PQ R;'' $< 3I( LBA0 QQD4 $C 4 :'' '4 6( '- 4 "08'/'- 4 " ( 4 " - ' / PQ?$( , PBBB C $( ' 1 :( , (-''$ I9 M N56 PA A!R BR QQQ $ $' ( "'-XX ( $(, " I9 M - 1 '- '- - 1 N $ ( N " X X ( 9 $ 4 '4 NN 4 N 4 N 4 PQ ?"'' +) plantas vento luz parasitas GAFANHOTOS predadores umidade outros gafanhotos ,'2'-'- 4 P '4 AE 4 LD 4 DL 4 EA PQ?D;M(0 ' .3e4< )=&K5 ,- 4 '4 4 - 4 - 4 PQ%F?>($5 BB" 1 8 ' B " BA$1 '1' BL$'2 ( BD$ ( - ' )PQ?25 '6Y)6" 4 $( '4 $ ' 4 $ 4 $ ' 4 $-' ++ +PQ??R" 4 '4 '- 4 ' 4 4 , P Q%F ? " ' 0 8 ( 60 Luz CO2 O2 O2 CO2 Moluscos Zooplâncton Insetos Fitoplâncton Peixes Bactérias e fungos BB"(( - B ( 1 '/ BA, '0' BL$'( (9 BDV ' 0 09- 3LA4 . P Q D R $ KKKu KKKu KKKu $ ' 4 +00 '4 + 4 +00 4 + 4 , P Q?? R $ / ( 6 4 '4 4 4 4 +, P Q D R 6 $1 '6( 4 '4 4 4 4 PQ?D) Milho Galinha Porco Piolho Solitária Homem ,( 4 '4 _ 4 A_ 4 L_ 4 _A_ PQ%F?H' ;" 3!e 4 ' ' $(?0 V'0F , ( ' 5 '0-@1' 5R M/''< $+]$lIF) G BB"$8/e B = - BA, - BL,(1 BD" / ' ( +. PQ ?)92' - 4 3 2 1 , $( 4 +→→→'( '4 +→→→ 4 +→'→→ 4 +→→5→' 4 +→→→' PQ? D"9 $9' 4 - '4 2 4 4 - 4 ' )PQUD,'+) )A $9 AL0 4 '4 4 4 4 2 2 2 + P Q? D " 'C / ' ( $01 4 "/(18 '4 "/(1 4 "'C(18 4 "'C(1 4 "/'C1 , P Q? D " 'C 3)"A4 ( SEB A!E 34 QESL E QSALDB60 ABEB 5 EEB PEB * )"A(/CO 4 *'-.' '4 *$1C. ' 4 $ 4 =. 4 = 1C. ( .PQ%F?" 'G BB"/9(9'( B "(-/ BA$ ' - BL$ 1 1 '9 PQ?D> -F $ (( 4 ^- '4 =-'' 4 ,/ 4 ?' 4 ?-- P QD ?'0 / ( 6 4 '( '4 4 4 4 , PQDD"'1 CO2 3 1 VEGETAIS 2 ANIMAIS , 4 5 COMBUSTÍVEIS DECOMPOSITORES "2 E 4 ' '4 ' 4 ' 4 ' 4 ' PQ?2=' `1 ?' "'(( 9 ( ' $ ( ('92 $' ' ' '- N $''( ' ( ( ' N $' - *O 4 $N '4 $N 4 $NN 4 $NN 4 NN PQD "10' 0( / $ ( 4 '4 4 4 4 , $ + I ' ' $ PQ?$'/8 ' = ' 1(1 ' 4 = '4 =1 4 = 4 I ( 4 '9 )PQD"/( (9 (9,1?' '( :'(/ :'(/( :'(9C N :'(C 6 4 '4 N 4 N 4 4 N +PQ ??5 ,s Ms 6s s , '9 4 ,r(Mr6 '4 ,r6(Mr 4 ,r6(Mr 4 ,r(Mr6( 4 ,(M61 , , P QDF ;$ < " ( 5 0 ?'0 $ " '(1 + 5 N + 5 , )0 ' 4 '4 4 4 4 N N N .PQ?D63434 *( O n n n a. c. t I I II II I t n II e. t n I I II b. II d. t PQ?2"'8'/ t % de sobreviventes I 0 II III IV Tempo $ 1 10'-( 4 '4 4 4 4 N N PQ?D]?D" (6 , B " $(F.