ
5����������RX�������
�
H�
и
з
ж
�
г
в
ʝаб
Я
ЭЮ
Ь ʝЪ
Ы
ЩЧ
Ш
Ц ʝ�ʝ�ʝ ��
�
���������
5������
3RWHQFLDomR
3RWHQFLDomR�GH�H[SRHQWH�LQWHLUR� 6HMD�D�XP�Q~PHUR�UHDO�H�P H�Q Q~PHURV
LQWHLURV�SRVLWLYRV��(QWmR�
D�����D�D�D�DD Q �Q�YH]HV� QPPQ DDD � ͐
�D
D
�D
DD
�D
Q
�
�
˫ȝ 
 
 
ʝ
� �
�E
E
D
E
D
DD
�DDDD
Q
QQ
QPQP
QPPQ
˫ȝ Ъ
Ы
ЩЧ
Ш
Ц
 
˫ȝ ͐¬
͐
ʝ
D�� �� ���
� ʝʝ�
5����������RX���������
E�� �� ���� ʝʝ ʝ�
5����������
�
F�� ������������ ����� ͐���ʝʝʝ�
5����
G�� � � ��
�
����
��
�
�
�
�
ʝ
ʝ
ʝʝ�
�Ъ
Ы
ЩЧ
Ш
Ц �ʝ
5�����������
3RWHQFLDomR�GH�H[SRHQWH�QmR�LQWHLUR� 7RGD�UDL]�SRGH�VHU�HVFULWD�QD�IRUPD�GH
SRWrQFLD�
Q
PQ P
Q
�Q
DD
DD
 
 
2EVHUYDomR��VH�Q IRU�SDU�H�VH�D������QmR�FDUDFWHUL]D�XP�Q~PHUR�UHDO�
5��ʔʝ
D�� ������������ ���� ¬ʝʝʝʝ�ʝʝ
5���
E��
�����
�����
�
��
ʝ�ʝ
ʝʝʝ
5���
�
([HUFtFLRV
���&DOFXOH�R�YDORU�GDV�H[SUHVV}HV�
D��
��
�
�
�
�
�
�
�
�
Ъ
Ы
ЩЧ
Ш
Ц¬�ØЪ
Ы
ЩЧ
Ш
Ц
5�����
E��
�
�
��
�
�
�
�
�
��
Ъ
Ы
ЩЧ
Ш
Ц ʝ
�
Ъ
Ы
ЩЧ
Ш
Ц ʝ
5������
F�� Ъ
Ы
ЩЧ
Ш
Ц ʝ¬ʝ¬�
�
������������
�
�
5������
G��
�������
�������
ʝ
ʝ
5�����
�
���$SOLFDQGR�DV�SURSULHGDGHV�GDV�SRWrQFLDV��VLPSOLILTXH�DV�H[SUHVV}HV�
D�� �
�
�
���� ͐ E��
�
���
���
�
�
����
͐
͐͐ ʝ
F�� � � ���
��
���
�����
͐
͐
ʝ
ʝ
G�� ��
���
�����
��������
͐͐
͐͐͐
ʝ
ʝʝ
5HVSRVWDV��D�� ���� ��E�� ��� F�� ����� ��G�����
���(VFUHYD�RV�Q~PHURV�DEDL[R�FRPR�R�SURGXWR�GH�XP�Q~PHUR� LQWHLUR�SRU�XPD
SRWrQFLD�GH����
D������ � E������� � F�������� �
G��������� � H� ����� � I���������� 
���&DOFXOH�R�YDORU�GH�
D�� � �� � E�� � �� 
F�� �
�
�� G�� �
�
�
�
���&DOFXOH�R�YDORU�GDV�H[SUHVV}HV�
D�� �
�
�
�� �������� �ʝʝ�ʝ E�� �
�� ��������� ʝ��͐
5��D���� �E���
���6LPSOLILTXH�RV�UDGLFDLV�
D�� ���� E�� � �� F�� � ����
5��D�� ��� �E�� � �� F���
���5DFLRQDOL]H�RV�GHQRPLQDGRUHV�GDV�H[SUHVV}HV�
D��
�
� E��
��
� F�� � �
�
G��
��
�
ʝ
H��
��
�
�
�
���(IHWXH�
D��
��
��
��
��
�
ʝ�
ʝ
� E��
�
�
��
�
�
� ʝ�
5HVSRVWDV��D��
�
���ʝʝ E��
��
��
��� &iOFXOR�FRP�1~PHURV�3HUFHQWXDLV
2V�Q~PHURV�SHUFHQWXDLV�VmR�LGHQWLILFDGRV�SHOD�QRWDomR���H�DSDUHFHP�FRP�PXLWD
IUHTrQFLD�
3DUD�WUDQVIRUPDU�XP�Q~PHUR�SHUFHQWXDO�HP�XP�Q~PHUR�UHDO��GHYHPRV�GLYLGL�OR
SRU�����
����� ���������� ����
���� ��������� �����
������ ����������� ��
3DUD�WUDQVIRUPDU�XP�Q~PHUR�UHDO�HP�XP�Q~PHUR�SHUFHQWXDO��GHYHPRV
PXOWLSOLFD�OR�SRU�����
����� !������[����� �����
�� !���[����� ������
([HUFtFLRV�
D�� &DOFXODU������GH�5����������
5��5��������
��
E��8PD�PHUFDGRULD�IRL�FRPSUDGD�SRU�5��������H�YHQGLGD�SRU�5��������
'HWHUPLQH�D�WD[D�GH�OXFUR�VREUH�R�SUHoR�GH�FRPSUD�H�D�WD[D�GH�OXFUR�VREUH�R
SUHoR�GH�YHQGD�
8WLOL]H� LS 
ႚ
��RQGH�S p�D SDUWH��3 p�R�WRGR��RX�SULQFLSDO��H�L p�D�WD[D�QD�IRUPD
UHDO
5��D������� �E��������
