×kvh}[oyzq ¬@u - usplaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

20

Upload: others

Post on 10-Apr-2020

2 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�������������� ������������� ��� ���

� "!$#"%�!'&)(�*�*�+,!-/.�0�13254-61 2 087:9;93<>=@? ACBEDGF"HEIJBED-61K2MLONOP�P�QRA,I:P;STPVUWHXP�YZPK[\?8]\P;]\^�.`_

a 1 2 HbQRcd[OQRe\^Kfg4Kh;YZP;e`]OQa 1 2 h;YZP;e\]OQifj43HbQRc@[OQReO^

-6kTe\ICQ:Y,lmQ:nRP;Aa e\P;Ao]\kpAmlrqP;e\I:kTP;A:UskTe`]\kTI:P;]O^;Y,QRA�QtI:P;Spkvu\YZPxwI�y^;QRAa e\P;A�z;QRSv^VI:kT]\P;]\QRAt{|]OQ:z@kp]O^KP�^}Ao?�^rz@kp?�QRe~lm^}AoHbQRI:[\STkTP�Y,QRA5��U�.��o0�1K2C4M�6.r�R����

-/H`P�YZPK�K����7�_`4~��Qt4d��]EyP�^�P�SvQRk�]OQt��[Ou\u`STQ-6P;Svh}[\e\A�YZQRA,[\Svl,P;]O^}A�YZQRICQRe~lmQRA

a 1 2 0){��J�������}�o���=V?)ACBED�F�HbIJBED�{|�\[\=@[Oh}kTl,PV_`P;AmlmY,^���H`�x J9;9;9}¡�9}�;¢}�a �M£V¤G¥¦Q:§©¨WY,^JªmQRICli{|�OY,Q:QR]`?KP;e"Q:loP;S�«$¬�9;9O7�_x­�HX®K¡;¡;¯@_X�d�;��U°1 2 0���¬3���±=@?'ACBED�F"HEIJBEDa³² F´­�¨��³Q:l,I�{�£@HbQ:Y,h;QRSbQ:loP;S�«°¬�9;9}¯@_x­oHx®d£x_E7C�~�@_µ7¶��¡}��U�<�0·9V¸¹�@7Rº 25» 2½¼B 25» 2m¾

¿ À\Á±%K#,ÂsÃ�%�ÄoÅE!$ÆÇ%�!)ÈÉ#,Æ`ÊËÃ�Á±ÂW#ZÃ-/H\YZkT?ÍÌP�Y�kv^}A:UsI:P;STkvu\Y�P;]O^}A�Hb^;Y�^;u`AmQ:Y,z�PxwI�y^;QRA�e`P3ÎMP;SRÌPJNOkTP�^}[©Hb^;Y�P�Y,h}[\?KQRe~lm^}A�lmQ�Ì^;YZkTIC^}A{ÏL\hO«o7¶�Ð NVQR?�H`Sv^}A:UWICQ:ÑÏQRkT]\P;AR_`ÒoÒÇÓ�§@YR_\Ôo^rzJP;AR_b£VÔÇÕ�P-6AmQRI:[\e\]�ÌP�Y�kv^}A:UWI:P;STkvu`YZP;]O^}A�QR?8h}P;SRÌPJNOkTP;A�IC^}?']\kTA,lrqP;e\I:kTP;A]OQ:lmQ:YZ?KkTe`P;]\P;A�Hb^;Y�kTe\]\kpI:P;]O^;Y,QRA�H\YZkp?ÍÌP�YZkv^}AÐ NVQR?�H`Sv^}A:UsYZQRSTPxwI�yP�^�]OQt¤�[\STST§~�Ö�×kTA,�\Q:YR_@رÙÚÜÛ×_\Ý`[\l,[\PxwI�y^;QRAo]O^�u`YZkTST�O^±A,[OHbQ:Y,LXI:kTP;S

-/lmQ:YZI:kRÌP�YZkv^}ARU$I:P;STkvu\Y�P;]O^}A�QR?8h}P;SRÌPJNOkTP;AoIC^}?Þ]\kTAmlrqP;e`I:kTP;A�^;u\l,kT]\P;AoIC^}?'kTe\]`kTI:P;]O^;Y,QRA�AmQRI:[\e`]�ÌP�YZkv^}AÐ NVQR?�H`Sv^OUsh}P;SRÌPJNOkTP;A�?KP;kTA�u\YZkpST�\P;edlmQRA�]O^}A�P�h}Sv^}?�Q:Y�P;]O^}A-6?/ÌQ:lm^@]O^}A�ѽÌßTA,kTIC^}AQCN@H`P;e`A:yP�^3]\P;AoÑà^;lm^}AmÑÏQ:YZP;A�]OQi£VÔÇl,kvHb^ÕZÕ�á\SvQRedlmQRA�h;Y�PRzVkvl,P;I:kv^}e\P;kTARáOQ:ÑàQRkvlm^�âxQRST]O^rz@kTI��V��£V[\ed§}P�Q:z

ã ä åÄ�%K(�+,Ä>%�!'Èæ#ZÆ\ÊËÃ�Á±ÂW#,Ã-6]OQ:L`e\k½wI�yP�^©U$ç´0�è)Úêéë0·¡×Sv^;h°4 �R� Úê¡"{ÏQR?Þ[\?KP�]\P;]`P±u`P;e\]\P~�-/Q:Y,Y,^KQR?8çÜ]\Q:z@kT]\^KPK[\?ÉQ:Y,Y,^�e\P�]\kTAmlrqP;e`I:kTPVUWìRçí0�¡O{|Sv^;h�îJ�JïñððÍò ¬@¸T7¶�xï�ðð-6Sv^;h;^O_XAmQ¦^3Q:Y,Y,^�Y,QRSTP�l,kTz;^KQR?)]\kTA,lrqP;e\I:kTP±ÑÏ^;Yo]OQK7:9~ó�_\^3Q:Y,Y,^�QR?'?3P�h}e\kvl,[\]OQRA�A,Q:Y`ÌPK]OQt9V«ô¬3?KP�h

7

Page 2: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[\Y,Q�7�U Ð A,I:P;SpPK]OQt]\kTA,lrqP;e\I:kTP;A:«

¬

Page 3: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ�¬@U���[OY,z�P�]OQtST[\nM]\Qiì��Q:H`�OQRk�«� � !��R!°#,%�Ã�Æ

-6A:yP�^�QRAmlmY,QRSTP;A�Y,QRSTP�l,kvz�P;?�QRedlmQKªm^¶z;QRe`A�c@[OQ´H`[\STA,P;? Hb^;Y3QRAml,P�Y,QR? e\P/Ñ|P;k NVP/]OQ´kpe\Aml,P�u`kTSpkT]\P;]OQ©eO^]\kTP�h;YZP;?KP3���ÖÒæ{ÏL\h}A:«°¬r���d�

-6P�H\Y,QRAmQRedl,P;?Þ[`?KP±Y,QRSTPxwI�yP�^KHbQ:Y¶ÌßT^@]O^��ÖSp[\?KkTeO^}AZkT]\P;]OQ�ubQR?)]OQ:LXe\kT]\P� é�� ò Úo¬@¸ô�V7ESv^;h�� ð� ���� ÚÍ7�¸ô¯;¡