$2 11( BA "F .0 BL ,) ' BD ,=0 ' BE6 6 0 / ' PQ ?) 8 > ( $ 2 $ V?"M6,6 4 '4 4 4 4 P Q? D $ F N ABBB N5 ' 5 ( ( '- 0 '( 1-' 5 1 -5' G"I,$H=$$I=6A!KSKS! " ' F 6 '( / $ 5 / - 6 ( 4 '4 4 4 4 PQ RH11+' '9'('9 - ' H5 4 =C'( '4 X)X 4 ?'-'( 4 ?'- 4 ?'-1 P Q?2 M ' 0(6 ' $ - ' 0 0 4 '4 4 4 4 ) P Q R 6 ' 0 ' " - 4 ' '4 4 4 0 4 + P Q?D 2 i)-0'd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i* - 1 '- 4 $ (('C +PQ?,3434/ '( ( 1 " ' ) B " BA "/ BD "' BS "/( P "58 ' LA $'5 +PQ R$ ? 34( A + 342 L ? 34 D ) 34- 34 $ ( 4 0A0 0L0D '4 L0 0A0D0L 4 D0 0L0L0A 4 D0A0 0 0A 4 D0A0 0 0L +PQ?$ $8F )$ )F 34@ ' 34+/ A 346/ L 34Y D 1 34M ., $ ('$( 4 L0D0A0L0 '4 L0A0 0L0D 4 D0L0D0 0A 4 D0A0 0L0L 4 A0L0 0D0L .. +)PQDD) 1 N $ 4 $ '4 $ 4 "N- 4 $(( 4 $ 0 ++PQR=( 1' $'1 $ 5 ' (2 4 '4 A 4 L 4 D +,PQ?D"$F Adulto Esporos A Adulto Gametas B Embrião Adulto Embrião Gametas 4 '4 4 4 4 '(' ' '( +.PQ?D*-'O 4 '4 4 4 4 $1- " $1 6 ] ,PQ?DF,C/9 6 $F-3 4 4 $ 2 '4 $ 2 4 $ 4 $ 2 4 $ 2 ,PQ ?)' %"$ " '176( ? = = 6 4 '4 4 4 4 " ( "( $( 1 $(1 , , P QR " " 2 L 2 A D " A D 4 '4 4 4 4 $(( $( + +( $( , P Q?2 "' 0- )''0 4 '4 4 4 4 $L( $P(5! $ A(1'-' "- (( ""AD(E ,PQ?DF= $ $' 1'1 (9 +"I*>6 $ 51 0 (0 4 '4 4 4 4 $ (5 $ (5 $ ( $ ( $ ,PQ?D2) '0 4 V1' '4 )(1 4 )'' 2 4 ?' ( 4 )('9 ,)PQFF>;(<(1 -' 4 '4 4 4 4 C( C1 ,+PQ?D2$-3-49 9 ' - 4 '4 4 4 4 9 0 1,0 0,02 B A 0,5 0,01 1 5 10 15 Ovulação 20 25 Concetração de B (ug/ml) Concetração de A (ug/ml) ,,PQ?D" C Dias Menstruação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e '-(,)"II6" 4 '4 4 4 4 "(' $(( e((2 C(C D(2 ..PQD6 ABB 5'- ^ aJ J $0 aJ J ' $ BBABB $ ' 1- ) M : : : 4 '4 4 4 4 /( ('( /( /( ('/ PQ ?> = 2 0 '- N 4 '4 4 4 4 ( / 2F F 2 - F ) + , .F F ) +F , .? ) + , .F F ) + , . F ??? F )F + , . ?? F F )) + , .???? )?? ) ) ) ) ) )) )+ ), ). + +F +F +) + + +) ++ +, +. , , , , , , ,) ,+ ,, ,. .F . .F . .F .F .) .