F��8P�FRPHUFLDQWH�UHPDUFRX�HP����R�SUHoR�GH�VXDV�PHUFDGRULDV��4XDO�p�R
QRYR�SUHoR�GH�XPD�PHUFDGRULD�TXH�HUD�YHQGLGD�SRU�5��������
5��5�������
G��8P�YHVWLGR�HVWDYD�H[SRVWR�HP�XPD�ORMD�FRP�SUHoR�GH�HWLTXHWD�GH�5���������
8P�FOLHQWH��DOHJDQGR�TXH�IDULD�SDJDPHQWR�j�YLVWD��VROLFLWRX�XP�GHVFRQWR�GH���
��H�IRL�DWHQGLGR��4XDQWR�SDJRX�SHOR�YHVWLGR�"
5��5��������
H��8P�IXQFLRQiULR�UHFHEH�XP�VDOiULR�EDVH�GH�5����������5HFHEH�XP�DGLFLRQDO
GH� �� �� SRU� WHPSR� GH� VHUYLoR� VREUH� R� VDOiULR� EDVH�� 5HFHEH� WDPEpP� XPD
JUDWLILFDomR�GH�FKHILD�GH������VREUH�R�VDOiULR�EDVH��'HVFRQWD�VH������GH�,166
VREUH�R�VDOiULR�WRWDO��4XDQWR�UHFHEH�HVVH�IXQFLRQiULR�"
5��5��������
��
I�� 8PD� SHVVRD� UHFHEH� PHQVDOPHQWH� 5�� ��������� GH� VDOiULR� GH� XPD� HPSUHVD�
5HFHEH� 5�� ��������� GH� DOXJXHO� GH� XP� SRQWR� FRPHUFLDO� H� 5�� ��������� GH
UHQGLPHQWR� GH� DSOLFDo}HV� ILQDQFHLUDV�� 4XDO� D� SDUWLFLSDomR� SHUFHQWXDO� GH� FDGD
IRQWH�HP�VXD�UHQGD�WRWDO�"
5��������������������
����&iOFXOR�DOJpEULFR�
���&DOFXOH�RV�YDORU�QXPpULFR�GDV�H[SUHVV}HV�
D�� �DE�D�ED ��� ��ʝ� ��SDUD�D� ���H�E� ���
E��
\
[[\ �ʝ ��SDUD�
��
�[ ʝ H�
���
�\ 
5HVSRVWD��D���� E��
���
��ʝ
���6LPSOLILTXH�DV�H[SUHVV}HV�UHGX]LQGR�DV�DR�Pi[LPR�
D�� � � � � � ��D�D�D�D��DD� ��� ʝ�ʝʝ����
��
E�� �FED�F�DFE�E�FED�D �ʝ�ʝ��ʝ�
5HVSRVWDV��D�� �D�D� � �� E�� ��� FED ��
3URGXWRV�QRWiYHLV�
� � ��
���
���
EDED�ED�
EDE�D�ED�
EDE�D�ED�
ʝ ʝ͐�
�ʝ ʝ
�� �
���'HVHQYROYD�RV�VHJXLQWHV�SURGXWRV�QRWiYHLV�
D��� ���[� � E��� ��\[� ʝ
F��� � � ��[��[� ʝ͐� G�� � � � �E�D�E�D� �� ʝ͐�
���6LPSOLILTXH�DV�H[SUHVV}HV�
D��� � � ���� �[�[�[ ʝʝ�ʝ
E��� � � � � ��P�P�P � ʝ͐�ʝʝ
F�� ��
��
[[
[��[�
ʝ
ʝ
��
G��
�[
��[�
�
ʝ
H�� � �
�[
�[
�
�
ʝ
�
I�
[\�
\[[\ �� ʝ
J��
�[
��[��[�
�
��
K��
�[�
�[�[�
�
��
L�� ��
��
Z[
]\
Z[
]\
ʝ
ʝ¬
�
ʝ
5HVSRVWDV��D��� E����P�� F��
�[
��[�
�
�
ʝ
ʝ G�� �[ ʝ H��
�[
�[
ʝ
� I��
�
[\ʝ
J��[��� �K��
�
�[ � L��
]\
Z[
�
ʝ
��
���(IHWXH�DV�RSHUDo}HV�LQGLFDGDV�
D�� � �
� �
� � � ��[�[
�[
�[�
�[ �
ʝ͐�
�͐
�
�
E��
�[�
�
[�
�
[�
[�[�
ʝ
�
ʝ
�
ʝ�ʝ
5HVSRVWDV��D�� � ��[�
�[
ʝ
� E��� ��[�ʝ
����(TXDo}HV�H�VLVWHPDV�GR��R�JUDX�
���5HVROYD�DV�HTXDo}HV�
D�� �
�
�[�
�
�[ ��ʝ
��
E��
[[
��
�[
�[
[
�[
� �
 
�
ʝʝ�
5HVSRVWDV��D��[� �� E��[� ��
��� 8P� SURGXWR� WHYH� VHX� SUHoR� DXPHQWDGR� HP� ���� SDUD� SDJDPHQWR� D� SUD]R�
UHVXOWDQGR�HP�XP�WRWDO�GH�5����������4XDO�HUD�R�SUHoR�D�YLVWD�GR�SURGXWR"
5�����
���'XDV�SHVVRDV�WHP�MXQWDV�5����������4XDQWR�FDGD�XPD�SRVVXL��VDEHQGR�VH�TXH
XPD�SRVVXL�R�GREUR�GD�RXWUD"
5�����H���
���8PD�SHVVRD� IH]�XP�DFRUGR� FRP�XPD�DGPLQLVWUDGRUD�SDUD�SDJDU� R� VDOGR� GH
VHX� FDUWmR� GH� FUpGLWR� HP� WUrV� YH]HV� VHP� MXURV�� 2� SULPHLUR� SDJDPHQWR