-6?KP�h}e\kvl,[\]\QRA�P�u`Am^}ST[\l,P;A:U$é � Us�ñ¬�P±���-/HxQ:YrÌßv^@]\^}A:UW¬��7R¡�9K]\kpP;A-/Y,QRSTPxwI�yP�^3HbQ:Y¶ÌßT^@]O^i�°ST[`?KkTeO^}A,kp]\P;]OQ��IC^;Y5 J?�Q:l,P;STkTI:kp]\P;]OQ;UW]\kTAZI:[OlRÌßvz;QRS-6�M£V¤G¥¦Q:§©¨WY,^JªmQRICl:U

a ¬;��h}P;SRÌPJNOkTP;A�]OQRedlmY,^3]\Q�¬;¡KF"HEIa I:P;STkvu\YZPxwI�yP�^�U$ÓµF��a 1 2 0���¡o��7R¡8=@? ACBEDGF"HEIJBEDi{ÏL\hO«°¡}�a Q:Y,Y,^}A�lRÌßTH`kTIC^}A:U×���ñ¡}ó�{�� Q:Y,Y,^}A�AZkTAmlmQR?ÍÌP�l,kTIC^}AR_`IC^}?�^�e`P�]\kTAmlrqP;e\I:kpP��P3ÓµF����a ]\kTAmlrqP;e\I:kpP;A�P�ÑÏQ:l,P;]\P;A�Hx^;Y©?�^rz@kp?�QRe~lm^}A"H\Y`Ì^;H\YZkT^}Aí{��mc@[OQR]\P�� Am^;u`Y,Q���kvYZh;^d��U ÌQÜeOQRICQRAZA\ÌP�YZkv^IC^;Y,YZkvh}kvY°P;Asz;QRSv^VI:kT]\P;]OQRAWIC^}? [\?�?�^V]OQRSv^¦HXP�YZP¦^tI:P;?�Hb^�]OQ�z;QRST^@I:kT]`P;]OQRAWeO^�[`e\kvz;Q:YZAm^¦Sv^VI:P;S

-/zJP�YZk¶ÌP�z;QRkTA�ÒoÒ Ó�§@Ya ªOÌP�ÑÏ^;YZP;?)IC^}e\ÑÏ[\e`]\kT]\P;A�IC^}?'P;A�ICQ:ÑàQRkp]\P;A��a QRAmlmY,QRSTP;Aoz;QRST�\P;A:_O^;u`A,Q:Y,zJP;]`P;A�QR?)P�h}Sv^}?KQ:YZP;]O^}A�h}ST^;u`[\STP�Y,QRAa A:yP�^3z�P�YZkRÌP�z;QRkTAo]OQtI:[OY,lm^�HbQ:Y¶Ìßv^V]O^OUs�O^;YZP;A��°]\kTP;Aa lCqQR? P�H\Y,^¶NVkp?KP;]\P;?�QRedlmQ�PK?�QRAZ?KPKST[\?3kTeO^}A,kT]`P;]OQ�?6ÌQR]\kpPVU� é � ò �M9V¸ô�a e\P�z;Q:YZ]\P;]\QK� é���]OQ:HbQRe\]OQ¦]\P�?KQ:l,P;STkTI:kT]\P;]\Q;U� é�� ò 9V¸ô¬�� �OQ �J�"!@��9V¸ô�}�

¯

Page 4: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OY,Qt¯@U �WP�Y�kTPxwI�yP�^�]\P�?3P�h}e\kvl,[\]OQ¦ÒÇIC^}?'P�Ñ|P;AmQtH`P�Y�P�]\[\P;A�ICQ:ÑÏQRkT]\P;A�]\Q�Fê7:9O7�«� �8Ä���Ã�Æ

-6A,kTAmlmQR?KP;Au`kpe�ÌP�YZkv^}A$^}e\]OQ�[`?KP�QRA,lmY,QRSTPilmYZP;e\AmÑÏQ:Y,QM?KP;A,A,PiH`P�YZP[\?KPiP;eEyPu\YZP;e\I:PV_@z@kpPi[\?æ]\kTAZIC^i]OQP;ICY@ÌQRA,I:kT?�^

-6cd[\P;e`]O^/[\?3PêICQ:Y,l,P6cd[`P;e~l,kT]`P;]OQ�]OQí?KP�lmQ:YZkTP;S±{ÏH\YZkTe`I:kvH`P;ST?�QRedlmQ"�¦�KAmQíP;I:[\?[\STPêA,^;u\Y,Q´P/P;eEyPu\YZP;e\I:PV_\^VIC^;Y,Y,Qi[\?KP�]OQ:lm^}e\PxwI�yP�^�ed[`I:SvQRP�Yoe\P�A,[\HxQ:YZÑ�ÌßTI:kTQ�]OQRAZA,P±QRAmlmY,QRSTP

-6]OQ:z@kp]O^ �PK]OQ:lm^}e\PxwI�yP�^´_`P�ST[\?3kTeO^}A,kT]`P;]OQ�]O^�A,kTAmlmQR?KP�P�l,kpeOh;Q�[\?8?ÍÌPJNOkT?�^�Qi]OQ:Hb^}kTA�]OQRI:P;k-6PK?KP�h}e\kvl,[`]OQtP�u`Am^}ST[\l,P�eO^K?ÍÌPJNOkT?�^�Hb^@]\QMP�l,kpeOh}kvY�é � ò Út7:9-/Y,QRSTPxwI�yP�^QRe~lmY,Q�P�ST[`?KkTeO^}A,kp]\P;]OQ�eO^�?ÍÌPJNOkT?�^tQ�A,[\P¦l,PJNOP]OQo]OQRI:P;kT?KQRe~lm^�{|cd[\P;edlm^±?KP;kTAWST[`?KkTeO^}A,PV_?KP;kTA�YZP�HXkT]\P;?�QRedlmQt]OQRI:P;kà��U

é�� ���� 0 Út7:9tÚê¬@¸ô¯×Sv^;hè^}e\]OQ�è {ÏQR? ?KP�h ]\kTP@BEDZ�íÌQ�^´lmQR?�Hb^ícd[OQ�P�e\^¶z�P´SvQ:z�P´H`P�YZP"LXI:P�Y±¬´?KP�h}e\kvl,[`]OQRA�?KP;kpA�ÑÏYZP;I:PP�HoÌ^}A�^3? ÌPJNVkT?K^

-/Q:Y,Y,^KlRÌßvHXkTIC^±QR?Þé � ���� U �·9V¸ ��?KP�h� �±(�Á��Â��Ã�Ä>%�!) �(��>#�Á±ÄoÆb#,%�Ã�%�!)%�Ã�Æ��8!$*�(�+ZÄoÆxÃ�Æ���+,Ã�Á±!×Ê�åÃ�Å�#,Ã�Æ

-/H\Y,^;h;QRe\kvlm^;YZQRA:UWQRAmlmY,QRSpP;AoIC^}?'é �� �;é��-6P;AÔ�¨$A�lCqQR? [\?KP©Ñ|[\e×wI�yP�^í]OQ�ST[`?KkTeO^}A,kp]\P;]OQ±P�H`P�Y,QRedlmQR?�QRe~lmQ©[\e`kvz;Q:YZA,P;S�_�cd[\Q�I:P;k°YZP�H`kT]\P;?KQRe~lmQeO^KQCNVlmY,QR?�^Ku\Y�kTST�\P;edlmQ

-/^;u`AmQ:Y,z�ÌP�z;QRkTAoP�l@ÌQ � 7R¡KF�HEI�_OQR?)h}P;SRÌPJNOkTP;A�]OQ¦lm^V]O^}Ao^}A�l,kvHb^}A

Page 5: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OY,QM�OUÒ�QRSTPxwI�yP�^KHbQ:Y¶ÌßT^@]O^��ÖSp[\?KkTeO^}AZkT]\P;]OQ�HXP�YZP�ICQ:ÑàQRkp]\P;A�QR?'P;STh}[\?KP;A�h}P;SRÌPJNOkTP;A:«

¡

Page 6: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ�¡@UMÒ�QRSpPxwI�yP�^"]\kTAmlrqP;e\I:kpPJ��z;QRSv^@I:kp]\P;]OQ±]OQ±h}P;SRÌPJNVkpP;A¦P�HXP�Y,l,kvY¦]OQ±ICQ:ÑàQRkT]`P;AK{|�M£V¤³=;Q:§´H\Y,^JªmQRICl���«­�Az;QRSv^VI:kT]\P;]\QRA�Ñà^;Y�P;?)IC^;Y,YZkvh}kp]\P;A�IC^}?)[\?'?�^@]\QRSv^�H`P�YZP±^3I:P;?KHx^K]\Q¦z;QRSv^@I:kp]\P;]OQRA:«

