cadernoCalculoNumerico

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" W Y UY U >F> > A[kRB V / / E '( + 2F ; 2µ: + 2 W + : ; [E =EH E]>=>HEk=E SEDB< DE>@X [=@?@SE B u dbib i` K èdbh C>D> >CDB]@H>D B ¤£¡ª SEDB FE E FE ABDH> > ¶ ª 4 £ª > GBkQEDn«kG@> [=@?@S>kFB 5 F@AEDEk=E FE<=> D>@SY PTX o>> @=ED>E<Y ZT<EDQ>RB H §4 £I A §¥ =[FB [E ABD kEGE<<D@B C>D> n>D>k=@D > GBkQEDn«kG@>Y UY M s <E B u dbib i` K èdbh C>D> EkGBk=D>D [H SEDB CB<@=@QB FE E ' ( F ; : W < : ; 2 ; + k[H @k=EDQ>?B EH [E QBG« CB<<> n>D>k=@D f s _jb_j > GBkQEDn«kG@> FB CDBGE<<BY H §4 £ I A §¥ > E<GB?o> FB @k=EDQ>?B E FB Go[=E @k@G@>?Y U ` ì ab í cbd ìø c ñ õì e bc ì d fc ð î b gah ð î b õ b UY ➠ A[kRB E '( + > ? ; G ; + =EH [H SEDB EH / Y y [>@< F>< A[kE< >T>@]B QBG« CBFE [=@?@S>D C>D> FE=EDH@k>D E<<E SEDB CE?B u dbib if i x s _bj jtfklì agwìijm fin H §4 £I A §¥Y UY9 EHBk<=DE [E > <E 8 «kG@> ' ' J ' ( >? +( ; +( G J ' ( ; + ; G > ? ' ; +( : ' J ' ( ; +(>? + F W + ' +( ; · ¸ ¹ CBFE <ED [=@?@S>F> C>D> G>?G[?>D rº # / Y UY = s =@?@S>kFB B E]EDGG@B >k=ED@BD G>?G[?E r»z Y UY D GoE B CBk=B FE @k ¼ E]RB½ F> A[kRB E '( >? ; F +Y UY W LE> > A[kRB E ' ( >? : ; +Y GoE B Q>?BD FE kB [>? E '( Y UY q y [EDEHB< FE=EDH@k>D > k@G> D>@S ! FE [H> A[kRB E N / ¾ O M [=@?@S>kFB B u dbib ifi xs _bj jtfklì agwìijm fiY DBQ>D [E <E J N / ¾ O M \ [H> A[kRB FE G?><<E P@<=B \ FED@QQE? GBH FED@Q>F> GBk=k[>X E >?\H F@<X J '( <E E < <E ! E PTX JP ' ( p q 6 / ¾ Ek=RB > <E 8 «kG@> / 5 J ' ( J ' ( C>D> #+ \ GDE<GEk=E E GBkQEDnE C>D> ! Y PL[nE<=RB ;<=[FE > A[kRB J k[H @k=EDQ>?B J '/ ( GBH p ! E YYYX ¿¥¡ª¥¤ À ¦ À a`Á f E N O M igf i m ` ` i ijc `_`hwjv m ` yÂ wbt E PP wbhd Ã hgf Ä ags bh Å f Æg` j E '( E '( " / Ä jj E P ' ( 7 / s f_f dbib 6 Ä Ç Ê·¸º· »¼ À ¸ È ¼ÄÈ· ³ ´µ Â·¸º· ¶½ ´ºÀ ¶ · Å´¼ ¸È· ³ »¼ µ [ ÄÀ µ · Á · ¶ , Á ¸¼µ »¼ µ ´ ¸À µ · Á · ¶ , ÁË UU êëìíîïîðñò òñóíì ôìíñò õì ö÷øùúìò jjj E PP '( h ¨ b d_bwf i` ijhfy `t Ä {hd ¨ b f i `ÆÉ Êhwjf b Ëdjif fsyjwfhib|i ` b \=BFB FE EÌ =Bk f E wbh m `_Í ` s f_f f Î hjwf _fj ! i` E `t i ` cb_ ì wbyÅ jib 5 6 wbh m `hj`hd`t`hd`Ä ~b_ `j `t sy bÂ ì wbyÅ `hib|i ` ~ i ` J '( 6 5 wf i wbhd_v_jb `t b f i `ÆÉ Êhwjf J ' (Â # +Â bhi` wbh m `_Í j_v s f_f ! Ä E' J '( ( E P ' ( UM ì í ìø ñ õì e bcìd fcðîb gahðîbõ b þ Ò ÿþ ` ab cbd c üýþÿ ÿþ Ð þ Ñ Ò Ó MYU ➠ >FB B <@<=EH> ?@kE>D BkFE Ï Ø E Ù×Ø P>X G>?G[?E > <B?[RB CE?B u dbib i` { yjtjhfk¨ b i` Ú fg ii @Y [=@?@S>kFB AD>E<Y @@Y [=@?@S>kFB >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH G >?n>D@<HB< <@nk@G>=@QB< PH>k =EkFB B <@<=EH> k> BDFEH F>F>XY @@@Y [=@?