FRUUHVSRQGH� j� PHWDGH� GD� GtYLGD� H� R� VHJXQGR� SDJDPHQWR�� 5�� �������� 4XDO� R
YDORU�GD�GtYLGD��VH�R�~OWLPR�SDJDPHQWR�HUD�GH������GD�GtYLGD�RULJLQDO"
5������
��
���5HVROYD�RV�VLVWHPDV�GH�HTXDo}HV�GR��RJUDX
D��
�
г
в
 ʝ
 �
��\[�
�\[
E��
�
г
в
 ʝ
 �
�\�[�
�\�[�
F��
�
г
в
 �ʝ
ʝ ʝ
���\��[
��\�[�
5HVSRVWDV��D������� E������� F��������
���$�VRPD�GH�GRLV�Q~PHURV�p����H�D�VXD�GLIHUHQoD�p�����&DOFXOH�RV�GRLV�Q~PHURV�
5HVSRVWD������H���
��
��� 8P� DOXQR� JDQKD� �� SRQWRV� SRU� H[HUFtFLR� TXH� DFHUWD� H� SHGH� �� SRQWRV� SRU
H[HUFtFLR�TXH�HUUD��$R�ILP�GH����H[HUFtFLRV�WLQKD�����SRQWRV��4XDQWRV�H[HUFtFLRV
HOH�DFHUWRX"
5HVSRVWD����
���$�GLIHUHQoD�HQWUH�DV�LGDGHV�GH�GXDV�SHVVRDV�p����DQRV��'DTXL�D�GRLV�DQRV��D
PDLV�YHOKD�WHUi�R�GREUR�GD�LGDGH�GD�PDLV�QRYD��4XDO�p�D�LGDGH�GH�FDGD�XPD"
5�����H����DQRV
����(TXDo}HV�H�VLVWHPDV�GR��R�JUDX�
���5HVROYD�DV�HTXDo}HV�
D�� ���[� � ʝ E��� � � � ���[��[� � ��ʝ�
F��
�[
��
�[
�[
� ʝ
 �
ʝ
ʝ G�� ��[�[� � ��
5HVSRVWD��D������� E�������� F������� G����������
��
���5HVROYD�RV�VHJXLQWHV�VLVWHPDV�GH�HTXDo}HV�
D��
�
г
в
 �
 �
��\[
�\[
��
E��
�
г
в
 ʝʝ�
 �
��\�[�\[
�\[
��
5HVSRVWDV��D���������������� E���������������
���5HVROYD�
D�� ��[[ �� ʝ�
E�� ���[�[� ʝʝ
F�� �[�[[� � � ʝ�
5HVSRVWDV��D������� E������� F�������
��
��� 8P� MDUGLP� GH� IRUPD� UHWDQJXODU� WHP� ��� P�� GH� iUHD�� 6H� DXPHQWDUPRV� R
FRPSULPHQWR�GHVVH�MDUGLP�HP���P�H�D�ODUJXUD�HP���P��D�iUHD�GR�MDUGLP�SDVVD�D
WHU�����P���&DOFXOH�DV�GLPHQV}HV�RULJLQDLV�GR�MDUGLP�
5HVSRVWD��F� ����P�H�O� ���P
��
&DStWXOR�����)XQo}HV
����'HILQLomR
8PD�IXQomR�p�XP�FRQMXQWR�GH�SDUHV�RUGHQDGRV�GH�Q~PHURV� �[�\��QR�TXDO�GXDV
GXSODV� RUGHQDGDV� GLVWLQWDV� QmR� SRGHP� WHU� R�PHVPR� SULPHLUR� Q~PHUR�� RX� VHMD�
JDUDQWH�TXH�\ VHMD�~QLFR�SDUD�XP�YDORU�HVSHFtILFR�GH�[��(P�RXWUDV�SDODYUDV�� R
YDORU�GH�\ GHSHQGH�GR�YDORU�GH�[�
([HPSOR�� D� iUHD� GH� XP� TXDGUDGR� p� IXQomR� GR� FRPSULPHQWR� GR� VHX� ODGR�� R
VDOiULR�p�IXQomR�GDV�KRUDV�WUDEDOKDGDV��R�Q~PHUR�GH�XQLGDGHV�GH�FHUWR�SURGXWR
GHPDQGDGDV�SHORV�FRQVXPLGRUHV�GHSHQGH�GH�VHX�SUHoR��HWF�
����6LVWHPD�&DUWHVLDQR�2UWRJRQDO
e�XP�VLVWHPD�FRQVWLWXtGR�SRU�GRLV�HL[RV��[ H�\��SHUSHQGLFXODUHV�HQWUH�VL��2�HL[R�[
p�GHQRPLQDGR�HL[R�GDV�DEVFLVVDV H�R�HL[R�\ p�R�HL[R�GDV�RUGHQDGDV��(VVHV�HL[RV
GLYLGHP�R�SODQR�HP�TXDWUR�UHJL}HV�FKDPDGDV�TXDGUDQWHV�
�R 4XDGUDQWH�R 4XDGUDQWH
�R 4XDGUDQWH �R 4XDGUDQWH
[
\
D
E 3�D�E�
(VVH�VLVWHPD�p XWLOL]DGR�SDUD�ORFDOL]DU�XP�SRQWR�QR�SODQR��DVVLP��R�SRQWR�3�D�E�
LQGLFDGR� QD� ILJXUD� WHP� DEVFLVVD� D H� RUGHQDGD� E�� �D�E�� p� GHQRPLQDGR� SDU
RUGHQDGR�H�UHSUHVHQWDP�DV�FRRUGHQDGDV�GR�SRQWR�3�
��
����)XQomR�3ROLQRPLDO�GR��R�JUDX