+?? .,F .. ) 2 E PQ FD] , 5 $3S A4 F3L P4 DEm PQDR] "9'( ($Fs3AD4)s3SD4 + 9 $ F(5 ) 4 §1 · ¨ , 0¸ ©2 ¹ '4 (1, 0 ) 4 §3 · ¨ , 0¸ ©2 ¹ 4 (2, 0) 4 §5 · ¨ , 0¸ ©2 ¹ 2A) PQ] , '0 $ F 3 A4 ) 3A L4 $ '"J"$ ( 4 '4 4 4 4 2A6 B L K A $($ 4 3EDr 27 4 '4 3PD4 4 SE4 4 3P 27 4 4 3PEr 27 4 2A$ PQDR] ?$s3K B4Fs3 B4)s34e4 (9 9$)( 4 '4 A 4 D 4 2 4 3 2AF PQ ?2] ) $ 3L 4 F 3 L4 " $ ( ( F 8JsA " ( $F(M3AA4 + $ 1 $F(Js N $9$ F))3LL4(A V 4 $( '4 $ 4 $ N 4 $ N 4 2A) )PQ D] ,$F)=( $9$3BB4( 4 30 '4 46 4 26 4 22 4 38 2A) +PQ?2] $ 9 ( 8 , 9 L4oDesBL4rDeo B sB( 4 BE '4 4 E 4 A 4 AE 2A= ,PQ FD] )9 9 Ar EJsPB$/ 9( 4 '4 A 4 L 4 D 4 E 2AF .PQ FD] , B J G Q J '? 0' P 4 's '4 'sKQ 4 'sKP 4 'srQ 4 'srP 2A6 PQ ?D] $ Js rLJsKLrA! J = , 4 DEE '4 DQE 4 EAE 4 EEE 4 ESE 2AF PQ?] , +3J4 ( / ? / 4 Dπ '4 Aπ 4 Pπ 4 Lπ 4 π 2A$ PQ?F] ?53 4 3LKA4 ? J s E ' 15 2 10 =− 3 3 = 2 10 = 3 15 = 2 4 x=− '4 x 4 x 4 x 4 x 2A= PQ?2] $ ;@+< $1 (AB` 4 * ( 9 L r DJsEBLrDJsAEO '4 * ( =O 4 * ( O 2A 4 E '4 =3! 4 4 s BB PQDD] , ' $ . 4 A '4 E 4 Q 4 S 4 P 2A) PQ?2] , !3PQ4(8 A r LJ s P ' 4 3 LB4 '4 § 35 · ¨ , 0¸ © 2 ¹ 4 3 SB4 4 § 39 · ¨ , 0¸ © 2 ¹ 4 3ALB4 2A= )PQ ?DD]. , $3 4 F3E 4 )3P L4 =3A L4 ( r : 3 x − 5 y − 11 = 0 $ 8 $F)= 4 LKEJKEsB '4 LKEJsB 4 PK BJK sB 4 QK EJKAsB 4 AKABJK sB 2A) +PQ?'%9 '"%D] , / λ 3BB4 rJs $ ' ( 4 π − 1 '4 4 4 2 π −1 4 π−2 2 π−2 4 4 πKA 2A= ,PQDD] $ / AKDr 3Jr 4AsB 4 3KA 4D '4 3AK 4A 4 3DK 4A 4 3K A4A 4 3AA4A 2AF .PQ?2] , / )3EL4 LrDJK AsB $ /( 4 ArJAK BKPJrAEsB '4 ArJAK BKPJrLPsB 4 ArJAK BKPJrDQsB 4 ArJAr BrPJr PsB 4 ArJAr BrPJrQsB 2A$ PQ DD] )$ s3K 4Fs3AA4 4 6 ( $ F '4 ?5 ) = 9 $F) S 2A 4 LrJsL '4 sKD PQ?2] )/ Ar JAs!$3J4 /( 4 AE '4 A 4 D 4 ! 4 AS 2AF PQ DD] ) 3AK4r 3A r 4J r S r D s B J (9 4 =9 J6 '4 )rLJr AsB s =$ " 6' / "$(9 2A 4 sA.3BKD4 '4 3rP4ArJAsLP⇔Ar ArJAsB PQUD] N-0( ( 1C ? / 6'' -0(5''8 ArJArArJr sB +' 8 ' 5'( ArJAK AKLJr sB $9 ( 4 2( 2 − 1) '4 A 4 2 2 4 2 − 2 4 5 2A$ PQ?F] + J s r L 5 8 / A K S r JA s Q 4 '4 4 4 4 3 5 4 3 8 5 5 3 9 4 2AF PQ?2] , I ? 