Page 7: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

� � !$+,à �Â��Ã�Ä %�!��í(�+Z+���� �Ü#,Æ�±!WÅ-/Y,QRSTPxwI�yP�^3QR?KH�ÌßvYZkTI:P±P�H`SpkTIEÌP�z;QRS�P±h}P;SRÌPJNOkTP;A�QRA,H`kvYZP;kTA¦{ÏL\hO«�}�-/Y,QRSTPxwI�yP�^3QRedlmY,Q�Sp[\?KkTeO^}AZkT]\P;]OQ�Q�P�STP�Y,h}[OY�P�]\P�STkTe\�`P]\Q�¬V7tI:?)]O^3��Õ5U

a� ����� _�� �·¯MÚ �´{|]\Q:HxQRe`]OQt]\P±u`P;e\]`P~�a� U$ST[`?KkTeO^}A,kp]\P;]OQa�� U$z;QRSv^@I:kp]\P;]OQt?�QR]\kp]\P±P±H`P�Y,l,kvYo]`P�STP�Y,h}[OYZP±]\P3STkTe\�\P]OQ�¬V7tI:?Þ]O^K��Õ?�QR]\kT]\P±Hb^;Y�Q:ÑÏQRkvlm^���^;H\H`STQ:YRUWPKSTP�Y,h}[\YZP±]\PKSTkTe`�\PiIC^;YZY,QRAmHb^}e\]OQ¦P���� 0������ ���

a e\P�H\Y`ÌP�l,kpI:PVU ��� ���� �½� 0! � �#" �A,kTe%$'& �IC^;Y,Y,QVwI�yP�^�HxQRSpPkpe\I:STkTe\PxwI�yP�^($]\P±h}P;SRÌPJNOkTPVU) $×0�9+*JUWh}P;S¶ÌPJNVkTP±zVkTAml,P�]\QtÑÏP;ICQ;_ � 0·9) $×0·¢�9+*JUWh}P;S¶ÌPJNVkTPKz@kTA,l,P�]OQ¦HbQ:Y,L`S�_ � 0 � ��� �½�� ��� �½� �·¬+� � � � _\^}e\]OQ,� � � � ÌQt^3?ÍÌPJNOkT?�^K]`P�I:[OY,z�P�]OQ¦Y,^;l,PxwI�yP�^a IC^;Y,Y,QVwI�y^;QRA¦eOQRICQRA,A`ÌP�YZkTP;A�H`P�YZP�P3P�H`STkpI:PxwI�yP�^�]O^�?/ÌQ:lm^@]\^OUokTe\I:STkpe\PxwI�yP�^´{Ïz;QRSv^VI:kT]\P;]OQiH\Y,^JªmQ:l,P;]\P~�Q�P�u`Am^;Y;wI�yP�^�kTedlmQ:YZe\P

a ÑÏ[\e`I:kv^}e\P�?�QRST�\^;Y�eO^�Õ �_\^}e\]\QtPKP�u`Am^;Y;wI�yP�^ ÌQ�?�QReO^;YRUé.-�0³Ú��d¸ô¢J�WSv^;h � ��� ��� ÚÍ7�¸T7;7

^}e\]OQ � �/� �½� ÌQtQR?8=V?)ACBEDRáOQ:Y,Y,^}Ao]OQ37:9J�ñ¬�9~ó-/u`P;AmQtѽÌßTA,kTI:PVU

a lmQ:^;Y,QR?KP3]\^�z@kvY�kTP;S�U0�21 ò43 é �65a YZP�n;yP�^�?KP;AZA,P±�$ST[\?3kTeO^}A,kT]`P;]OQ�IC^}e\A,l,P;e~lmQ;U 7� éa u\YZkTST�\^A,[\HxQ:YZL`I:kTP;SbIC^}e\Aml,P;edlmQ;U � 5 1a QRe~l:yP�^O_ 7� � ¼

-6�M£V¤��Ö¥t¨�U\1K2o0·�@7��6���Í�æ=V? A BED F�HEI BED {|4 ��¬�9J�Z7:9;9�F�HEI¶�-6P3AmQR?�QRSp�\P;e×wI:P3]\QRA,AmQtz�P;Sv^;YMIC^}?'^�^;u\l,kT]O^3IC^}? ICQ:ÑÏQRkT]\P;Aokpe\]\kTI:P�c@[OQ�^}A�?�^¶zVkT?�QRedlm^}A�HbQRI:[\STkTP�Y,QRAeEyP�^3A:yP�^3?[\kvlm^�ÑÏ^;Y,lmQRA�]OQRe~lmYZ^3]OQK7:9±�¬�9�F"HEI

8 � !$+,à �Â��Ã�Ä %�! �±Ã�*�!WÅ9�;:¦Ã�Â'<tÆxÄ�Á =V�?> � �A@-6P�H`STkTIEÌP�z;QRS�P Ð Q£V9 � Û ¼Û×U$]\kTAmHbQ:YZARyP�^±ICQRedlmYZP;Sµ]OQ¦z;QRSv^VI:kT]\P;]OQRA�]`P±h}P;SRÌPJNVkpP{|?�QR]\kT]\P±Hb^;Y�Q:ÑÏQRkvlm^���^;H\H`STQ:YoP�H`P�Y,l,kTY�]\P�STP�Y,h}[OY�P�]OQtSTkTe\�`P;A]\QtP�u`Am^;Y;wI�yP�^©�

-6kTe\ICQ:Y,lmQ:nRP�e\P�]\kTAmlrqP;e`I:kTP±]OQt[\?KP±h}P;SRÌPJNOkTPVU ��¯;¬}ó-/H`STP;eO^�Ñ|[\e\]\P;?KQRe~l,P;SE]\P;A Ð U � Û ¾5» ¼�B �DC B 25» EGF�{Ïu`P;e\]\P�Y¶áH�Wªm^;Y,h;^rz@Am=VkJIK��P¶z@kpA�7R¢;�}�d_X­�HX®�¯V7R¯@_x¡;¢}�Û×U�]\kpAmHbQ:YZA:yP�^�]\Qz;QRST^@I:kT]`P;]OQRAsICQRe~lmY�P;S�á`�DC � U�u`YZkTST�O^�A,[OHbQ:Y,L`I:kpP;S~?6ÌQR]\kv^¦]OQRedlmY,^¦]O^MYZP;kv^MQ:ÑÏQ:l,kvz;^

Page 8: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQi�@UÒoQRSTPxwI�yP�^�]OQ�¤�[\STSv§d�Ö�×kTA,�OQ:Y�e\P;Aou`P;e\]\P;A���_XÒt_XÕ�_X�³H`P�YZP�h}P;SRÌPJNOkTP;A�]O^�Î�Y�[OHb^KÓ�^VI:P;S°{Ïlm^;Hb^d��_]O^�P�h}Sv^}?KQ:YZP;]O^K]OQ���YZA,P�F�Prªm^;Yi{|ICQRedlmY,^d�°Qt]OQ �MkvY,h;^"{ÏQR?Éu`P;k NV^d��«WÔo^;lmQicd[OQMP�kTe\I:SpkTe\PxwI�yP�^±]\PY,QRSTPxwI�yP�^P;[\?KQRe~l,P�QiPK]\kTAmHbQ:YZARyP�^±]`kT?KkTe@[\k`IC^}e\Ñà^;YZ?KQ�AmQtz�P;kEH`P�YZP�IC^}?KH\YZkT?�QRedlm^}A�]OQ¦^}e`]\P�?KP;kv^;Y,QRAR«

Page 9: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ��dU×ÒoQRSTPxwI�yP�^iرÙÚKÛ©H`P�Y�PMh}P;SRÌPJNVkpP;A$]O^}AWP�h}ST^}?�Q:YZP;]O^}A°]OQ ��kTY,h;^tQ �^}?3PK{ ��YZQRA,A,SvQ:YWQ:lP;S�«�7R¢;�}�;��«> � !$+,à �Â��Ã�Ä��������

