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tesson/ift-66975/Notes15751.pdf! "$#%# &(') * ,+-#% /. #10 2 435#%67#%89 :#% 4. ;+< "=#5.>#1?@8 A...

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+ :M�i��896;:<4�w 4�C =PG>L-DmIdAB=@GCHP;CKF9BLOKF6(?+ADC ]<? I8]BLO687WIXLC=�Eb?<K 3 K C =@?<G>=@7#S<DF=�A<=@GiNtLZIXLCGi=@G L= A ��A A �GA A�� A A � m G(DqC I8DR9BYbITS=PL =PG>L= � A �gm G �\=PG>L ]<?<= ;>=@DmI LOKR68? A<= LO;CI8?<GCKMLOKF6(? KR?BH@DR]BGC= AbI8?BG= A ��A A �GA A�� A A � m+o = � A �gm o = A ��A A �GA A�� A A � m G A �Q=@G>L\DqC NPLOIXL KR?BKFLOKRI8D^=PL = A �YA A � m =PG>L\DqC =@?yZG>=@7#S<DF=UA<=PG NPLZI LOG�Eb?bIX]?U 3 K IQ;C=PDmIXLCKR6(? � ?<=!H@6(?eLOKF=@?eL 9bI8GoA<=ULO;>KR9<DF=PL A<6(?eL DmIQ9B;C=@7TK��P;C=HP6(7:96(GCI8?eLO= =@G L A � ` KFD<?DC o I 9bI8G A<= LO;CI8?<G>KFLOKF6(? fh]<Kp6(;>KR_(KF?<=!A<= A � c �(9bIX; H@6(?<G>N@fh]<=P?hL�G�:?DC =PG>LS9bI8G ]<?<= ja6(?BHPLOKF6(?i=PL5D C I8] LO6(7:IXLO=Q?DC =PG>L59bI8G A<NtLO=P;C7TKR?<KFG>LO=X3

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>��yA � A�� H A9>��yA � A � H A9>���A � A � H>��yA � A H A9>��yA � A� H A9>���A � A H>� �A � A H A9>� �A � A� H A9>� yA � A H>���A � A H A9>���A � A� H A9>���A � A H�m

+ :M�i��896;:<4�w 4�C =PG>L-DmIdAB=@GCHP;CKF9BLOKF6(?+ADC ]<? I8]BLO687WIXLC=�Eb?<K 3 K C =@?<G>=@7#S<DF=�A<=@GiNtLZIXLCGi=@G L= ��A��yA� �A � m GBDqC I8DF9<YbITS=PL =PG>L@= � A � A � m GIF =PG>LS]<?<=k;C=PDmIXLCKR6(?iA<= LC;OI8?<G>KFLCKR6(?-KR?BH@DR]BGC= AbI8?BG= ��A��yA� �A � m�o = � A � A � m+o = ��A �yA� yA � m G 2g=@G L\D C NtLZIXLVKR?<KMLOKmIXD�=PL = � m =@G LkDqC =@?<G>=@7#S<DF= A<=PGNtLZIXLCG�Eb?<I8]?U�` KFDb?DC oTIkfh]DC ]<?lNtLZIXL�Eb?bIXD ct3 K I ;C=PDmIXLCKR6(? F H@68?hLCKR=P?hL DF=@G LO;CKF9<DR=tLOG_>��yA � A � H=tL'>��yA � A� H G�f ]BK A<NPH@;>KFq(=P?eL A<=P]?U�LO;OIX?<GCKMLOKR68?<G A<K h N@;>=@?eLO=PGEDF6(;CG A<=TDmI-DR=PHPLO]B;C= ADC ]<? �AbIX?<G DqC NPLZI L�l �b9<I8; H@6(?BGCN@fh]<=P?eLJG<F ?DC =PG>L59bI8G ]<?B= ja68?<HPLCKR6(?-=PL D C IX]BLO6(7:IXLC=V?DC =@G>LS9bI8GA<NtLO=P;C7TKR?<KFG>LO=X3�L ?<H@6(;>=\]B?<=kja68KRG�GB;C=@7:I8;>f ]B= �kf ] C KFD�?<=kj IX]BL59bI8G GC=sEb=@;Ss DqC KRA<=P?hLCK EbH@I)ZLC=@]<;V] LOKRDFKRG>Nk96(]<;5?<6(7T7T=@;5DmITja68?<HPLCKR6(? 6(]#DmIT;C=PDmIXLCKR6(? ` KFH@KqGIF A<NPGCKR_8?<=E]<?B= ;C=PDmIXLCKR6(?fh]<K ?DC =@G LS9<I8G ]<?<= ja6(?<HtLOKR68?pct3