@S>kFB >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH G >?n>D@<HB< <@nk@G>=@QB< E GBk FEk<>RB C@QB=>?Y PTX lB?B[E <E QEDF>FE@DB E o <E A>?HEk=BY BGBDDE EDDB FE >DDEFBkF>HEk=BY <EHCDE ABDkEGE > <B?[RB E]>=>Y MYM ➠o>SEkFB<E > =D@>kn[?>D@S>RB FE [H <@<=EH> FE BDFEH G CE?B u dbib i` { yjtjhfk¨ b i` Ú fg ii [=@?@S>kFB >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH >?n>D@<HB< <@nk@G>=@QB< E GBkFEk<>RB C@QB=>? BT=@QEHB< + G 2/ ÔÕ / ØØ ÕÖ » Ù + 2 +/ × / ÔÕÕ / / Ö / / + / / G / / 2 / G / G + / / + / / < / G / P>X l>?G[?E ÛÜÝ Y PTX l>?G[?E > @kQED<> FE Y PGX l>?G[?E > H>=D@S BD@n@k>?Y MY o>SEkFB<E > =D@>kn[?>D@S>RB FB <@<=EH> G / ÔÕÕ / ÕÕ + / Ö / 2 k¨ Ú 2 / G / / G / ii G / 2 / G / / 2 ÔÕ / ÕÖ 2 2 Ø Ù×Ø GBH / G / 2 / + / + / + / + / + / + E : G ØØ ×ØØ Ù CE?B u dbib i` { yjtjhf b i` fg GBH GBkFEk<>RB C@QB=>? E [=@?@S>kFB >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH >?n>D@<HB< <@nk@G>=@QB< BT=@QEHB< ÔÕÕ ÕÕ Ö 2 / / < W / W / / W G / + < / »» / < / + W + < / » + / + G + 2 + < + / / W + < / +/ ØØ ×ØØ Ù GBH 2 : 2 E F 2 U êëìíîïîðñò òñóíì Þðòcìd bò ßðø ìbíìò P>X l>?G[?E > <B?[RB FB <@<=EH>Y PTX o>> [H> E=>C> FE DEk>HEk=B FE <B?[RBY MY9 F>FB B <@<=EH> ?@kE>D ~ + ; +/ } 2 / { »/ » ; 2} ; » { < / 2 ; G} ; 2 { C?@G>kFB<E B u dbib i` { yjtjhfk¨ b i` Ú fg ii GBH GBkFEk<>RB C@QB=>? E >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH >?n>D@<HB< <@nk@G>=@QB< à H>=D@S FB <@<=EH> >G@H> BT=@QEHB< 2 G / 2 / ÔÕÕ / < + ØØ GBH G E : G G < Ö / Ù × GG / W G o>> [H> E=>C> FE DEk>HEk=B C>D=@kFB FE '5 }5 { 5 ( '/ W » + G » ( MY= ➠lBk<@FEDE B <En[@k=E <@<=EH> ~ G + ; G : ; : ; : ; F ; V G : ; V 2 'á á á V á : F ( [E =EH [H> k@G> <B?[RB Y P>X Z <@<=EH> <>=@<A>S B â_jd _jb i` afii `hc`yin H §4 £I A §¥Y PTX B<=DE [E > <E 8 «kG@> FE @=ED>F>< FB u dbib i` Ú fg ii|a`ji`y GBkQEDnEY MYD kQED=> > H>=D@S >T>@]B [<>kFB B u dbib i` { yjtjhfk¨ b i` Ú fg ii GBH GBkFEk<>RB C@QB=>? E M >?n>D@<HB< <@nk@G>=@QB<Y MYW Z <@<=EH> ?@kE>D BkFE ÔÕ + ÕÖ + » / »/ / < / / / / + / / / + / + ØØ Ù× 2 E / / ÔÕÕ + Ö // P>X <>=@<A>S B â_jd _jb ifi ã jh Å fi n H §4 £I A §¥Y PTX <>=@<A>S B â_jd _jb i` afii `hc`yi n H §4 £I A §¥Y Ø Ù×Ø + ÔÕ / ÕÖ / Ø Ù×Ø U9 ì í ìø ñ õì e bcìd fcðîb gahðîbõ b Z [E <E CBFE >DH>D F> GBkQEDn«kG@> FB u dbib i` Ú fg ii|a`ji`y EH P>X E EH PTXn MYq LE>H : / Õ Ô Ø ÔÕÕ / ØØ E ÕÖ : ÙØ :: :F Ö Ù × F / FF × F GBH ¬¬ 7 / ÛÜÝ ' ( 7 / Y lBk<@FEDE B <@<=EH> å Eå> <E 8 «kG@> 'äå ä:å äFå ( nED>F> CE?B u dbib i` Ú fg ii|a`ji`yY LE> æ ¬ä ä¬ ¬ BkFE ' : F ( \ > <B?