-6P�H`STkTIEÌP�z;QRS�P Ð Q£V9"{ÏL`hO«�;� Û�D » 1ر٠ò IC^}e\Aml:¸

a رÙXU�]`kñqP;?�Q:lmY,^i{|?KQR]\kT]O^oIC^}? P�ubQ:Y,l,[OYZPoI:kvYZI:[\STP�YC�xl,P;S~c@[OQ$^�u\YZkTSp�O^�A,[OHbQ:Y,L`I:kTP;S;?6ÌQR]`kv^o]OQRedlmY,^]OQRA,AmQ�]`kñqP;?�Q:lmY,^�QR? � ÌQ�� ç� �0·¬�9V¸¹��¡3?KP�h3P�YZI:AmQRI B 1

a kTe\ICQ:Y,lmQ:nRP�e\P�]\kTAmlrqP;e`I:kTP±]OQt[\?KP±h}P;SRÌPJNOkTPVU ��¬;¯}ó{ÏH`P�YZP��h}P;SRÌPJNOkTP;A�QR?)[`?)P�h}Sv^}?�Q:YZP;]\^O_ �·¬;¯}ó � � �

a QRAml,PKY,QRSpPxwI�yP�^�ÌQ�IC^}e\AmQRc@[EqQRe\I:kTP3]O^3¨$SpP;eO^��\[\e\]\P;?KQRe~l,P;Sµ]\P;A Ð {|Ó�§@e`]OQReV� �QRSTSbQ:loP;SW7R¢;�}�;�-6�M£V¤��Ö¥t¨�U\1 2 0·����� ����7:9'=@? A:BEDÇF"HEIJBEDQRAml,[\]O^3]\QtÓ�Q:^KÕ5_���kTY,h;^KQt�O^;YZe`PJNx_xIC^}?'I:P;STkvu`YZPxwI�yP�^K]OQtICQ:ÑÏQRkT]\P;A

¢

Page 10: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

��� �Ü+Z(iÊE(±Ã � �Äo!WƳ%�!)*±Å�#�+ �±Ä Æx(���!WÅ��KÂW#ZÃ�+-6?/ÌQ:lm^@]O^�P�H`STkTIEÌP�z;QRS�P Ð _X£��³Q¦ux^Jªm^}A�{Ïh}P;SRÌPJNOkTP;AoH\Y`Ì^�NOkT?KP;A:_OL\hO«$�}�-/H\YZkTe\I;ÌßTH`kv^OUb^MÝ`[VNV^�c@[OQI��OQ:h}P¦]OQ�[\?KP Ð H\Y`Ì^�NOkT?KP�QR? I:P;]`PoH`kvN@QRS@]OQ�[\?Ç]\Q:lmQRIClm^;Y�� �%� H`Y,^¶zWÌQR?©_H\YZkTe\I:kTH`P;ST?�QRedlmQ;_O]OQt[\?KP;A�Hb^}[\I:P;A�QRAmlmY,QRSTP;A�h}kTh}P;e~lmQRA

-/h}kvh}P;e~lmQRARU$Hb^;H`[\STPxwI�yP�^�z;QRSp�\PV_\YZkTI:P±QR?'?�Q:l,P;kTA�é��60��¦¬@¸ô¡@_ �é � 0��±7�¸ 9V_ �é 0��M9V¸ 9V_ �é - 0 Út7�¸ô¡

-6AmQ�ªmP �^KeMÌ[\?�Q:Y,^K?6ÌQR]\kT^3]OQ¦h}kvh}P;edlmQRA�Hb^;Y�H`kvN@QRSxQ �� ^�Ý`[ON@^K?6ÌQR]\kT^3]OQtI:P;]\P�h}kTh}P;e~lmQ-/^Ku\YZkTSp�O^AZ[OHbQ:Y,L`I:kTP;Sb]O^�H`kvN@QRSEAmQ:YXÌP CÍ0 ��

^}e\]OQ � ÌQ�PÍÌP�Y,QRP3]O^�H`k NVQRSW{|P�YZI:AmQRIJB 1 �-6AmQ¦^KeMÌ[\?�Q:YZ^±]\Q�h}kTh}P;e~lmQRAoHx^;Y�HXk N@QRSoÌQ�[\?æH\YZ^@ICQRA,A,^�Hx^}kpA,Am^}e\kTP;e\^O_@P�kTe`ICQ:Y,lmQ:nRP±QR? ÌQ � QtPzJP�YZk�qP;e\I:kTP"{|c@[OQíÌQt^3c@[\P;]OYZP;]\^K]O^K]OQRAmzVkv^�H`P;]OY¶yP�^d��]OQ,C�AmQ:YXÌP

Û 1 0 �� 1� 1

Sv^;h;^O_XIC^}?iu`kTe\P;e`]O^±QRA,A,P;A�QRc@[\PxwI�y^;QRA�z;QR?'c@[OQ�� 0 � Û 1 C

P;A,A,kT?©_x?�QR]\kTe`]O^��ÖAmQ�^�u\YZkTSp�O^KA,[OHbQ:Y,L`I:kpP;S C·Q±A,[\P�ÝX[Ol,[\PxwI�yP�^�Û {ÏHb^;Y�QCN@QR?KH`Sv^O_xÑÏP�n:QRe\]\^3z�ÌP�YZkTP;AkT?KP�h;QRe\A���_×ÌQ�Hb^}A,A¶Ìßvz;QRS~QRA,l,kT?KP�Ym�ÖAmQ�^MÝ`[VNV^M?/ÌQR]\kv^¦]OQ�[\?KP�h}kvh}P;e~lmQ�Q;_dIC^}e\�OQRICQRe\]O^��ÖA,Q�P�?3P�h}e\kvl,[\]OQP�u`Am^}ST[Ol,P3?/ÌQR]\kTP�]OQRA,AZP;A�QRAmlmY,QRSpP;A:_\]OQ:lmQ:YZ?Kkpe\PJ�ÖAmQtPK]\kpAmlrqP;e\I:kTP�]\P±h}P;S¶ÌPJNVkTP

-6�M£V¤��Ö¥t¨�U\1 2 0��;¢��6��� �É=V? ACBEDÇF�HEIJBEDI:P;STkvu\YZPxwI�yP�^�IC^}?Þ�±h}P;SRÌPJNOkTP;A¤�^}eOYZ§�Q:loP;S�«�{½7R¢;¢;¢}��U132�0G�;���6���Í�É=@? A BED F"HEI BED{Ïh}P;SRÌPJNVkpP;Ao]\kvÑÏQ:Y,QRedlmQRA:á\?�^V]OQRSv^}A�]\Qt?�^¶zVkT?�QRedlm^}A�HbQRI:[\STkpP�Y,QRA�]\kvÑÏQ:Y,QRedlmQRA��

-6?�^¶zVkT?�QRedlm^}AoHbQRI:[\SpkTP�Y,QRA:U �³P;Svh}[\?3P;A�ICQRe~lmQRe`P;A�]OQ¦=V?)A BEDf ^�Q:Y,Y,^3Y,QRSTP�l,kvz;^Ke\PKz;QRSv^@I:kp]\P;]OQ¦Hb^@]\QMA,Q:Y�h;YZP;e\]OQt]\QRe~lmY,^�]OQ �¦¡�93F�HEI

��� � � ÀOÃ-6eEyP�^KlCqQR?ÞSpkTe\�\P;A�]OQt� Q���QteO^KQRAmHbQRIClmY,^-6?�^@]\QRSv^¦H`P;]OYRyP�^OUs]OQRA,lmYZ[\k½wI�yP�^¦lmQ:YZ?K^}ed[\I:STQRP�Y°]OQo[`?KP¦P;eEyP¦u\Y�P;e\I:Pt]OQ �°���·cd[OQ�I:P�H\l,[OY,^}[K?3P�ldÌQ:Y�kTP]OQ�[\?KP�IC^}?KH`P;e\�OQRkvY�PP�l@ÌQ±P�l,kTeOh}kvY�P3?KP;A,A,P�STkp?KkvlmQ¦]OQ ���\P;e`]OYZP;AmQ:=V�\P�Y

-6I:[OY,z�PK]OQtST[On;UsQRe\Q:Y,h}kTP±H\Y,^V]\[OnRkp]\P�HbQRSv^K]\QRI:P;kT?�QRedlm^3]O^ BGF Ô�kEQ BGF �^��9V¸ô¡;é �Í]OQtÔ�kMÌQtQ�ª½Q:l,P;]`PKe\P�QCNVH`Sv^}A:yP�^