7RGD� IXQomR� SROLQRPLDO� UHSUHVHQWDGD� SHOD� IyUPXOD� I�[�� � D[�E RX� \� � D[�E�
GHILQLGD�SDUD�WRGR�D�E H�[ UHDLV�H�FRP�D GLIHUHQWH�GH�]HUR��p�GHQRPLQDGD�IXQomR
GR��R JUDX�
([HUFtFLR��&RQVWUXD�QR�SODQR�FDUWHVLDQR�R�JUiILFR�GD�VHJXLQWH�IXQomR�
\� ��[��
[ �� �� � � � �
\
[
\
2EVHUYDomR�
���SDUD�D !���D�IXQomR�GR��R JUDX�p�FUHVFHQWH��H�SDUD�D ����HOD�p GHFUHVFHQWH�
��� GHQRPLQD�VH� ]HUR� RX� UDL]� GD� IXQomR� I�[� D[�E� R� YDORU� GH� [� TXH� DQXOD� D
IXQomR��LVWR�p��WRUQD�I�[� �
([HUFtFLR��&DOFXOH�D UDL]��GD�IXQomR�GR�H[HPSOR�DFLPD�
����)XQomR�3ROLQRPLDO�GR��R�JUDX
7RGD� IXQomR� SROLQRPLDO� UHSUHVHQWDGD� SHOD� IyUPXOD� I�[�� � D[��E[�F RX
\� �D[��E[�F�� GHILQLGD�SDUD� WRGR�D�E�F H�[ UHDLV� H� FRP�D GLIHUHQWH� GH� ]HUR�� p
GHQRPLQDGD�IXQomR�GR��R JUDX�RX�IXQomR�TXDGUiWLFD�
��
([HUFtFLR��&RQVWUXD�QR�SODQR�FDUWHVLDQR�R�JUiILFR�GD�VHJXLQWH�IXQomR�
D��\� �[�����[����
; �� �� � � � � �
<
[
\
E��\� ���[�����[����
; �� �� � � � � �
<
[
\
��
2EVHUYDomR�
���SDUD�D !���R�JUiILFR�GD�IXQomR�GR��R JUDX�p�XPD�SDUiEROD�FRP�FRQFDYLGDGH
YROWDGD� SDUD� FLPD�� H�SDUD�D ���� HOD� p� XPD� SDUiEROD� FRP� FRQFDYLGDGH� YROWDGD
SDUD�EDL[R�
���GHQRPLQD�VH�]HUR�RX�UDL]�GD�IXQomR�I�[� D[� ��E[���F�R�YDORU�GH�[ TXH�DQXOD�D
IXQomR��LVWR�p��WRUQD�I�[� �
���QR�FiOFXOR�GDV�UDt]HV�WHP�VH�
6H�ʑ!��D�IXQomR�WHP�GXDV�UDt]HV��]HURV��GLIHUHQWHV
6H�ʑ ��D�IXQomR�WHP�XPD�UDL]��]HUR�
6H�ʑ���D�IXQomR�QmR�WHP�UDt]HV��]HURV�
���R�YpUWLFH�GD�SDUiEROD�p�XP�SRQWR�TXH�p�GHWHUPLQDGR�SRU� Ъ
Ы
ЩЧ
Ш
Ц ʑʝʝ
D�
�
D�
E
��� TXDQGR�D !� �� �FRQFDYLGDGH� SDUD� FLPD��� R� YpUWLFH� p� R� SRQWR� GH�PtQLPR� GD
IXQomR��4XDQGR�D �����FRQFDYLGDGH�SDUD�EDL[R���R�YpUWLFH�p�R�SRQWR�GH�Pi[LPR
GD�IXQomR�
([HUFtFLRV�� &RQVWUXD� QR� SODQR� FDUWHVLDQR� R� JUiILFR� GDV� VHJXLQWHV� IXQo}HV� H
GHWHUPLQH�RV�SRQWRV�GH�Pi[LPR�RX�GH�PtQLPR��FRQIRUPH�R�FDVR�
D��\� ���[�����[����
; �� � � � �
<
[
\
��
E��\� ���[�
; �� �� � � �
<
[
\
&DStWXOR�����(VWXGR�GD�5HWD
����&RQGLomR�GH�DOLQKDPHQWR�GH���SRQWRV
6H� WUrV� SRQWRV� HVWmR� DOLQKDGRV�� RX� VHMD�� SHUWHQFHP� D� PHVPD� UHWD�� GHYH�VH
VDWLVID]HU�D�VHJXLQWH�FRQGLomR�
��
��
��
��
[[
\\
[[
\\
ʝ
ʝ 
ʝ
ʝ
[
\
[� [�
\�
\�
\�
[�
$
&
%
��
([HUFtFLR��9HULILTXH�VH�RV�SRQWRV�$��%�H�&�HVWmR�DOLQKDGRV�
D��$��������%������ &����� E��$������ %��������&�����
����&RHILFLHQWH�DQJXODU�RX�LQFOLQDomR�GH�XPD�UHWD��P��
e� R� YDORU� TXH� H[SUHVVD� D� WDQJHQWH� WULJRQRPpWULFD� GR� kQJXOR� GH� LQFOLQDomR� GD
UHWD�
��
��
[[
\\
P
ʝ
ʝ 
2EV�� 'XDV� UHWDV� VmR� SDUDOHODV� TXDQGR� VHXV� UHVSHFWLYRV� YDORUHV� GH� P IRUHP
LJXDLV��4XDQGR�IRUHP�SHUSHQGLFXODUHV�
�
� P
�P ʝ 
[
\
P�!��
[
\
P� ��
[
\
P����
2EVHUYDomR�� TXDQGR� D� UHWD� ILFDU� QD� YHUWLFDO�� WRGRV� RV� VHXV� SRQWRV� SRVVXHP� D
PHVPD�DEVFLVVD��[� �[����H�R�YDORU�GH�P WHQGH�DR�LQILQLWR�
����(TXDomR�JHUDO�H�UHGX]LGD�GH�XPD�UHWD�
$�HTXDomR�JHUDO�p�GR�VHJXLQWH�IRUPDWR�
� � � ��� [[P\\ ʝ ʝ �
UHVXOWDQGR�HP�
�FE\D[ ��
��
([HPSOR��'HWHUPLQH�D�HTXDomR�GD�UHWD�TXH�SDVVD�SHORV�SRQWRV�$��������H�%������
6ROXomR��SULPHLUR�GHWHUPLQD�VH�R�YDORU�GH�P�
�
�
�
�
����
����
[[
\\P
��
�� 
ʝʝ
ʝʝ 
ʝ
ʝ 
8WLOL]DQGR�R�SRQWR�$�
� � � �
� � � �
� � � �
� � � �
��\�[�
���\�[�
�[��\�
�[��\�
�[
�
��\
���[
�
����\
[[P\\ ��
 ʝʝ
 ʝ��ʝ
� �
� �
� �
ʝʝ ʝʝ
ʝ ʝ
$�HTXDomR�UHGX]LGD�p GD�VHJXLQWH�IRUPD�
EP[\ � 
R�TXH�JUDILFDPHQWH�SRGH�VHU�UHSUHVHQWDGR�SRU�
[
\
E
1R�H[HPSOR�DQWHULRU�WHP�VH�XWLOL]DQGR�P �����H�R�SRQWR�$�
� � � � � � � �
� � � �
�
�[
�
�\�
�
�[
�
�\
�
�[
�
��\�[
�
��\
���[
�
����\[[P\\ ��
ʝ ɝʝ� 
ɝ� �ɝ� �
ɝʝʝ ʝʝɝʝ ʝ
��
([HUFtFLRV�
���'DGD�D UHWD�GH�HTXDomR��[���\����� ����HVFUHYD�D�HTXDomR�GD�UHWD�SDUDOHOD�j
UHWD�GDGD�H�TXH�SDVVD�SHOR�SRQWR�$������
5HVSRVWD���[��\����� ��
���6mR�GDGRV�RV�SRQWRV�$������ H�%���������'HWHUPLQH� D� HTXDomR� GD� UHWD� W�� TXH
SDVVD�SHOR�SRQWR�&�������H�TXH�p SDUDOHOD�j�UHWD�GHWHUPLQDGD�SHORV�SRQWRV�$�H�%�
5HVSRVWD���[����\����� ��
����,QWHUVHomR�GH�UHWDV�
&RQVLGHUHPRV�GXDV� UHWDV� U H� V�� TXH� VH� LQWHUFHSWDP�QXP�SRQWR�3�D�E���&RPR�R
SRQWR�3�GHYH�SHUWHQFHU�DV�GXDV�UHWDV��VXDV�FRRUGHQDGDV��D�E��GHYHP�VDWLVID]HU�DV
HTXDo}HV� GDV� GXDV� UHWDV�� VLPXOWDQHDPHQWH�� 3RUWDQWR�� REWHPRV� DV� FRRUGHQDGD
�D�E��GR�SRQWR�3��UHVROYHQGR�R VLVWHPD�IRUPDGR�SHODV�HTXDo}HV�GDV�GXDV�UHWDV�
([HPSOR�� 'HWHUPLQH� R� SRQWR� GH� LQWHUVHomR� GDV� UHWDV� ��\[ ʝ� H
��\[� �ʝ
�\��\�
�[��[�
BBBBBBBBBBB
��\[�
��\[
 ɝ ʝ�
 ɝ ʝ
�
г
в
 �ʝ
 ʝ�
3�����
��
3RGH�VH�WDPEpP�LJXDODU�DV�HTXDo}HV�QD�VXD�IRUPD�UHGX]LGD�
�\�[
�[�
��[�[
�[��[
�[�\��\[�
�[\��\[
 ɝ 
ʝ ʝ
ʝ ʝʝ
� �ʝ
�
г
в
� ɝ �ʝ
�ʝ ɝ ʝ�
����$SOLFDomR�HP�DGPLQLVWUDomR
([HPSOR�� 8PD� HPSUHVD� LQYHVWH� 5�� ����� HP� HTXLSDPHQWRV�� 2� FRQWDGRU� GD
HPSUHVD� XVD� R�PpWRGR� GD� OLQKD� UHWD� SDUD� D� GHSUHFLDomR� HP� ��� DQRV�� TXH� p� D
HVWLPDWLYD� GH� YLGD� GR� HTXLSDPHQWR�� LVWR� p�� R� YDORU� FRQWiELO� GR� HTXLSDPHQWR
GHFUHVFH�D�XPD�WD[D�FRQVWDQWH��GH�WDO�IRUPD�TXH�DR�ILP�GRV����DQRV�DTXHOH�YDORU
FRQWiELO�VHUi�]HUR��6XSRQKDPRV�TXH�R�YDORU�FRQWiELO�GR�HTXLSDPHQWR�VHMD�\DR
ILP� GH�[ DQRV��$VVLP�� TXDQGR� [� �� �� \� � ������ H� TXDQGR� [� � ��� �� \� � ��� $
HTXDomR� GD� UHWD� TXH� Gi� D� UHODomR� HQWUH� [ H� \ p� D� GD� UHWD� TXH� XQH� RV� SRQWRV
���������H���������HQWmR�
���
���
�����
[[
\\
P
��
�� ʝ 
ʝ
ʝ 
ʝ
ʝ 
8WLOL]DQGR�R�SRQWR��������
� � � �
� � � �
����[���\
��[����\
[[P\\ ��
�ʝ 
ʝʝ ʝ
ʝ ʝ