[RB FB <@<=EH>Y DBQE [E P>X å å å ` ab cbd c x æ ä¬ : :F F æ ä¬ : R æ ä¬ : :: FF PTX $ç å ¬ | + E G <E E < <E R " + è é ä¬ PGX « [H E]EHC?B FE [H <@<=EH> ?@kE>D G ê G [E kRB <>=@<A>> B â_jd _jb i` afi| i `hc` y i H>< C>D> B [>? B u dbib i` Ú fg ii |a`ji` y <E> GBkQEDnEk=EY MYV >FB B <@<=EH> + / G + ÕÔÕ G + + Ö/ + Ø w ÕÔ Ø ÕÔ + Ø Ù×Ø ÕÖ : Ù×Ø ÕÖ Ù×Ø F + Ú ii P>X E<B?Q>B CBD { yjtjhfk¨ b i` fg GBH GBkFEk<>RB C@QB=>? [=@?@S>kFB >D@=H\ =@G> FE CBk=B ¼ [=[>k=E GBH G >?n>D@<HB< <@nk@G>=@QB< k> H>k=@<<>Y PTX E=EDH@kE > U GB?[k> F> @kQED<> F> H>=D@S FB< GBEG@Ek=E< § 4 £B£ë ¡ > =D@>kn[ ?>D@S>RB AE@=> kB @=EH P>XY MYU LE>H + + Õ Ô ÔÕÕ W + ØØ E ÕÖ µ Ù×ØØ Ö Ù× G 2 + W P>X E<B?Q> CE?B u dbib i` { yjtjhfk¨ b i` Ú fg ii GBH GBkFEk<>RB C@QB=>? E >D@=H\=@G> FE CBk=B ¼ [=[>k=E GBH >?n>D@<HB< <@nk@G>=@QB<Y PTX s <>kFB B ¤¥¤¡ ¤ 4 ¡ ¡ >G@H> G>?G[?E ÛÜÝ Y PGX ;]C?@[E >< <En[@k=E< >DH>E< @Y B CDBGE<HEk=B FE [H> <B?[RB >CDB]@H>F> BT=@F> CE?B u dbib i` { yjtjhfk¨ b i` Ú fg ii >< BCED>E< EkQB?Q@F>< kB G?G[?B FB< DE<F[B< FEQEH <ED AE@=>< GBH CDEG@<RB H>@BD FB [E > [=@?@S>F> kB< G?G[?B< DE<=>k=E< PCBD E]EHC?B F[C?>CDEG@<RBXY @@Y >D> DE<B?QED B <@<=EH> B DE<F[B \ GBkQED=@FB C>D> CDEG@<RB <@HC?E<Y x c r U= êëìíîïîðñò òñóíì Þðòcìd bò ßðø ìbíìò MYUU E<E><E DE<B?QED B <@<=EH> ?@kE>D 2 + ÔÕÕ G + Ö + + < ØØ w ÕÔÕ } ØØ ÕÔÕ / Ù× Ö { Ù× Ö + Ø Ù×Ø CE?B u dbib i` Ú fg ii|a`ji`yY L >TE<E [E > <B?[RB E<= kB G[TB G G ê G G ê G G Y ;<GB?o> [H Go[=E @k@G@>? E F@n> [>? B k HEDB FE @=ED>E< kEGE<<D@>< C>D> <E =ED GED=ES> [E B EDDB <ED HEkBD [E / / + Y H §4 £I A §¥Y MYUM E<B?Q> B <@<=EH> ?@kE>D >T>@]B CE?B u dbib i` { yjtjhfk¨ b i` Ú fg ii GBH GBkFEk<>RB C@QB=>? [<>kFB >D@=H\=@G> FE CBk=B ¼ [=[>k=E FE >?n>D@<HB< <@nk@G>=@QB<Y °4 ¥ £ ¡ ± k=E< FE @k@G@>D > >C?@G>RB FB H\=BFB QBG« FEQE C><<>D B< GBEG@Ek=E< k[H\ D@GB< FB <@<=EH> C>D> >?n>D@<HB< <@nk@G>=@QB<Y + ÔÕÕ + Ö MYU lBk<@FEDE B< <@<=EH>< ?@kE>DE< / » 2 + W / /» W / µµW Øw Ù×Ø ÔÕÕ Ö : F ~ 2 ; +} ; +{ W} ; +{ G + ; +} ; + W { 2 / W / 2 » Ø ÔÕ 22 Ù×Ø ÕÖ » µ Ø Ù×Ø ~ W ; } ; W { W} ; +{ G + ; +} ; + W { 2 E ' ( ZT<EDQE [E B <@<=EH> PMX AB@ BT=@FB FB <@<=EH> PUX <[T<=@=[@kFB<E > CD@HE@D> E[>RB FE PUX CE?> <BH> FE<=> GBH > ?=@H> E[>RB FE PUXY BD=>k=B E?E< <RB E[@Q>?Ek=E<Y y [EDEHB< EkGBk=D>D > <B?[RB FB <@<=EH> PUX PB[ PMXX [<>kFB B u dbib i` Ú fg ii | a`ji`y C>D=@kFB FE [H GED=B Go[=E @k@G@>? ]>FB '5 }5 { 5 ( FE ABDH> > BT=ED > HE?oBD CDEG@<RB CB<<QE? k> Q@n\<@H> @=ED>RBY [>? FB< FB@< <@<=EH>< FEQEHB< >C?