8' JsA $3BL4 F3DB4 $'I?( 4 KBDE '4 KBEE 4 KBPE 4 KB!E 4 KBSE 2A= )PQ?] > 5 AA S AB P ' " ' + 9 -( 4 L '4 D 4 E 4 P 2A) +PQ ?2] $ $ F ( 4 ArAJAKPKSJsQ '4 ArAJAKPKSJsKQ 4 ArAJAKPrSJsKQ 4 ArAJArPKSJsKQ 4 AArJAKSKPJsQ 2AF ,PQ?2] ? 3KA4ArD3Jr E4AsLPJ r ( 4 S '4 ! 4 P 4 D 4 L 2A) .PQ] $ 5 ( x 2 y2 + = 1 ( $ s 'π a 2 b2 6 PA r AEJA s DBB PArQJAs DD( 4 Aπ '4 ABπ 4 Sπ 4 AEPπ 4 π 2A) PQD] ?' C A r DJA s Q '( 9( B 0 BA $ C '3LB43KLB4 BD ?$FC = 6 C 9 $=6 F=6 BS $ / 2 C P " §¨ 2 © 2, 1· ¸ 8C 2¹ 2AAL PQ%"<'F] $- + +A B '- 1 f ( x ) = ( x − 3) 2 + 5 9 ) ' 0 0 B $ 9 ( P BA $9( B BL + +A / P B BD " - !+A BE " - 10 m 9+ 2ABD PQD] $ ( ArJAs AKJAs '( 9( B $ ' BA $ (' BD " BS " C A K JA s ' P $ K J r A s B ArJAs 2AAP PQ?] > '- 5 R 2 @RR' ?'0- 1 1 1 ''- ) ' $ 4 NN '4 NN 4 N 4 4 N 2A6 PQ FR] $ 34 ArLJKPsBAJKLKAsB 34 (3J4 "JAArPJKLJAsQ( 34 r 'J r s B ' 's B 34 JsAJs x "J2 @&&&' ) 5 ' x = y2 12 ( ' 5 R ' ) ' 1 1( 3BL4 91( ( ' 5 R ( A 3 4 1 1( 3LB4 N 1(0P N 9 1 ( ( ' 5 R(L 3 4 (1, 2 ) 2 ( 34 8 /ArJAs (8 /ArJAsA $ 2 4 B '4 4 A 4 L 4 D 2A) PQDF] ?∈Is − 1 ( x = 5 cos t ® ¯ y = isent 4 '4 4 4 4 2A6 = >/ >'( = >(' ^DC PQ DD] " - 2 1 s AB D K QS!( 4 2 '4 B 4 3 4 2A$ PQ?2] ) C +34sDrLr'Arr '0+3A4s+3Ar4sBAsK , r'rr( 4 '4 4 4 4 KA K P S Q 2A6 PQ] ?J20 - 2 z = x − iy ( x + iy 4 '4 A 4 A_JA 4 J 2A$ PQ DD] ) 2 AsK 6Br rArLrerAB L 4 B '4 4 4 r 2A= ?521 sAK!1A s r E 1L s K r L " 2 31 r1Ar1L4A(O 4 '4 4 4 4 I ? * + PQ%"<5D] ) ' 2 2A6 )PQ?F] ?21 s r L 1A s K K L ( - 2AN-s 40 5 π u.v. +PQUD] I0 $F)(9 2 1 1A1L12'S 1 s A ) ' 4 3KA B4 ( ( 9 '4 1A(51 4 1AsK1L 4 1Ar1LsKA 4 K1 s1A 2A= ,PQ?F] ?1 1A 1A K A1 r D s B z1 z 2 + z 2 z1 ( PQ?2] ,$07 $F)= 2 ]B] ]A]L]D]E 4 K '4 − i 3 4 B 4 i 3 4 ) 2A$ .PQ 2] ) 1 1A 2 1 2 + x = −2 , ( x 1 r1A 4 '4 A 4 D 4 L 2AF PQ?22] )'C344s4DKAE 4 45 2344tB. '4 344/ C. 4 0 2 5(1344 2A 4 − 5 < x < 5 '4 @0 '(0 2 8 1 ( 52 4 $ (1C( B ? ]B 