-/lmQ:^;YZkTPVUé � 0³Ú�7R¢@¸ô��eO^3?ÍÌPJNOkT?�^K]`P�I:[OY,z�P�]OQtST[On-6�M£V¤��Ö¥t¨�U\1K2o0��;��� ¬�� ¡É=V? A BED F�HEI BEDI:P;STkvu\YZPxwI�yP�^�IC^}?Þ�±h}P;SRÌPJNOkTP;A�{ÏL`h}A:«°¢r�Z7:9~�

7:9

Page 11: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ¦�@U°­�h}P;SRÌPJNOkTP±L`IClRÌßTI:kpP��P�]`kvY,QRkvl,PiQRAml\ÌP�]\[\P;A�z;Q:n:QRA�?KP;kTA�]\kpAml,P;e~lmQ¦c@[OQtP±]\P±QRA,c@[OQ:YZ]\PV«°£EÌßT?�ub^}Sv^}A?KP;kT^;Y,QRA�Y,Q:H\YZQRAmQRe~l,P;? P;A�h}kvh}P;edlmQRAKQ"^}AKHx^}edlm^}AKP;A3QRAmlmY,QRSTP;AK]`P AmQRcd[EqQRe`I:kTP H\YZkpe\I:kvH`P;S�«6­'h;Y�P;]OQ©Y,QC�H\YZQRAmQReOl,P"^}AH`kvN@QRSTA�]OQ�[\? � �%�«µÔ�^;lmQ©cd[\Q�P"ÝX[Ol,[\PxwI�yP�^íY,QRSTP�l,kvz�P�eO^íeMÌ[\?�Q:YZ^�]OQ3h}kTh}P;e~lmQRA±]\kT?3kTed[`kIC^}eOÑÏ^;YZ?�QtP3]\kTAmlrqP;e\I:kpPP;[`?�QRe~l,PV«°­ÇkT?3P�h;QR?)]\P±QRA,c@[OQ:YZ]\P/ÌQtA,kp?KkTSTP�Y�P�^Kc@[OQtAmQ¦QRAmHbQ:YZP�YZkpP]`P�kT?KP�h;QR?e\P±uXP;e\]\PiÕeO^±YZP;kT^Q:ÑÏQ:l,kvz;^K]OQt[`?KPh}P;SRÌPJNVkpPPK¬�9;9�HEI¦]OQt]`kTAmlrqP;e\I:kTPIC^}?)[\? � �%�ÇIC^}?)H`k NVQRSTA°]\QK7�� �Ï«��¿ ä å!×ÊxÄt%�Ä�%�Ã��±Ä�ÊxÄ�Æ �¶!WÅEà !�� ��� �±Ã�Á±Æ �Ã�Ä = � � Êb# ��Ä>ÀbÀ @

-/zJP�YZkpP;e~lmQ�]\^K?/ÌQ:lm^@]O^�]OQ ��P;P;]OQC� ² QRA,AmQRSpkTeO=- £VÔ�l,kvHb^�Õ,Õ5U}^VIC^;Y,Y,QMcd[`P;e\]O^i[`?KPtQRAmlmYZQRSTP�?KP;AZA,kvz�P�{ � �;é��W�WP;I:[`?i[\SpP37�« ��é �ê]OQoQRSvQR?KQRe~lm^}A�]O^h;YZ[OHb^K]O^K�OQ�e\^Ke�Ì[\I:SvQ:^O_OÑÏ^;YZ?KPK[`?KPQRAmlmY,QRSTPK]\QteOQR[OlmY,^}e\A�Q�QCN@H`ST^@]OQMQ�ªmQ:l,P;e\]O^3[`?KP±QRe~z;^}STl\Ì^;YZkTPYZkTI:P�QR?)�

-/zJP;?�^}A�A,[OHb^;Y�c@[OQ¦QRA,A,P�QRedz;^}Svl\Ì^;YZkpPKAmQtQCNVH`P;e\]OQ¦QRA,ÑàQ:YZkpI:P;?�QRe~lmQ�QtQR?KkvlmQtIC^}?�^�[\?8IC^;Y,Hb^KeOQ:h;Y,^-/Ý`[VNV^�H`Y,^¶z;QRe\kTQRe~lmQK]OQ�[\?3P�QRedz;^}Svl\Ì^;YZkpP�]\QY�P;kv^©Ò QR?Kkvl,kTe`]O^�IC^}?�^´[\? IC^;Y,Hb^�e\Q:h;Y,^©IC^}? lmQR?±�HxQ:Y�P�l,[OYZP�¤�PK[`?KP�]\kTAmlrqP;e`I:kTP±4\U

��� 0 {Ï��� 5 1¶��� � { �M����E4 1

-/l,P;?KP;e\�O^3P;e\h}[\STP�Yo]\P±QRedz;^}Svl\Ì^;YZkpP� 0 ¬ 5

4 0� ����� � { �M�

-75G0�5 2 �6.x{��sÚ�� 2 ��_\^}e\]OQ�� 2 ÌQt^3kTe\A,l,P;e~lmQt]\PKQCN@H`ST^}A:yP�^K]\P�£VÔ-/H`P�YZP"AmQK]\Q:lmQ:YZ?KkTe\P�Yt4í]OQ:z;QC�ÖAmQ�]OQ:lmQ:YZ?KkTe`P�YR_�]O^©QRAmHbQRIClmY,^O_ ��� _�� QKP©z;QRSv^VI:kT]\P;]\QK]OQ�QCN@HXP;e\A:yP�^]\P�QRedz;^}Svl\Ì^;YZkTPV_\.

-/Ñà^}edlmQRA�]\Q¦Q:Y,Y,^OUW^;H`P;I:kp]\P;]OQ;_OlmQR?�HbQ:YZP�l,[OY�PV_`PRz;Q:YZ?KQRST�\P;?�QRedlm^- £VIZ�\?3kT]Ol�Q:loP;S�«o{½7R¢;¢J�d��U�1 2 0���¯o�Í¢É=@? A BED F�HbI BED

7;7

Page 12: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ±¢@UMÒ�QRSTPxwI�yP�^©QRedlmY,QKP�?KP�h}e\kTl,[\]OQ±eO^�? ÌPJNVkT?K^�Q±^�Y,QR]\AZ�\kvÑÏloH`P�YZP�A,[OHbQ:YZe\^¶z�P;A�l,kTHx^�Õ½P�]\^��¦£V¤¥¦Q:§ ¨$Y,^Jª½QRICl:« Ð A,cd[\Q:YZ]\PVU�P;?�^}A,lmYZP"IC^}? ¡�9í£VÔ�A:« ��QRe~lmY,^OUP;?�^}AmlmYZP´]OQ�¯;�í£VÔ�A�P;]O^;l,P;]\PV« �MkvY,QRkvl,PVUP;?�^}A,lmYZPKP;]O^;l,P;]\PV_xkTe\I:ST[`kTe\]O^[\?KP�IC^;Y,Y,QVwI�yP�^�H`P�YZPKP±ÑÏ^;YZ?KP3]\P�I:[OY,z�P�]OQtST[On;«

7R¬

Page 13: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

Supernova Cosmology Project

���

���

���

���

��

���

��=0.3,

� =0.7

�=0.3,

=0.0

�=1.0,

=0.0

m-M

(m

ag)

High-Z SN Search Team

0.01 0.10 1.00z

����� �

� � ���

� � �

� ���

��� �

� (m-M

) (m

ag)

�×kvh}[OYZQ�7:9VU �MkTP�h;YZP;?3P©]OQ��[Ou\uXSvQiHXP�YZP"£VÔ�Õ½P {|ÒokvQRA,A�Q:ltP;S�«�7R¢;¢;�}�Mc@[OQ�SvQ:z;^}[ ÌP�H\Y,^;Hb^}A,k½wI�yP�^©]OQ±[\?[\e`kvz;Q:YZAm^K]O^}?3kTe\P;]O^±HbQRSTPQReOQ:Y,h}kTPKQRA,I:[OYZPV«