@G>D B u dbib i` Ú fg ii|a`ji`y <En[kFB E<<E BTE=@QB n H §4 £I A §¥Y MYU9 B<=DE [E B <@<=EH> >T>@]B \ GBk<@<=Ek=E <E E <BHEk=E <E + B[ + [<>kFB B u dbib i` { yjtjhfk¨ b i` Ú fg iiY ' +( ~ ; } ; } ; G} ; } ; { ; G{ ; 2{ ; { + ; : 2 ' + ( MYU= >D> B< @=Ek< >T>@]B DE<CBkF> <E > >DH>RB AE@=> \ m `_ifi`j_f B[ cfyi f C §4 £I ¡ >=D>Q\< FE [H> CDBQ> B[ GBk=D>E]EHC?B P>X y [>kFB [<>HB< [H H\=BFB @=ED>=@QB C>D> FE=EDH@k>D [H k HEDB ! GBH [H> G>?G[?>FBD> GBH[H E >C< > U @=ED>RB B< Q>?BDE< BT=@FB< C><<>H > <E DECE=@D P : F X Ek=RB GED=>HEk=E ! Y UD ì í ìø ñ õì e bcìd fcðîb gahðîbõ b PTX KBFB <@<=EH> ?@kE>D [E <>=@<A>S B â_jd _jb i` afii `hc`yi =>HT\H <>=@<A>D B â _jd _jb if i ã jh Å f i Y PGX >FB [H <@<=EH> ?@kE>D <EHCDE E]@<=E [H> BDFEH C>D> >< E[>E< EH [E B <@<=EH> <>=@<A>S B â_jd _jb i` afii `hc`y iY PFX B u dbib i` { yjtjhfk¨ b i` Ú fg ii E kB @=ED>=@QB FE Ú fg ii|a`ji`y GBHE=EHB< EDDB FE =D[kG>HEk=BY MYUD P>X A[kRB ' { ( ` ab cbd c J '{ ( : : : :: CB<<[@ [H k@GB CBk=B ]B ! EH M Y B<=DE [E <E ìì ì ìì : : ììì " + :: Ek=RB > <E5å 8 «kG@> { ä å J '{ äå ( GBkQEDnE C>D> ! [>?[ED [E <E> B CBk=B @k@G@>? { ä E<GB?o@FBY PTX B <E DE<B?QED B <@<=EH> ?@kE>D x ; : } : ; :: } : CE?B u dbib åi` Úå fg ii|a`ji`y GBH >CDB]@H>RB @k@G@>? ' ä5å } ä5å ( BT=\H<E [H> <E 8 «kG@> ' ä } ä ( [E GBkQEDnE C>D> > <B?[RB FB <@<=EH> <BT GED=>< GBkF@E<Y B<=DE [E > 5å<E8 «kG@> äå GB@kG@FE GBH > <E 8 «kG@> FEk@F> kB @=EH P>X GBH Q>?BD @k@G@>? ä { ä5å Y UW êëìíîïîðñò òñóíì ñ e e í î üýþÿ ÿþ ï ï ð YU ➠/ LE> E ' ( E <E>H 5 '( '( : '( E F '( B< CB?@k ¯ H@B< FE IEnEkFDEy FE nD>[ + E G DE<CEG=@Q>HEk=EY B >CDB]@H>DHB< E kB @k=EDQ>?B + + CE?B CBD [H CB?@k ¯ H@B FE nD>[ Q BT=@QEHB< G ' ( / 5 '( ; ' ( ; / : '( < y + + B >CDB]@H>DHB< E kB @k=EDQ>?B CE?B CBD [H CB?@k ¯ H@B FE nD>[ Q G BT=@QEHB< '( 5 5 '( ; '( ; : : ' ( ; F F ' ( E=EDH@kE B Q>?BD FE 5 : E F Y >D> B< @=Ek< >T>@]B DE<CBkF> <E > >DH>RB AE@=> \ m `_ifi`j_f B[ cfyi f C §4 £I ¡ YM ➠>=D>Q\< FE [H> CDBQ> B[ GBk=D>E]EHC?B P>X lBk<@FEDE > A[kRB E ' ( ,-. ; G .Ü% ; W ,-. +/ CED@F@G> FE CEDBFB 1 Y xhv j i ` ñ f_t hjwf FE E >=\ B o>DH ¯ k@GB FE BDFEH q BT=E ;k=RB >B A>SEDHB< > y DEHB< ò '( ,-. ; G .Ü% Y PTX LE B CB?@k ¯ H@B 'ó ( óF ABD >CDB]@H>FB CE?B y EH + + CBD [H CB?@k ¯ H@B F> ABDH> ô 5 'ó ( õ ¬ ó : ¬ ¬ö5 Ek=RB B EDDB [>FD=@GB GBHE=@FB <ED k[?BY PGX B A>SEDHB< > xhvyji ` ñ f_t hjwf FE +E '( ,-.: . Ü% >=\ B o>DH ¯ k@GB FE + BDFEH G BT=EHB< > >CDB]@H>RB ò '( 2 .Ü% ; 2 .Ü% G Y > A[kRB E =>TE?