2EVHUYH�TXH�D�LQFOLQDomR�GD�UHWD�p�������H�HVWH�Q~PHUR�Gi�D�TXDQWLD�VHJXQGR�D
TXDO�R�YDORU�FRQWiELO�PXGD�D�FDGD�DQR��GHFUHVFH��5������SRU�DQR�
([HUFtFLRV�
���8PD�FRPSDQKLD�FRPSURX�XPD�PiTXLQD�QR�YDORU�GH�5���������6DEH�VH�TXH�R
YDORU�UHVLGXDO�DSyV����DQRV�VHUi�GH�5��������8VDQGR�R�PpWRGR�GD�OLQKD�UHWD�SDUD
GHSUHFLDU� D�PiTXLQD� GH�5�� ������ SDUD�5�� ����� HP���� DQRV�� TXDO� R� YDORU� GD
PDTXLQDULD�GHSRLV�GH���DQRV�"
��
5HVSRVWD��5������
���2� IDEULFDQWH� GH� GHWHUPLQDGD�PHUFDGRULD� WHP� XP� FXVWR� WRWDO� FRQVLVWLQGR� GH
GHVSHVDV�JHUDLV� VHPDQDLV�GH�5�������H�XP�FXVWR�GH�PDQXIDWXUD�GH�5�����SRU
XQLGDGH�� �D�� 6H� [� XQLGDGHV� VmR� SURGX]LGDV� SRU� VHPDQD� H� \ p� R� FXVWR� WRWDO
VHPDQDO�� HVFUHYD� XPD� HTXDomR� UHODFLRQDQGR� [ H� \�� �E�� )DoD� XP� HVERoR� GR
JUiILFR�GD�HTXDomR�REWLGD�HP��D��
���2�FXVWR�WRWDO�SDUD�XP�IDEULFDQWH�FRQVLVWH�GH�XP�FXVWR�GH�PDQXIDWXUD�GH�5����
SRU�XQLGDGH�H GH�XPD�GHVSHVD�GLiULD�IL[D���D��6H�R�FXVWR�WRWDO�SDUD�SURGX]LU����
XQLGDGHV� HP� �� GLD� p� GH� 5�� ������ GHWHUPLQH� D GHVSHVD� IL[D� GLiULD�� �E�� 6H� [
XQLGDGHV� VmR� SURGX]LGDV� GLDULDPHQWH� H� \ p� R� FXVWR� WRWDO� GLiULR�� HVFUHYD� XPD
HTXDomR�UHODFLRQDQGR�[ H�\���F��)DoD�XP�HVERoR�GR�JUiILFR�GD�HTXDomR�REWLGD�HP
�E��
��
���8PD�IiEULFD�GH�HTXLSDPHQWRV�HOHWU{QLFRV�HVWi�FRORFDQGR�XP�QRYR�SURGXWR�QR
PHUFDGR��'XUDQWH�R�SULPHLUR�DQR�R�FXVWR�IL[R�SDUD�LQLFLDU�D�QRYD�SURGXomR�p�GH
5����������H�R�FXVWR�YDULiYHO�SDUD�SURGX]LU� FDGD�XQLGDGH�p 5������'XUDQWH�R
SULPHLUR�DQR�R�SUHoR�GH�YHQGD�p�GH�5�����SRU�XQLGDGH�� �D��6H�[�XQLGDGHV� VmR
YHQGLGDV�GXUDQWH�R�SULPHLUR� DQR�� H[SUHVVH�R� OXFUR�GR�SULPHLUR� DQR� FRPR�XPD
IXQomR� GH� [�� �E�� 6H� ������� XQLGDGHV� IRUHP� YHQGLGDV�� TXDO� VHUi� R� OXFUR�� �F�
4XDQWDV�XQLGDGHV�SUHFLVDP�VHU�YHQGLGDV�SDUD�QmR�KDYHU�SUHMXt]R�"
5HVSRVWDV��E�����������F�������
���2�FXVWR�PHQVDO�GH�XPD� IiEULFD�TXH�SURGX]�HVTXLV�p�GH�5���������H�R�FXVWR
YDULiYHO� GH�5�����SRU�SDU�GH�HVTXLV��2�SUHoR�GH�YHQGD�p�GH�5������� �D�� 6H� [
XQLGDGHV� VmR� YHQGLGDV� GXUDQWH� XP� PrV�� H[SUHVVH� R� OXFUR� PHQVDO� FRPR� XPD
IXQomR�GH�[���E��6H�����SDUHV�IRUHP�YHQGLGRV�HP�XP�PrV��TXDO�VHUi�R�OXFUR���F�
4XDQWDV� XQLGDGHV� SUHFLVDP� VHU� YHQGLGDV� SDUD� QmR� KDYHU� SUHMXt]R� GXUDQWH� XP
PrV�"
5HVSRVWDV��E��������� F����
��
���8P�IDEULFDQWH�GH�UHOyJLRV�SRGH�SURGX]LU�XP�GHWHUPLQDGR�UHOyJLR�D�XP�FXVWR
GH�5�����SRU�XQLGDGH��(VWi�HVWLPDGR�TXH�VH�R�SUHoR�GH�YHQGD�IRU�[��R�Q~PHUR�GH
UHOyJLRV� YHQGLGRV� SRU� VHPDQD� VHUi� GH� ���� �� [�� �D�� ([SUHVVH� R� OXFUR� VHPDQDO
FRPR�XPD� IXQomR� GH� [�� �E�� 6H�5�� ��� IRU� R� SUHoR� GH� YHQGD�� TXDO� VHUi� R� OXFUR