7R¯

Page 14: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

��ã "!$ÁMÊx!WÆ�� ÅEà �#½ÊxÃ�ÂW#ZÄ�Á±Ã�#ZÆ-6cd[\P;e`]O^�[\? c@[\P;A,P�YAm^;ÑàYZQ3[\? Q:ÑÏQRkvlm^´]OQKSTQRe~lmQKh;Y�PRzVkvl,P;I:kv^}e\P;S$Hx^V]OQR? AmQ:YiH\Y,^V]\[OnRkT]`P;A�kp?KP�h;QRe\A?�Ì[\Svl,kvHXSTP;A¦{ÏL\hO«o7;7¶�

-6IC^}?�^´P�lmYZPrªmQ:l\Ì^;YZkTP�]O^}A¦ÑÏ^;lm^}e\Atc@[OQ�H\Y,^V]\[On:QR? I:P;]\P�kT?KP�h;QR? ÌQ3]\kTÑàQ:Y,QRedlmQ;_�[\? ÑàQReµq^}?KQReO^©H\Y,^��]\[OnRkT]O^�eO^�cd[\P;AZP�YoAmQ:Y`ÌP±^;u`A,Q:Y,zJP;]\^KQR?)kTe\A,l,P;e~lmQRA�]\kvÑÏQ:Y,QRe~lmQRA�QR?)I:P;]\PKkT?3P�h;QR?�{ÏL\hO«o7R¬}�

-6?�^@]\QRSv^K]OQ¦u\YZkpe\cd[\QR]O^�{Ïl,[`]O^3eOQ���lm^}e`kTP;eO^�QtIC^;nRkTe\�`P;]O^Oá\z;Q�ª,PKP�L\h}[OY�P©7R¯}��Ua zJP;?�^}A�AZ[OHb^;Yc@[OQ�^;u`AmQ:Y,z�P;?�^}A�[\? �mcd[`P;A,P�Y�]\[OH`ST^ �V_dkTAmlm^/ÌQ;_\A,[\PST[OnMIZ�\Q:h}PP±e�Ì^}AHb^;Y�]O^}kTAI:P;?KkTe\�O^}Ao]\kvÑÏQ:Y,QRe~lmQRAo]OQ:z@kp]O^ �P�H\Y,QRAmQReswI:P�]OQ�[\?KP�STQRe~lmQ3{Ïh}P;SRÌPJNOkTP~��eO^KI:P;?KkTe\�\^

a AmQ�ªmP;?ÞØ���QtØ�� � P;A�]`kTAmlrqP;e\I:kTP;A �P3SvQRe~lmQ�QtQRe~lmYZQ�P�SvQRedlmQtQ�P±ÑÏ^}e~lmQa QR?'IC^}e\AmQRc@[EqQRe\I:kTPKz;QR?�^}A�¬±kp?KP�h;QRe\A:_`A,Q:H`P�YZP;]\P;A�Hb^;Y � �a eOQRA,AmQt?�^V]OQRSv^O_\P�]`kvÑàQ:YZQRe×wI:P±]OQ¦lmQR?�Hb^�]OQtIZ�OQ:h}P;]`PK]\P�ST[On¦]OQ:zVkT]O^ �P�]\kTÑàQ:Y,QReswI:Pe\^±IC^}?KH\YZk �?�QRe~lm^�]\P;A�lmYZPrªmQ:l\Ì^;YZkTP;A�AmQ:YZkTP� � � ò {|Ø 1� ��� 1¶� D�� 1$�·{|Ø 1� � ��� 1R� D�� 1�Ú {|Ø��V��Ø�� � �a IC^}?�^ � � ò � �JØ���_bA,[Ou`A,l,kvl,[\kTe\]\^��$e\P�QCN@H`Y,QRA,A:yP�^©P;I:kT?KP�Q±QCN@HXP;e\]\kTe\]\^3P;A�QCN@H\YZQRA,A:y^;QRAMQR?AdÌQ:YZkvQ�]OQi¤µP¶§@Sv^;Y�P�ldÌQ±AmQ:h}[\e`]\P±^;YZ]OQR?8QR? � � _O^;u\l@ÌQR?±�ÖAmQ ��� � ò Ø����� ����1 {½7°� �������� �

a ÑÏP�n:QRe\]\^31 2 ØÉ0�.�0��C�3QtA,[Ou`Aml,kTl,[\kTe\]O^^}A�Ø e\P�QCNVH\Y,QRA,ARyP�^KP;I:kT?KPV_� � ò������ ��� �� �1 {½7°� �

��� B �

� �a P;A,A,kT?©_\IC^}e`�OQRICQRe\]O^��ÖAmQ�^�� �"!$#%'&(#�)�*,+ � ��_\P�AmQ:HXP�YZPxwI�yP�^�P;eOh}[`STP�Y�QRe~lmYZQtP;AokT?KP�h;QRe`A � � Q¦^}AY,QR]\A,�\kTÑàl,A�]\P�STQRe~lmQtQi]O^Kcd[`P;A,P�Y�Hb^@]\QC�ÖAmQt]OQ:lmQ:YZ?Kkpe\P�Y�1K2

-6e\P�z;Q:YZ]\P;]\Q¦^-� �"!$#�%.&(#�)�*/+¦lmQR?)l,P;edlm^�[\?KP�IC^}?KHx^}e\QRe~lmQth;Q:^}?6ÌQ:lmY�kTI:P�c@[\P;edlm^Kh;YZP¶z@kvl,P;I:kT^}e\P;S-6kTe~lmQ:YZzJP;Sv^K]\QtlmQR?�Hb^�QRe~lmYZQi¬�kT?KP�h;QRe`A�­GQ ��H\Y,^V]\[OnRkT]\P;AHb^;Y�[\?KP�STQRe~lmQ�e\^�Y,QR]\A,�\kTÑàl��¶��U

� �W0 {½7°���r�à�? Ø � �TØ � �Ø�� � & 00007¬ {�1 �32 1 1 Ú41 � � 1 1 Ú.�$5 2 � � 0000

^}e\]OQ � ÌQMPi]\kpAmlrqP;e\I:kTPtP;e\h}[\STP�YQRe~lmY,QMPkT?KP�h;QR? Q�PiÑà^}edlmQ;_H�$5 ÌQMPi]`kvÑàQ:YZQRe×wI:Pt]OQ�Hb^;lmQRe\I:kTP;S\QMØ 76A:yP�^�]\kpAmlrqP;e\I:kTP;A�]OQt]`kñqP;?�Q:lmY,^�QRedlmY,QtQRedlmY,Qt^K^;uXAmQ:Y,z�P;]O^;Yi{Ï^d��_XSTQRe~lmQ3{|Sà��QtP�Ñà^}edlmQ�{|A��-/QRA,A,P;Ao]`kTAmlrqP;e\I:kTP;A�]\Q:HxQRe`]OQR?ÉÑàY�P;I:P;?�QRe~lmQ]OQ98 � Q�?KP;kTA�ÑÏYZP;I:P;?�QRedlmQiP;kTe`]\P�]OQ98;:-/H`P�YZPK[\?8[`e\kvz;Q:YZAm^K]\Qt�OYZkvQR]\?3P;e\eEU

Ø�� � 0¬ �1 2� 7°�<8 � �¶�Ö{�¬tÚ=8 � ��8 � � � ��Ú � 7°�>8 � � � {�¬¦Ú=8 � �<8 � �r�Ï�8 1� {½7°��� � � 1 {½7°� �¶�à�{|Ø � �µQtØ � � ARyP�^3I:P;Am^}A�QRA,HxQRI:kpP;kTA�]OQRA,A,PKÑJÌ^;YZ?[\STP~�

- �$5�U$]OQ:HbQRe\]OQ¦]\P�]\kpAmlmYZkvu`[`k½wI�yP�^]\Qt?KP;A,A,PK]`P�SvQRe~lmQ�ÚXf�UW?KP;kv^;Y�kTe\ICQ:Y,lmQ:nRPK]\^K?/ÌQ:lm^@]O^-69}¢;¡}�;�¦¡;�V7�U�PKSvQRedlmQíÌQ�[\?KP Ð h}kvh}P;e~lmQed[`?)P�h}Sv^}?�Q:YZP;]\^1 2 0��;��º 1'?B 1 ¼ =V? ACBEDÇF�HEIJBEDt{ �Q:YZe`AmlmQRkTe I �×kTAZ�OQ:Y�7R¢;¢;¢}�

-6¨Î±7;7;7R¡}�M9}��9VU�PKSTQRe~lmQ ÌQ�[`?KP Ð QR?'[\?8h;YZ[OHb^�IC^}?�H`P;IClm^1 2 0��;���6�KP��;¡o� ¡É=V? ACBEDGF�HEIJBEDi{|]OQ:HbQRe\]OQRe\]O^�]\PKF  JÓ6]\P±h}P;SRÌPJNOkTP~�

- �9}¬V7R�}�t¯;¡}�d_ �M7R��9}�}�¦�;¡;�@_ ¨°¥i£b7R�;¯�9J�ñ¬V7;7�U1K2o0��r��� �8=@? A BED F"HEI BED H`P�YZP$8·HxQRc@[OQReO^"{|¥¦^@^;H`?KP;e`A I �\P;A,AZe\P;IZ�dli7R¢;¢;¢}�

7C�

Page 15: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OY,QK7;7�UWÕ½?KP�h;QR?Þ]O^3c@[\P;A,P�Yo]\[\H`Sv^��t£��³9}¢;¡}�;�¦¡;�V7­i_ ��«

�×kvh}[OYZQ�7R¬@U"��[OY,z�P;A�]OQSp[On]\^�c@[\P;A,P�Y¦]\[OHXSv^��t£ ��9}¢;¡}�;�¦¡;�V73­�_ ��«�­�P;e�ÌP;SpkTAmQ±kTe\]\kTI:P�[\? P�lmYZP;Am^"]OQ�~¬J�O«ô¢�]\kTP;A�e\P;A�zJP�YZkpPxwI�y^;QRAo]OQt[\?3P�kT?KP�h;QR?)QR?)Y,QRSTPxwI�yP�^�P±^}[\lmYZPV«

7R¡

Page 16: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OY,QK7R¯@U�Î�Q:^}?�Q:lmYZkTP3]O^3?�^V]OQRSv^�]OQtu`YZkTe\c@[OQR]O^H`P�YZP±QRAml,kp?KP�l,kvz�P�]OQ�1 2 IC^}?'STQRe~lmQRA:«� � � �R!$#½ÊbÄ���!$+Z%�Ä��i#Z � ���i(�Á���Ã�! �

-6P�h}Sv^}?�Q:YZP;]O^}AoHb^}A,A,[OQR?8hWÌP;A�cd[\QRe~lmQ�c@[OQ¦QR?KkTlmQ¦YZP;kv^}A��a � �³7:9���ÚÍ7:9 E ¥a�� �³7:9 B ¼ ÚÍ7:9 B 1¦I:? B ¾a�� �³7:9/?�ÚÍ7:9 DmD �a é� � � �·9V¸ 9}¡tÚÜ9V¸ô¡;é � �{|PKÑÏYZPxwI�yP�^3]OQ¦uoÌP�Y�kv^}e\A�lmQR?'P;STl,P�Y,QRSvQ:z�qP;e\I:kTP�IC^}A,?K^}SRÌ^;h}kTI:P~�

-/Q:ÑàQRkvlm^�âxQRST]O^rz@kTI��V��£V[\ed§}P�Q:zÜ{ÏL\h}A:«�7C���Z7R¡}��U^}A�ÑÏ^;lm^}e\Ao]\P±Y�P;]\kTPxwI�yP�^3IEÌ^}A,?3kTI:PK]OQ¦Ñ|[\e\]O^"{ � ò ¬@¸¹��¯K¥�_\QRe\Q:Y,h}kTP;A�?[\kvlm^�HbQRc@[OQRe\P;A��A:yP�^�QRAmH`P;ST�\P;]\^}AKQ P;cd[OQRI:kp]O^}A3HbQRSv^}A�QRSvQ:lmY,^}e`A3Y,QRSpP�l,kvzxÌßpAml,kTIC^}A3]\^êhWÌP;A©c@[OQRe~lmQ {ÏQ:ÑÏQRkvlm^ ��^}?�H\lm^}ekTe~z;Q:Y�Am^d�

-6[\?Ç?3P�H`Po]\PolmQR?�HbQ:YZP�l,[OYZP�]\PoÒ ���´e\P�YZQ:h}k�yP�^�YZQ:z;QRSTP�Y`ÌP�[\?KP �m?KP;e`IZ�\P��M]OQ°lmQR?�HbQ:YZP�l,[OYZP�?�QReO^;Y{ �¹�e\P¦Hb^}A,k½wI�yP�^�]\^�P�h}Sv^}?�Q:YZP;]\^�Hb^}kTAWe\PtY,Q:h}k�yP�^i]\QoÒoP¶§@SvQRkTh}�V�ñ®;QRP;e\A°]O^tQRAmHbQRIClmY,^�^�Ý`[VNV^t]\kT?3kTed[`k{Ï^}A�ÑÏ^;lm^}e\A�zxyP�^KH`P�YZPKQReOQ:Y,h}kTP;A�?3P;kTA�P;Svl,P;A��

-/H`P�YZP[\?KP�]`kTAmlmYZkvuX[\k½wI�yP�^MQRAmÑRÌQ:Y�kTI:P±]OQohWÌP;A�IC^}?É]OQRe\A,kp]\P;]OQ�QRSvQ:lmY�q^}e\kTI:P � � _dlmQR?�HbQ:YZP�l,[\YZP�QRSTQ:lmYJq^}e\kTI:P� � QtYZP;kv^ 5±_\PKÝ`[Ol,[\PxwI�yP�^3]`P±lmQR?�HbQ:YZP�l,[OYZP�]\P�Ò ��� ÌQ� �� ò Ú � � �è � � 1 Û�� � � 5^}e\]OQtè � ÌQiPK?KP;A,A,P3]O^�QRSvQ:lmY,^}e©QiÛ�� ÌQ�PKA,QVwI�yP�^�]OQtI��O^@c@[OQt]OQi¤��O^}?KAm^}ezJP;Sv^;YZQRA�QRAmHbQ:YZP;]O^}ARU0� � � ��É7t?K¥

-/QRA,AmQtQ:ÑÏQRkvlm^KHb^V]OQMH\Y,^¶z�P�Y�c@[OQtP�Y�P;]\kTPxwI�yP�^3]OQ¦Ñ|[\e\]\^z;QR?Þ]OQtP;Svlm^}AoY,QR]\A,�\kTÑàl,A��-6ST[\?KkTe\^}A,kT]\P;]OQ��³]O^�hWÌP;Ai{Ïu\YZQR?KA,AmlmYZP;�`ST[\eOhd��U

� ��� 1� � D�� 1� 5 ¾7R�

Page 17: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQt7C�OU×­�STkpe\�\P�A\Ì^}STkT]\P�Y,Q:H`Y,QRAmQRedl,PtPt]\kTA,lm^;Y;wI�yP�^�eO^¦QRAmHbQRIClmY,^i]\PMYZP;]\kTPxwI�yP�^iIEÌ^}A,?KkTI:Pt]\Q�ÑÏ[\e`]O^K{|STkTe\�\PlmYZP;ICQ�ª,P;]\P~��]OQ:z@kp]O^KP�^KQRAmH`P;Sp�\P;?�QRedlm^ �^}?�H\lm^}e�kTe~z;Q:Y�Am^O«

-/Ý`[VNV^K]OQ¦YZP;kv^}A��U� � 0 �

���E4 1�-/l,P;?KP;e\�O^3P�HXP�Y,QRe~lmQ]O^KP�h}Sv^}?�Q:Y�P;]O^OU � � 5 �J4@�-6IC^}?�u`kpe\P;e\]O^�QRA,AZP;A�Y,QRSTPxwI�y^;QRA�U

4 1� �J4 � 0�4~��{½7°���d� 1 � � �� & 1 �� ¾ � 1� � �

-61 2 0·¡J����7C�'=@? A BED F"HEI BED {�F�§;Q:YZA�Q:loP;S�«o7R¢;¢}�;�-/H\Y,^;u`SvQR?3P;A�IC^}?)^K?6ÌQ:lm^V]O^OU°P�ÑÏQ:l,P;]O^�HxQRSpP�]\kTAmlmYZkTu`[\k½wI�yP�^]O^KhWÌP;A�Q¦ÑÏ^;YZ?KP3]O^KP�h}Sv^}?�Q:YZP;]\^