>F> >T>@]B CBD [H> A[kRB F> ABDH> ò ' ( 5 ; ,-. ; Y CDB]@HE : . Ü% Y 1 1 ) 1 ) 1 E '( U M M U Y9 lBk<@FEDE B< <En[@k=E< CDBF[=B< @k=EDkB< P@X ÷ ø ù ú û ü '(ø '(ù '( þ BkFE ý '( \ [H> A[kRB GBk=k[> EH ý ý ' ( p / C>D> " " Y P@@X ÷ ø ù ú õ ¬ø '¬ (ù '¬( ¬ö ý | + ¯ BkFE ý ¬ p / E Q ¬ Q C>D> Y ÷ L E> ÿ ö5 [H> A>H?@> FE CB?@k H@B< BD=BnBk>@< DE?>=@Q>HEk=E > ú PkB G>X <E ô '( \ [H CB?@k ¯ H@B FE nD>[ " Ek=RB Y PTX <E '( \ [H CB?@k ¯ H@B FE nD>[ô Ek=RB ÷ô ô ` ab cbd c ÷ ô ú / ô ~û ü ' ' ÷ô ú p ( ( ô : þ ô ý õ ¬ '¬( : ú p ¬ö ý PGX <E '( \ [H CB?@k ¯ H@B÷ FEô nD>[ Ek=RB / <E " Y / ô ¬ ú / q | + ' ( / PFX '( =EH SEDB< DE>@< F@<=@k=B< kB @k=EDQ>?B kB G>?B [E GBk=\H ÿ kB G>@< DE?>=@Q>HEk=E >B CDB Y= ➠F[=B E=EDH@k>D ÷ @k=EDkB E ò ú û ' + : ( E ' ( ò '( þ E=EDH@k>D B< =D«< CD@HE@DB< CB?@k ¯ H@B< H ¯ k@GB< BD=BnBk>@< DE?>=@Q>HEk=E >B CDBF[=B YD @k=EDkB ÷ E ò ú õ E ' t(ò ' t( ö5 YW ➠ P>X EDE B< =D«< CD@HE@DB<CB?@k ¯÷H@B<BD=BnBk>@< H ¯ k@GB< EH DE?>RB >B CDBF[=B @k=EDkB û : 'ó ( 'ó ( ó : þ ó ú : : PTX ;kGBk=DE E FE ABDH> > H@k@H@S>D ' ( û : 'ó : ó ó : ( : ó : þ ó Yq ➠ P>X s <E B< CB?@k ¯ H@B< FE IEnEkFDE C>D> >CDB]@H>D E CE?B y kB @k=EDQ>?B + W CBD [H CB?@k ¯ H@B ¦ FE nD>[ HEkBD B[ @n[>? > FB@< BkFE ~ C>D> + Q ó Q G E 'ó ( + + C>D> G " ó Q W Y PTX l>?G[?E B EDDB [>FD=@GB GBHE=@FB >B [=@?@S>D =>? >CDB]@H>RBY Ê·ÁÀ¸ µÀ·¾ µ ¸À¶·¾ ¾È· ,Å´¼Á¼¾ ¶´¹· º¼½µ· »¼ µ ,À·½ å½,´ º¼µ ¶·¼Z ¶À¼¸º¼ ´¸Àº[½À· Ë UV êëìíîïîðñò òñóíì ñ e e í YV ➠o>H?@> kRB ?@kE>D kB< C>D HE=DB<Y P>X M = q UU U9 UW MW U = 99 E ' ( V 9 Yq qVYW qUY W 9 YV D qYW D9 Y 9 VY 99 Y VYU UYD <>D B y C>D> BT=ED [H> >CDB]@H>RB F> A[kRB =>TE?>F> CBD [H> A[kRB F> s A>H?@> @Y E ü? @@Y +) ' ; ( @@@Y ) ' ; ( PTX U M E '( U U UYW MY= <>D B y C>D> BT=ED [H> >CDB]@H>RB F> A[kRB =>TE?>F> CBD [H> A[kRB s D>G@Bk>? ; : ; YU P>X 0LE>H A[kE< FEk@F>< k[H DE= kn[?B 0 ê M : « CBk=B< FE F@<=@k=B< M > M } } CBk=B< FE =>HT\H F@<=@k=B< M > M E Y B<=DE [E ÷ « òú õ õ '¬ } ( ò '¬ } ( ¬ö ö ò 6 FEkE [H CDBF[=B @k=EDkB EH Y P;<=E CDBF[=B @k=EDkB CBFE <ED FEnEkED>FB XY PTX LE>H A[kE< FEk@F>< k[H DE= kn[?B ê þ @k=EnDQE@< M: EH ê þ E÷ Y B<=DE [E òú û ü û ' } ( ò ' } ( þ} þ ò 6 ÷ FEkE [H CDBF[=B @k=EDkB EH Y P;<=E CDBF[=B @k=EDkB CBFE <ED FEnEkED>FBXY B<=DE =>HT\H [E <E ABDEH GBk=k[>< EH ê þ Ek=RB ú \ kRB FEnEkED>FB EH Y L E>H E ' } ( [H> A[kRB FEk@F> k[H DE= kn[?B 0 ê YUU F@<=@k=B< M : CBk=B< FE 0 M > M E } } CBk=B< FE =>HT\H F@<=@k=B< M > MY \ F>F> [H> =>TE?> E ¬ E '¬ } ( + Q | Q + Q Q t @]>FB< S " E " t [EDEHB< >CDB]@H>D E<=> =>TE?> CBD [H CB?@k ¯ H@B FE F[>< Q>D@QE@< F> ABDH> o U ò U ' } ( õ õ̧ } ¸ ö5 ö5 ! 