2 ( / $F)= 2 ( 4 ] '4 ]A 4 ]L 4 ]D 4 ]E 2AF PQ?F] ? z ⋅ (1 + i 3 ) 21 ( 4 E '4 !E 4 PE 4 AAE 4 LDE 2A6 PQ?F] "2111Ss P r1r1Ar1Lrer1!sKPKL( 4 1s 2 '4 1sK K 4 1sK r 4 1s K 4 1s 2A) PQD] ,'( 2 3 $ K 7 9 / )0 B r = 3 2 ) ( 2 z c = cos 4π + isen 4π 3 BA r=2 3 3 ) ( 2 z c = cos 7π + isen 7π 6 BL r=2 3 ) ( 2 z c BD r= 3 = cos 5π 5π + isen 3 3 )(2 z c = cos BE 6 11π 11π + isen 6 6 r= 2 ) ( 2 -A 2ABD +PQD2D] )211 r z K sL?'1 ?9(B( D 3 5( 4 − 4 2 − 4 2 i '4 − 4 2 + 4 2 i 4 − 4 2 i 4 4 2 i 4 4 2 2A= PQDD] ( 2]]rL ⋅]s A 2A/ L )PQ%"<'F] ?'0 2 π π· § z1 = 2¨ cos + isen ¸ 6 6¹ © 3π 3π · § z 2 = 2¨ cos + isen ¸ 2 2 ¹ © ( π 3 B 1sD BA 1AsKSrS 3i BD 1K z sD 3i BS "1L(π P 1⋅ z (2 2AL ,PQ?F] ?521 sDBmr ⋅DBm1AsDBmK⋅DBm " 2 1 ⋅1A ( 4 Bm '4 ABm 4 DBm 4 SBm 4 PBm 2A$ .PQ ?DD] ,$0734 $(21s rJ5-314( + OA 5 3θ4(9 OA 0 I 314 " 2 1 s ( ;< 4 4 4 =2 1s3rA4D(2 '4 ? 1 2 1 ( 1B 5 ( 3B 4 u B 1 2A$ D ` HSM2IF PQ FD] $ ' C +34 Em 21 2A 4 "2BA0A '4 D PQ?22] )C34sLKQArAE0 AE?'021s Ar ( 1 9 5 ( 1 4 '4 " 2 1 C *34 *34sAK+34( 4 4 '4 4 4 4 2A) A L D E , PQDD] "CArr'(rA K "K'( 4 '4 4 4 4 B A L D )PQ DD] )C34sAK r#r A ( # 9'( 4 +9# 34K ( LO '4 ?#sD' '134 2A= §π π· sen ¨ + ¸ ©a b¹ PQ?D] "'C34s LrAr'r?'K r α α u B 1 34sB34 3K 4(S 4 α. '4 343r 4 (AsK 2A 4 αsA '4 AKArE 2A 4 #s '4 1 − 2 +PQ?] , 34sLr'Arr ?'34(34sAK Q3D4 PQD'(D("9W'%"'] " C D KLL r !AKrDAKAr ( 4 '4 4 4 4 DA D S Sr SK 2A) PQ?RD] "C+ 34s3r 4⋅3Ar 4⋅3Lr 4⋅ e⋅3 BBr 4+A34sA r r *34 I34?*34 + 34 r( 4 '4 4 4 4 2A$ EBDQ E AEAP EBE B 4 '4 4 4 2A= , ( 1 E LA AS . ,PQ?D] )C34sDr 4 $134 '4 6 34 C 2A 4 '4 .PQ?2] =0'C+34s3r 4E 1 ( 4 P '4 AD 4 LA 4 DB 4 DS 2A) PQDD] $ LKLArDKAsB 1?1 4 (1 + 3 ⋅ i ) (1 − 3 ⋅ i ) '4 3 r43 K4 4 3Ar43AK4 4 3K r43K K4 4 (− 1 + 3 ⋅ i ) (− 1 − 3 ⋅ i ) 2AF PQ ?2] > C 1 L J L , C( 4 34sKLrLAKrL '4 34sLrLAKrL 4 34sKLrLAKKL 4 34sKLLrLAKrL 4 34sKLrLAKLrL 2A$ PQ?D] " C 344 s 4D r 4L r 4A r 4 K S 2 2 r 1 ' 1( 4 =1344 '4 ?' 1 344 C 1 2A 4 s0A's0AsS134 A0A r 0 '4 34s#⋅30 43rL43Ar 4.