7¶�

Page 18: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OY,QK7R¡@U ��u`AmQ:Y,z�PxwI�y^;QRAo]\^KQ:ÑàQRkTlm^�£V[\ed§}P�Q:z~��âbQRST]O^¶zVkTI��©QR?8z�ÌP�YZkv^}A�P�h}Sv^}?KQ:YZP;]O^}A:«

7R�

Page 19: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[\Y,QK7R�@U0�MkTAmlmYZkTu`[\k½wI�yP�^�]OQ¦H\YZ^;u`P�u`kTSTkp]\P;]OQRA]OQtI:P;]\P�z�P;Sv^;Yo]OQt1 2 eO^K�M£O¤�¥¦Q:§�¨WY,^JªmQRICl:«� � � Ä�Á±ÂW+Z(±Æ �Äo!WÆ

-/^}A°?6ÌQ:lm^V]O^}AQR? h;Q:Y�P;S`IC^}e\IC^;YZ]`P;? ]OQRedlmY,^]OQ �±7:9~ó'{|IC^}?�H`P�YZP;]\^IC^}?æ[\?�Ñ|P�lm^;YM7�«ô�teO^IC^}?�QVwIC^]O^}AoP;eO^}A�¢�9~��U1 2 0 {���¬o� �}��=@?)A:BED�F"HEIJBED�{|�M£O¤�¥¦Q:§©¨WY,^JªmQRICl:_\L\h}AR«�7R¡r�Z7R�}�

-6?KP;A:«v«v«a lm^@]O^}Ao^}Ao?6ÌQ:lm^V]O^}AoP;AZA,[\?�QR?)c@[OQtPKÓ�F ��QRAml\ÌP3PK¡�9�=@HEI{ÏçÜ0 7R�@¸ô¡}��?KP;A�^;u`AmQ:Y,z�PxwI�y^;QRAMY,QRICQRedlmQRAMkTe\]\kTI:P;?ÞkTe\ICQ:Y,lmQ:nRP;A�]OQ±¬�9~ó'e`P3]\kTA,lrqP;e\I:kTPV_XIC^}? çQRe~lmY,Q�7R�@«ô¬�9KQ37R�@«ô��9

-6�\[O=V[Oh}kvl,PVU$1 2 QRA,l\ÌP�QRe~lmYZQ�9V«ô¢;¡�Q37�«T7R¡3]O^�z�P;Sv^;YoP;I:kT?KPHxQ:Y�?KkvlmQt1 2 QRedlmY,Qi��9�Qi¢�9K=@?)A:BED�F"HEIJBED

7R¢

Page 20: ×kvh}[OYZQ ¬@U - USPlaerte/aga5751/aula3.pdf · 1 a 1 2 ¢

�×kvh}[OYZQ�7¶�dU�ÒoQRSTPxwI�yP�^©]\kTAmlrqP;e`I:kTPJ��Y,QR]\A,�`kvÑàl�e\^��¦£V¤ ¥¦Q:§�¨WYZ^Jª½QRICl:«M­�STkTe`�\PKA\Ì^}STkp]\P�Y,Q:H\YZQRAmQRe~l,P�1 2 0 ��¬=V?)A BED F�HEI BED QiP;A�lmYZP;ICQ�ª,P;]\P;AM��7:9~ó�«� � � �i!WÅEÂMå� ÂW#ZÄoÆ7�«���?KP�ICQ:ÑàQRkT]`PíÌQ�^;u`AmQ:YZzJP;]\PtQR? F´�V7�IC^}?�^���[Ou\uXSvQo£@H`P;ICQo¤µQRSvQRA,IC^;HbQ;« Ð STPMlmQR? [\?KPt?3P�h}e\kvl,[\]OQ?/ÌQR]\kTP�è �ê0�¬;¡@¸ô��Q�[\?ÉHbQ:Y¶ÌßT^@]O^�]OQ�¡K]\kTP;A:« Ð Aml,kT?�Q¦PK]\kpAmlrqP;e\I:kTP±]OQiFí�V7�«

¬@«���AmQ"P L`h}[OYZP �íH`P�YZP QRAml,kp?KP�YKP ]\kTAmlrqP;e`I:kTPíY,QRSTP�l,kvz�PíQRe~lmY,Q©^}A3P�h}Sv^}?�Q:YZP;]O^}A3]OQ �oY�A,P F�Prªm^;YKQ��kvYZh;^O«

¯@«���AmQKP�YZQRSTPxwI�yP�^"رÙKÚ�Û/HXP�YZP�QRAml,kT?KP�YtP�]\kpAmlrqP;e\I:kTP�Y,QRSTP�l,kTzJP�QRedlmY,Q�^}A¦P�h}Sv^}?�Q:YZP;]\^}At]OQ�h}P;SRÌPJNOkTP;A]OQ"�MkvY,h;^�Q �^}?3P"{ÏL\h}[OYZP3�;��«

�O« �^}e\A,kT]\Q:Y,QK[\? ?�^V]OQRSv^"]\QK�OYZkvQR]\?3P;e\eÜIC^}? 8 � 0æ9V¸ô¯@« �¦[\P;SiÌQ3P"]\kTÑàQ:Y,QReswI:P©]\P"]\kTA,lrqP;e\I:kTP©]OQ]\kñqP;?�Q:lmY,^O_~QR? F"HEI�_}QRedlmY,Qo]\^}kTA×^;uVªmQ:lm^}A$P�^tSv^}eOh;^t]`P¦STkTe\�\P�]OQ�zVkTA,P;]\PV_}[`?³QR?��0�9V¸T7�Q�^¦^}[OlmY,^QR? �K0G9V¸ô¬�� Ð A,Qi^}A�^;uVªmQ:lm^}A�QRA,l,kvz;QRA,AmQR?ÞQR?Þ�K0Ç9V¸ô¡3Qi�K0Ç9V¸ô�@_xYZQRAmHbQRICl,kvzJP;?KQRe~lmQ��/Ò�Q:HXkvl,P�^IEÌP;STI:[\Sv^KHXP�YZP�8 � 0³7�«

¡@«�­ c@[\P;e~lm^©IC^;Y,YZQRAmHb^}e\]OQ;_bQR? �ÍHbI B 1J_b^�u\YZkTSp�O^3A,[OHbQ:Y,LXI:kTP;S�ç �·0æ¬V7�?KP�h©P�YZI:AmQRI B 1���£@QQRA,AmQu\YZkTST�\^ ÌQ¦H\Y,^V]\[OnRkT]\^tHb^;Yh}kTh}P;e~lmQRA:_Xcd[\P;SoÌQ¦^�eMÌ[\?�Q:YZ^]OQRSpP;A°Hb^;Y�HEI 1 �"­Çcd[OQM]\kTA,lrqP;e\I:kTPiQRAml,P�YZkTP±Ph}P;SRÌPJNVkpPKAmQ�P±Ý`[\l,[\PxwI�yP�^KY,QRSTP�l,kTzJP�]OQ�u\YZkTST�\^iA,[OHbQ:Y,LXI:kTP;SbÛ ��C�ÑÏ^}A,AmQtkTh}[\P;SEPK9V«T7��

�@«M£V[OHb^}e\�\P�c@[OQKP©ÓµF�� QRAmlmQ�ª,P�P"¡�9©=@HEI�]OQK]\kTA,lrqP;e\I:kTP�QKlmQRe\�\P©[`?KP�z;QRSv^VI:kT]\P;]OQ�l,P;eOh;QRe`I:kTP;SW]OQ¬;¬�9©=@?� JA:« Ð A,l,kT?�Q±AmQR[ ]OQRA,Sv^VI:P;?�QRedlm^©P;eOh}[\STP�YK{ÏQR? AmQ:h}[`e\]O^}AM]OQ�P�YZIC^d��e@[\? kTe~lmQ:YZzJP;Sv^�]OQ©7:9P;eO^}A:«

¬�9