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Ü% 1 / / ¹ ö · CE?B ÷ y DE?>=@Q>HEk=E >B CDBF[=B @k=EDkB E ò ú û : E '( ò ' ( þ Pk?@<E >DH ¯ k@G> BHk@B GBk=k[BXY P>X CDE<Ek=E >< E]CDE<<E< C>D> <E G>?G[?>D B< GBEG@Ek=E< # / E # +Y H § 4 £ I A §¥Y / # + E [E <E E \ [H> A[kRB PTX B<=DE [E <E E\/[H> A[kRB C>D Ek=RB HC>D Ek=RB # / Y YUD o>> > k?@<E >DH ¯ k@G> F> A[kRB >T>@]B >=\ B o>DH ¯ k@GB FE BDFEH Y M U W D = 9 M U U M 9 = D W . 0 2 1 MM ` ì ab í cbd ìø c ñ õì e bc ì d fc ð î b gah ð î b õ b YUW k?@<E >DH ¯ k@G> P BHk@B F@<GDE=BXY L E> E CED@F@G> FE CEDBFB 1 Y L [CBko> [E E E<= =>TE?>F> kB< CBk=B< + CED=EkGEk=E< >B @k=EDQ>?B / 1 Y E<E><E >CDB]@H>D E CBD [H> A[kRB F> ABDH> U ò U '( 5 ; õ & ,-. ; . Ü% * ö 3 S " CE?B y DE?>=@Q>HEk=E >B CDBF[=B @k=EDkB ÷ : E ' ò ' Eòú õ ( ( ö P>X B<=DE [E ô : Ü% õ . . 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F>< F[>< >CDB]@H>E< \ HE?oBD n [<=@[EY PTX >F> > =>TE?> U M E ' ( U U U >CDB]@HE> CBD [H> DE=> CE?B y Y ;<=> HE<H> DE=> >[<=> CE?B y > =>TE?> U Y= U n E '( U U U >D> > =>TE?> U U M E '( U U U QBG« =EH GBkF@E< <EH A>SED B< G?G[?B< FE F>D @kABDH>E< <BTDE > DE=> [E HE?oBD > >CDB]@H> CE?B y n H §4 £I A §¥Y YUV B A>SEDHB< > >CDB]@H>RB FE [H> A[kRB E CBD [H CB?@k ¯ H@B F> ABDH> 4 5 4 5 5 ; ; : : ; F F ¯ o [=@?@S>kFB B y BT=EHB< [H CB?@k H@B FE nD>[ MY >SEkFB > >CDB]@H>RB FE E CBD [H CB?@k ¯ H@B F> ABDH> 5 ; ; : : ; F F ; V V BT=EDEHB< kBQ>HEk=E [H CB?@k ¯ H@B FE nD>[ M n H §4 £I A §¥Y ÷ >F> [H> A[kRB E =>TE?>F> EH = CBk=B< >C?@GB[<E B y C>D> >CDB]@H?> CBD[H/ YM CB?@k ¯ H@B ò FE nD>[ HEkBD B[ @n[>? > E BT=EQE<E [H> DE=> GBH E ò E ò ú Y ;k=RB E ' ( \ [H> DE=> n [<=@[EY YM U ➠l>?G[?E E DE>@< =>@< [E 4 4 5 5 E ' ( û : & + : * : þ : <E> Hk@HBY '( > >CDB]@H>RB BT=@F> C>D> E '( CBD [H CB?@k ¯ H@B FE nD>[ S [<>kFB B YM M LE> yòYUDBQE ÷ [E ÷ Q E ò U E ò U ú E òU E òU ú M9 ` ì ab í cbd ìø c ñ õì e bc ì d fc ð î b gah ð î b õ b YM >FB< P@X ÷ E<C>B QE=BD@>? <BTDE M Y P@@X ú CDBF[=B @k=EDkB EH Y P@@@X U ò 5 òU E U ò 5 ò U òU <[TE<C>B< QE=BD@>@< FE PkB=E [E U U ; M ò U XY P@QX E 6 Y ÷ ;k=RB <E U E U <RB >CDB]@H>E< =@H>< FE E DE?>=@Q>HEk=E > ú EH U E U DE<CEG=@Q>HEk=E =EHB<÷ ÷ + + + + + E U E U ú Q E U E U ú + k=EDCDE=E E<=E DE<[?=>FBY E E A[kE< DE>@< F@<=@k=>< kRB @FEk=@G>HEk=E k[?><Y Z [E FEQE >GBk=EGED >B YM9 <ELE>H =Ek=>D >CDB]@H>D E k[H @k=EDQ>?B CE?B y CBD ò ' ( 5 ' ( ; E ' ( 6 l>?G[?E 5 E B EDDB [>FD=@GB û ü E ' ( ò '( 8 : þ 7 YM = ➠B<=DE [E B< CB?@k ¯ H@B< + ÷ : F kRB <RB BD=BnBk>@< EH DE?