VHPDQDO�"��F��4XDO�R�YDORU�GH�YHQGD�SDUD�VH�REWHU�XP�OXFUR�Pi[LPR�"
5HVSRVWDV��E�������� F����
���8P�IDEULFDQWH�GH�EULQTXHGRV�SRGH�SURGX]LU�XP�GHWHUPLQDGR�EULQTXHGR�D�XP
FXVWR�GH�5�����FDGD�XP��HVWLPD�VH�TXH�VH�R�SUHoR�GH�YHQGD�IRU�[��R�Q~PHUR�GH
EULQTXHGRV� YHQGLGRV� SRU� GLD� VHUi� GH� ��� �� [�� �D��([SUHVVH� R� OXFUR� GLiULR� FRPR
XPD�IXQomR�GH�[���E��6H�5�����IRU�R�SUHoR�GH�YHQGD��TXDO�VHUi�R�OXFUR�GLiULR�"
�F��4XDO�R�YDORU�GH�YHQGD�SDUD�VH�REWHU�XP�OXFUR�Pi[LPR�"
5HVSRVWDV��E������ F������
����(TXDo}HV�GH�'HPDQGD�H�GH�2IHUWD
*HUDOPHQWH�� D� TXDQWLGDGH� GH� PHUFDGRULD� GHPDQGDGD� QR� PHUFDGR� SHORV
FRQVXPLGRUHV� LUi� GHSHQGHU� GR� SUHoR� GD� PHVPD�� 4XDQGR� R� SUHoR� EDL[D�� RV
FRQVXPLGRUHV�SURFXUDP�PDLV�D�PHUFDGRULD��&DVR�R�SUHoR�VXED��RV�FRQVXPLGRUHV
SURFXUDUmR�PHQRV�
��
6HMD� S R� SUHoR� GH� XPD� XQLGDGH� H [ R� Q~PHUR� H� XQLGDGHV� GHPDQGDGDV�� XPD
UHODomR�HQWUH�S H�[ p�GHQRPLQDGD�HTXDomR�GH�GHPDQGD��3DUD� UHSUHVHQWDU�HVVD
HTXDomR�HP�XP�JUiILFR�� XVXDOPHQWH�XWLOL]D�VH�R�HL[R�YHUWLFDO� SDUD�R�SUHoR� H�R
KRUL]RQWDO�SDUD� D�GHPDQGD�
([HPSOR�� 8PD� FRPSDQKLD� GH� WXULVPR� WRPRX� FRQKHFLPHQWR� GH� TXH� TXDQGR� R
SUHoR� GH� XPD� YLVLWD� D� SRQWRV� WXUtVWLFRV� p� GH� 5�� ��� D� PpGLD� GR� Q~PHURV� GH
LQJUHVVRV�YHQGLGRV�SRU�YLDJHP�p�����H�TXDQGR�R�SUHoR�SDVVD�D 5������R�Q~PHUR
PpGLR� GH� LQJUHVVRV� YHQGLGRV� p� VRPHQWH� ���� 6XSRQGR� OLQHDU� D� HTXDomR� GH
GHPDQGD��HQFRQWUH�D�H�WUDFH�XP�HVERoR�
6ROXomR�� $� HTXDomR� GD� UHWD� TXH� Gi� D UHODomR� XQH� RV� SRQWRV� ������� H� ��������
HQWmR�
�
�
����
���
[[
\\
P
��
�� ʝ 
ʝ
ʝ 
ʝ
ʝ 
8WLOL]DQGR�R�SRQWR��������
� � � �
� � � �
��[
�
�S
��[
�
�\
��[
�
��\
[[P\\ ��
�ʝ 
�ʝ 
ʝʝ ʝ
ʝ ʝ
(TXDomR�GH�'HPDQGD
���
���
���
���
���
����
����
����
����
� � � �� �� �� �� �� �� ��
1~PHUR�GH�LQJUHVVRV�GHPDQGDGRV
3U
Ho
R�
GR
�LQ
JU
HV
VR
��
([HUFtFLR����'H]�UHOyJLRV�GH�SXOVR�VmR�YHQGLGRV�TXDQGR�R�VHX�SUHoR�p�5��������
���UHOyJLRV�VmR�YHQGLGRV�TXDQGR�R�VHX�SUHoR�p�5���������4XDO�p�D�HTXDomR�GD
GHPDQGD�"�7UDFH�R�JUiILFR�
[
\
5HVSRVWD�� ���[�\ �ʝ 
([HUFtFLR� ���8PD� ILUPD� DQDOLVRX� VXDV� YHQGDV� H� FRQFOXL� TXH� VHXV� FOLHQWHV� LUmR
FRPSUDU� ����D�PDLV� GH� XQLGDGHV� GRV� VHXV� SURGXWRV� SDUD� FDGD� UHGXomR� GH�5�
�����QR�SUHoR�XQLWiULR��4XDQGR�SUHoR�p�5��������D� ILUPD�YHQGH�����XQLGDGHV�
4XDO�D�HTXDomR�GD�GHPDQGD�SDUD�HVVH�SURGXWR��WUDFH�R�JUiILFR�
[
\
��
5HVSRVWD�� ��
��
[\ �ʝ 
$V� HTXDo}HV� GH� RIHUWD HP� JHUDO� VmR� SRVLWLYDV�� LVWR� p� �� D�PHGLGD� TXH� R� SUHoR
DXPHQWD�D RIHUWD�DXPHQWD��1HVVH�FDVR�Vy�LQWHUHVVDP�RV�YDORUHV�SRVLWLYRV�GH�[ H
\�
([HUFtFLR����4XDQGR�R�SUHoR� IRU�GH�5��������� ���PiTXLQDV� IRWRJUiILFDV� HVWmR