#∈ Ig PQ?2] >C34sAr' r12AK E63'r4( 4 E '4 LL 4 AE 4 AA 4 2A) PQ DD] " C 34 s L K AA K Q r S /1K 4 = '4 ) 314 1 s r ( 2A 4 sDs±L '4 314s!K PQDD] ?'0 LrDArKPs B1(8 "5 3?4 ( 4 ?sKLKAK '4 ?sKLKAr 4 ?sr rArL 4 ?sK rArL 4 ?sKAr rL 2AF )PQUD] ?αβγ1 LrA r r s B α s K A ( 1 α⋅β⋅γ( 4 E '4 Q 4 K E 4 K A 4 KQ 2A) +PQ?2] ? 1 A K A# r LP s B # ( ( 4 9 1 ( 4 4 + 3 7 '4 8 + 2 7 4 D 4 6 + 4 6 4 8 + 4 6 2AF ,PQ?F] ? ( ( 1 C 34 s AA r r E ! 134sLArKAA3 4(( 1C34r34 4 D '4 DE 4 E 4 SE 4 Q 2A$ .PQ?2] $ AL K LA K L r A s B 5 K ' +Ar'A( 4 13 '4 4 4 7 2 15 4 4 D 4 17 4 2A6 PQDD] > C +34 K *34 A * C ( K A *34L+ *3 4r*3A4( 4 '4 B 4 KA 4 K 4 A 2A6 RI PQ?D] $(8 2 , '(O 4 *52 ' ( a + b = a + b '4 *52 'AK'AsB( s' 4 * 5 2 ( a 2 = a 4 *52 ' t ' ( R't R 4 * 5 2 Bt (At a 2A6 PQ ?] G ' > '' ' , 8 ' 4 !R A '4 ER A 4 !RAD 4 ERAD 4 !RP 2A) PQ ?] ) 5 E 2 2 3 2 53*K,4)∪]O 4 2 '4 B 4 K 4 π 4 A L 2A6 PQ?F] ?5,]*I52 = 7s ∈ ] 90 n ∈ , @ s ∈ * A∈]=s∈I x ∈*( 4 @∩=⊂, '4 @∩](51 4 2 ∈3=K*4 4 7∪=⊂@ 4 7∩@∩=A 2A6 PQD] $'( 9( B BA BD BS §1 1· 1 2¨ − ¸ = © 2 3¹ 3 3 > 2 2 1 = 0,01010101 ... 90 15 7 3 80 4 3 TADU P $ 2 2 2ABL )PQ?R?2] =0 T'U U'T U'U T'T 3' K 4 = MsTL BU,sUP DT+sTE AT 3M∩+4∪3+K,4( 4 '4 L 4 E 4 ! 4 Q 2A) +PQ?22] , I':q# ( ! : ! 0 $ 50s( ! : D s ! 0 : s 0 ! : '( ' - 5 =0 5 3$∩F4) K ) 4 '(' '4 '(- 4 ' 4 ' - 4 5 2A$ ,PQ ?2] = EB ) ,:' E-AE , - = 4 Q '4 B 4 DB 4 AA 4 L 2A$ .PQ?D] , @ • N/O • N/1( 2'O ) ' 60N , • >(5. • $ ( 5 . • +(51 ( 2' = 2 ;?< 8 2 ;,< 8 4 '4 4 4 4 !S PA !SDS QBPB QBA B !DA!B 2AF PQ?F] EBB ' Y n ] = DB AABY !Bn SBYn ) ' 0 4 !B] '4 B] 4 EB] 4 QB] 4 ( ] 2A) PQDR] > *1 AB AA * O 4 E '4 L 4 AA 4 AB 4 A 2AF PQ ?2] " SBB 3M4 3@4 3*4 $ ' Disciplina M F Q M e F F e Q M e Q M, F e Q Número de 400 1220 1080 220 800 180 100 estudantes + ( '( 9( 2 / ( 4 BB '4 ABB 4 QBB 4 ABB 4 PEB 2AF PQ?] > 2 ' 0AE` 0 !`' 0 E` ' 0 S`2 , 0 * ) >YQ \\Q * ) ' 0 * ' ) PZQ $'( 9 4 $ '4 $ 4 $ 4 , 2A$ PQ?] ?' 