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� �= � m = � m = �yA � m= m � =�� m

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F�> = �yA � m A � H�

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lRl � ���������� �� ��� � ���� V� ��=� ����� ������r ������� �� �p �����

l 3�> = � �gm�� = � � A ��mnH �vB3 � �

+ : �X��896X:�4�w � 6(]<; DR=PGVA<=P]?U�9<;C=P7:KF=@;>GV9<;C6TS<D��P7:=PG�G A<68?<?<6(?<G DF=@G Yh]<KML 9<;C=P7:K �@;C=PG GCNPf ]B=@?<HP=@G` 9<I8; 6(;CAB;C= A<= DR6(?B_(]<=@]B;VH@;>6(KRG>GOI8?eLO=Jct3 � 6(]<; DR=gA<=P;C?<KF=@;/G KRD =@G>Lk96(GCG>KaS<DF=gA<= A<6(?<?B=@;VLO68]BLO=PGDR=PG GCN@fh]<=P?<H@=PG@32(3 >�= � �gm s = ��� A ��mnH �

= � � A ��� A ��m ��

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= � � � � A � �gm ��

= � A � � � � A � � A � � � � � � � � A � � � � � � A � � � � ��� A � � � � A � � � � � � � � � � � � Agwgwgw mvB3 � � 0 = ��m

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K C IX]BLO6(7:IXLC= � ' ITDRIEja6(;C7T=� ' 0 >i? ' A = � A � A � m A�� ' A � ' A)( ' H A

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=PL

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lRl 2

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=y> ��A � A � H A9>��yA � A � H A9>��yA � A� H�m s =y>� �A � A � H A9>���A � A � H�m�

=y> ��A � A � H A9>��yA � A � H A9>��yA � A� H A9>� �A � A � H A9>���A � A�� H�mK = A<KRI8_(;CI87:7T=QAB= LC;OI8?BGCKFLCKR6(?BGUA<= � ' =@G>L5DF= GC]<KMq8IX?hL�[

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� 3 �56(? 3 K =@G 9bI8;>=@?eLOY��@GC=PGQG>6(?eLS7:I8D NPfh]<KRDFKaS<;>N@=@GP3QB3 �56(? 3 n Db7WIX?<fh]<=SDF=@G 9bI8;>=@?eLOY��@GC=PGU= U LC=@;C?B=@G@3 K C = U 9<;C=PGCGCKF6(?h>[> � s ��H � �p��H Ge=@DFDR=HG(=@G L!]<?B== UB9B;C=@G>GCKF6(?�;>N@_(]<DFK��P;C=83

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+ : �X��896X:�4�w K =PGUH@DRI8]<G>=@GU7T=@?eLOKF6(?<?<NP=@G AbI8?<GUDRIEGC68DR]BLCKR6(?TGC6(?eL HP=@DFDR=@G A<=VDRI\A<N Eb?<KFLCKR6(?�2(3F282 u 32(3 u >�> � � > � s ��H[H�H

� 4!DRI8]<G>= � 3��u > � H � u >�> � s ��H[H

� 4!DRI8]<G>= vB3��u > � H � > u > � H s u > ��H�H

� 4!DRI8]<G>=�l 3��= � m�� >�= � m s = �gmnH

� BSN/Eb?<KMLOKF6(?iA<= DqC ]<?<KF6(?iA<= DmI8?B_eI8_(=PG@3��= � m�� = � A �gm

� BSN/Eb?<KMLOKF6(?iA<= DmIgH@68?<HJIXLCN@?bI LOKR68?�AB=kDRI8?<_eIX_(=@GP3��= � � A � �gm 3

l 3 u >�>�> � � � H � sS> � s ��H � H�H�

� 4!DRI8]<G>= vB3��u >�> � � � H � H s u >�> � s ��H � H

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lRl8v

> u > � H � u > � H�H � sS> u > ��H s u > ��H�H ��

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