GLVSRQtYHLV�QR�PHUFDGR��TXDQGR�R�SUHoR�IRU�GH�5�������� ������PiTXLQDV�HVWmR
GLVSRQtYHLV��4XDO�D�HTXDomR�GD�RIHUWD�"�7UDFH�R�JUiILFR�
[
\
5HVSRVWD�� ��
�
[\ � 
��
&DStWXOR�����0pWRGR�GRV�0tQLPRV�4XDGUDGRV��5HJUHVVmR�/LQHDU�
2�PpWRGR� GRV�PtQLPRV� TXDGUDGRV� p� XP�PRGHOR�PDWHPiWLFR� TXH� GHWHUPLQD� D
UHWD�TXH�SRGH� UHSUHVHQWDU� �VH�DMXVWDU�D� ��XPD�VpULH�GH�YDORUHV�[ H�\ TXH�QmR�VH
DOLQKDP�SHUIHLWDPHQWH�
([HPSOR��$�WDEHOD�DEDL[R�QRV�IRUQHFH�D� UHFHLWD� WRWDO�DQXDO�GDV�YHQGDV�GH�XPD
IiEULFD�GXUDQWH�RV� VHXV�SULPHLURV����DQRV�GH� RSHUDomR�� RQGH� [ p� R� Q~PHUR� GH
DQRV�HP�RSHUDomR�H�\ p�R�Q~PHUR�GH�PLOK}HV�HP�YHQGDV�DQXDLV�
[ � � � �
\ � � � ��
$�UHWD�GHQRPLQDGD�UHWD�GH�UHJUHVVmR p�HVFULWD�QR�IRUPDWR�\� �P[���E ��RQGH�RV
YDORUHV� GH�P�H� E� VmR� R� UHVXOWDGR� GH� XP� VLVWHPD� GH� GXDV� HTXDo}HV� GR� �R JUDX
GHPRQVWUDGDV�DEDL[R�
� � � � � �
� � � ��
г
в
 ͐�͐
͐ ͐�͐
ʜʜ
ʜʜʜ
LL
LLL
�
L
\EQP[
\[E[P[
RQGH�Q�p�R�Q~PHUR�WRWDO�GH�SRQWRV
3RUWDQWR�PRQWD�VH�D�VHJXLQWH�WDEHOD�
[L \L [L� [L ��\L
� � � �
� � � ��
� � � ��
� �� �� ��
ʜ ��� ʜ ��� ʜ ��� ʜ ���
(�UHVROYH�VH�R�VLVWHPD�
� � � � � �
� � � �
�E�E�
��E��P��
��E��P��
��E�P��
��E��P��
\EQP[
\[E[P[
LL
LLL
�
L
 ɝʝ ͐ʝɝ
�
г
в
 ͐�͐
 ͐�͐
ɝ
�
г
в
 ͐�͐
 ͐�͐
е�
е
г
в
 ͐�͐
͐ ͐�͐
ʜʜ
ʜʜʜ
6XEVWLWXLQGR�
�
��
��P
����P��
����P��
 
ʝ ͐
 ͐�͐
5HVSRVWD��D�HTXDomR�GH�UHWD�TXH�VH�PHOKRU�DMXVWD�p���\� ��[����
��
([HUFtFLRV��'HWHUPLQH�D UHWD�GH�UHJUHVVmR�SDUD�RV�VHJXLQWHV�GDGRV�
D�
[L \L [L� [L ��\L
� �
� �
� �
� �
� �
�� �
ʜ ʜ ʜ ʜ 
5HVS�� ���\��[�
��
��[
�
�\ �ʝɝ� 
��
E���8P�TXDGUR�IRL�FRPSUDGR�HP������SRU�8��������6HX�YDORU�HUD�8�������HP
������8�������HP�������H�8�������HP�������4XDO�R�VHX�YDORU�HP������"
[L \L [L� [L ��\L
ʜ ʜ ʜ ʜ 
5HVS�� ��������\����[���\ ɝ� 
��
F�� 1D�WDEHOD�DEDL[R��[ GLDV�SDVVDUDP�VH�GHVGH�R�DSDUHFLPHQWR�GH�FHUWD�GRHQoD��H
\ p� R� Q~PHUR� GH� QRYRV� FDVRV� GD� GRHQoD� QR� [�pVLPR� GLD�� �D�� $FKH� D� UHWD� GH
UHJUHVVmR� SDUD� RV� SRQWRV� GDGRV�� �E�� 8VH� D� UHWD� GH� UHJUHVVmR�SDUD� HVWLPDU� R
Q~PHUR�GH�QRYRV�FDVRV�GD�GRHQoD�QR�VH[WR�GLD�
[L \L [L� [L ��\L
� ��
� ��
� ��
� ��
� ��
ʜ ʜ ʜ ʜ 
5HVSRVWD��D��\� ����[�������� �E����
��
%,%/,2*5$),$�
'$17(��/��5��0DWHPiWLFD��&RQWH[WR�H�$SOLFDo}HV��6mR�3DXOR��(GLWRUD�ÈWLFD�������
*,29$11,�� -��5��� %21-2512�� -��5���*,29$11,� -U�� -�� 5��0DWHPiWLFD� )XQGDPHQWDO�� 6mR� 3DXOR�
(GLWRUD�)7'�/WGD�������
/(,7+2/'��/��0DWHPiWLFD�$SOLFDGD�j (FRQRPLD�H�$GPLQLVWUDomR��6mR�3DXOR��(GLWRUD�+DUEUD�/WGD�
�����
0('(,526���0DWHPiWLFD�%iVLFD�SDUD�&XUVRV�6XSHULRUHV��6mR�3DXOR��(GLWRUD�$WODV�6�$��������
:(%(5��-��(���0DWHPiWLFD�SDUD�(FRQRPLD�H $GPLQLVWUDomR��6mR�3DXOR��(GLWRUD�+DUEUD�/WGD���D HG�
�����

Outros materiais