>RB > E ò ú û ü E '( ò ' ( þ [>@<[ED [E <E>H E P p XY M= êëìíîïîðñò òñóíì øcìía ñhbù ñ üýþÿ ÿþ Ð þÿ Ò 9 YU E=EDH@kE B< Q>?BDE< FE '! ( C>D> B< [>@FBD F> =>TE?> ➠ U M 9 ¬ E '¬ ( U U ! : U= =EH nD>[ MY 9 YM L E>H 5 6 F@<=@k=B< M > M E <E> E [H> A[kRB GBk=k[> EH ➠ GBH FED@Q>F>< E P E PP E ä5åGBk=k[>< EH Y L E> ò ' ( B CB?@k ¯ H@B FE nD>[ Q < [E HE?oBD >CDB]@H> > =>TE?> 9 : ; < = > ? @ @A CE?B y Y B<=DE [E <E 9 @ 5 www E '5 ( E ' ( w w w B § 'E ò ( / Ek=RB 5 E ' 5 ( C ' ' ' E ' ( ò ' ( Q 5 ( ( w w w D ( E äI å '{ ( »E F G üH m i C Y >D> B< @=Ek< >T>@]B DE<CBkF> <E > >DH>RB AE@=> \ `_ifi`j_f B[ cfy f §4 £I ¡ >=D>Q\< FE [H> CDBQ> B[ GBk=D>E]EHC?B P>X '( W F ; + \ B CB?@k ¯ H@B @k=EDCB?>FBD FE U U M M Y ¬ E '¬ ( U = = PTX K>TE?>HB< E '( ; < + EH UU CBk=B< F@<=@k=B< M > M 5 www 5 Y E '5 ( E ' ( w w w E ' 5 ( ;k=RB >B >CDB]@H>DHB< E<<> =>TE?> CE?B y CBD [H CB?@k ¯ H@B FE nD>[ Q » GED=>HEk=E BT=EDEHB< [H CB?@k ¯ H@B FE nD>[ = Y PGX CDB]@H>HB< [H> A[kRB /E GBk=k[> CE?B y CBD [H CB?@k ¯ H@B FE nD>[ HEkBD B[ @n[>? > kB @k=EDQ>?B + E BT=@QEHB< EDDB [>FD=@GB @n[>? > SEDBY BFEHB< Ek=RB GBkG?[@D [E E \ [H CB?@k ¯ H@B FE nD>[ HEkBD B[ @n[>? > Y PFX LE [H CB?@k ¯ H@B ¦ FE nD>[ = \ =>TE?>FB EH U CBk=B< @n[>?HEk=E E<C>>FB< E <E § \ B CB?@k ¯ H@B @k=EDCB?>FBD F> =>TE?> BT=@F> Ek=RB B nD>[ FE § \ HEkBD B[ @n[>? > DY PEX LE [H CB?@k ¯ H@B ¦ FE nD>[ = \ =>TE?>FB EH = CBk=B< F@<=@k=B< E <E § \ B CB?@k ¯ H@B @k=EDCB?>FBD F> =>TE?> BT=@F> Ek=RB B nD>[ FE § \ = Y ±½½· ´ ,»½[ºÀ¶·Ë J KL M N O MD ` ì ab í cbd ìø c ñ õì e bc ì d fc ð î b gah ð î b õ b 9 Y9 lBk<En[@HB< > <En[@k=E =>TE?> FE [H> GED=> A[kRB E M 9 U Y } U MYW = YU99 U qWY9 M 9 qV MqM 9 YM V = D= y [EDEHB< [<>D @k=EDCB?>RB C>D> >CDB]@H>D B Q>?BD FE E '/ W( FE ABDH> > =ED > HEkBD >Q>?@>RB FE EDDB CB<<QE?Y L >TEkFB [E E \ GBk=k[> =EH FED@Q>F>< FE =BF>< >< BDFEk< å GBk=k[>< E <>=@<A>S E ä '( Q > C>D> =BFB 6 / 2 DE<B?Q> kB< E F« > HE?oBD >Q>?@>RB [E C[FED C>D> B EDDB GBHE=@FBY 9 Y= E=EDH@k>D B CB?@k ¯ H@B FE nD>[ Hk@HB [E C><<> CE?B< CBk=B< D U 9 Y } Uq D Mq = 9 YD =D>Q\< F> =>TE?> C>D> } . Ü% [E <E <En[E I UYM UY UY9 UY= UYD } YV M 9 YV D =D YV q =9= YV VW9 V YV VV = W EkGBk=DE GBDDE<CBkFEk=E > } / µµ » Y 9 YW H> =>TE?> FE <EkB< \ F>F> GBH >Dn[HEk=B< Q>D@>kFB FE nD>[ EH nD>[Y E?@H@=>D B s =EDHB GBHC?EHEk=>D C>D> CB?@k ¯ H@B< @k=EDCB?>FBDE< FE nD>[ + E G Y 9 Yq lBk<@FEDE > =>TE?> 5 www Y E '5( E ' ( w w w E ' ( P>X LE>H ò '( B CB?@k ¯ H@B @k=EDCB?>FBD FE E DE?>=@Q>HEk=E > 5 E '( B CB?@k ¯ H@B @k=EDCB?>FBDô FE E DE?>=@Q>HEk=E > : Y B<=DE [E ' ' ' ò' ' ( 5 ( ( ( ( 5 E 5 P K \ B CB?@k ¯ H@B @k=EDCB?>FBD FE DE?>=@Q>HEk=E > Y PTX s <>kFB B @=EH P>X BT=Eko> > ^ _tg yf i` èdbh C>D> > @k=EDCB?>RB CB?@kBH@>?Y MW êëìíîïîðñò òñóíì øcì íbù ñ üýþÿ ÿþ Ð þ ÿ Ò Ñ ÿ Ò = YU B<=DE [E [>kFB > DEnD> FE ajt s i bh \ >C?@G>F> C>D> ➠ 9 R Q : < S ? T U û : 3 . Ü% þ 5 B EDDB \ SEDB <E ><<[H@DHB< [E kRB oB[QE EDDB FE >DDEFBkF>HEk=BY >?E B HE<HB C>D> û 5 3 V: ,-. : þ 6 YM ➠l>?G[?>D û : ,-. þ 5 +; CE?> ADH[?> FB< _fs jbi E CE?> ADH[?> FE ajt s i bh GBH C><D B< =EDHB< GBHC?EHEk=>DE<Y = Y o>> > >k?@<E o>DH ¯ k@G> F> A[kRB =>TE?>F> kB< CBk=B< ➠ 1 1 ) 1 ) 1 E '( M U U M >=\ B =EDGE@DB o>DH ¯ k@GB G>?G[?>kFB >< @k=EnD>@< CE?B u dbib ibi _fs jbi E CE?B u dbib i` ajt s i bhY = Y9 =@?@SE > =>TE?> >T>@]B C>D> BT=ED [H Q>?BD >CDB]@H>FB F> DE> <BT > G[DQ> s M MYM MY MY9 MY= MYW E '( YW W YD W 9 YD = V YD 9= YD M YD V = Y= P>X « [H> GBkF@RB <[G@Ek=E C>D> [E B u dbib ib i _fs jb i <E> E]>=BY FEH C>D> B u dbib i` ajt s i bhY PTX LE> ~ : ; G ; + <E / Q " 2 <E ; G 2Q" E ' ( : <E Q"» » Q " + <E + <E + Q Q +2 1 y [>? B HE?oBD H\=BFB C>D> >CDB]@H>D = 3V û V 5 E '( þ 6 § £ §¥Y PGX ;<=@HE B EDDB GBHE=@FB C>D> B G?G[?B F> @k=EnD>? FB @=EH PTX >B <E [=@?@S>D B u dbib ibi _fs jbi E B u dbib i` ajt s i bh GBH +) Y H 4 IA Mq ` ì ab í cbd ìø c ñ õì e bc ì d fc ð î b gah ð î b õ b = YD lBk<@FEDE > A[kRB E ' ( >? Y CDB]@HE E kB @k=EDQ>?B CE?B y CBD [H ➠ CB?@k ¯ H@B FE nD>[ Q [<>kFB B< CB?@k ¯ H@B< FE IEnEkFDEY l>?G[?E >< @k=EnD>@< [E EkQB?Q>H E CE?B u dbib i` ajt s i bh GBH M DECE=@E<Y = YW L E> E [H> A[kRB GBk=k[> EH =>? [E E]@<=>H >< FED@Q>F>< E P E PP E PPP E E äVå E]@<=>H E<E>H" GBk=k[>< EH Y L E> '( B CB?@k ¯ H@B @k=EDCB?>FBD FE E EH 9 F CBk=B< 5 " : " F Y CDB]@H>HB< ü E ' ( þ CBD ü F '( þ Y B<=DE [E B EDDB GBHE=@FB <>=@<A>S W W B ' B Q ( E äVå '{ ( 2 F G üH = Yq LE> E ' ( ,-. 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B ' ( o E å '] ( ' 5 ( ' ( w w w ' ( ä ' ; +( E DH[?> FB< KD>C\S@B< DECE=@F> QESE< û ü E '( þ Ba o ] æ E '5 ( E 6 0 E '5 ( ; E ' ( ; w w w ; E ' ( ; E ' (` ' F E PP '] ( (F E PP '] ( ] 6 + + : ^ _ DH[?> FE L@HC<BH DECE=@F> QESE< û ü E '( þ Bb E '5 ( ; 2 E ' ( ; E ' ( ; 2 E ' ( ; w w w ; E ' ( ; 2 E ' ( ; E ' (` : F : : : : ' ] 6 E ä c å '] ( (V E ä c å '] ( »»/ µ/ ¯ é E '( 5 ; õ & ,-. 1 ; . ç% 1 * / / ö ^ G _ k?@<E >DH k@G> BkFE + 5 / û . E '( þ . + 1 / û . E ' ( ,-. / þ . + û . E ' ( . ç% 1 þ / / .

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