5 ' $s4∈3gR4tABB Fs4∈0R4(2S )s4∈0R4(2L 5 # D6MN 5 # d\ 5 # 7 Z R YNN R N 0 06DRLdM $'( 9 4 '4 4 4 2A) $ $ ( $ PQD2D] ?'5$sALEFsLD )$∩)sAF∩)sD$∪F∪ )s ALDE B $∩F∩)s∅ BA )KFs A BD )K$sLE BS L∈) P 3$∩F4∪)s AE 2ABL ?SM2IF PQ?F] >Y'P ( IDBBB " n ' IEBB ( ' E ) ' - 5 nY 4 '4 4 4 4 AAB( AAB( LAB( LAB( DDB( DB LAB ADB LAB ADB 2A) PQ?2] > ' I Q SBBBB IDEBB) ( I PEBB ?5 1 5AB`$ ( 4 '4 4 4 4 2A= A L D E P PQ ?D] " N - $ F N$34sABBrLNF34sEBBBKL = - 4 sEBB '4 sPBB 4 s!BB 4 sSBB 4 sQBB 2A= PQ FD] + 1 9$ J ( ) B BB ' ( = $ EB = F 5 EB $5'' ' ($ F( 4 '4 4 4 2A= 4 PQDD] $ 34 s r ' ( 0 ?'034sA'3'4sA "3L4( 4 A '4 D 4 KA 4 B 4 K 2A) )PQ?2] > / $ ( 0 ' ( sKBDrABB?5# #A 2 ( IA BBBBB"# r#A( 4 DEB '4 EBB 4 EEB 4 PBB 4 PEB 2AF +PQ DD] "/ (' + ( B2' ( AB + ( AB D 2' B 2' ) 34 2' 4 6' 34 BLB ) + '4 +D 2' ( 2'O 6 AE 2'O 2A 4 4 634≠3AA4 f ( 2 ) = 2 O 2A 4 f ( 2 ) = 2 22++22 f ( 2 ) = 2 22++22 ⋅ = 2 −2 2 −2 4−4 2 +2 2 −4 −2 = ( 2 ) = − −2 22 f ( 2 )= 2 f '4 3K B43B 4 4 '4 I E 2' I LAB 2' ,PQ?D] = m f (x) = 2 − x+n ≠K 4 ,ssA f ( 2 ) = 2 '4 , s s A 4 , s s A ' u KA ' 4 '4 >1 ' 4 .PQ?'%9 '"%D] $ / +"A ( / ( $ +"A 1 = EB +"A B` +"A : 4 SELE '4 QPAE 4 EQQE 4 !QSE 4 QS E 2AF PQ?D] " 8 I @ ( ' ' " ( OA, AB, BC, CD DE G ' I DLSBBBB + ' I BBBBB $ PQDD] ?1 AAKEKDsB 1 + 1 ( m n 4 '4 4 4 4 5 4 3 − 2 3 4 7 4 5 2 − , 2A$ PQDD] $ x + 3 3x + 1 = x −1 x+3 2 4 '4 4 4 4 2A6 PQ?2] " 2 ( 1 A DKALKLArr's B"⋅'( 4 '4 4 4 4 KS KD KLA K P KPD 2A) 4 '4 4 4 4 2A) I BBBB IABBBB IAAEBB IDEBBB IPBBBB PQ?2] "5 3AK D4A⋅ 3LJKQ4Ls BSJ 3 J4 ? ( 4 '4 4 4 4 2A) B A D S PQ?2] 6 (IDBBBB "?G !S (AA" ?G( 4 '4 4 4 4 I I I I I BAPBBBB BL!BBBB BDSBBBB BEQBBBB B!BBBBB 2AF )PQ ?] , ' ( ' 5 ( J s r ' r + ' ' ' ' 4 '4 4 4 4 2A= +PQR] " ' $F')34 $(F3LB4 " 9 ) ( DE " $F 4 E '4 P 4 3 5 4 6 2 2A) ,PQ D] 6 2 - -JsKArPBr BBsB( $- 2 2 - 2 ( " 2 ( 5 2 ( 4 LL '4 L 4 LD 4 LP 4 LS 2AF .PQ ?D] $ '' @ 5-'/ ' ( 9 1X sKB Ar A r AE = ' . 4 '4 4 4 4 P '4 PL 4 !A 4 !E 4 SL 2A$ PQ?'" "9(!( ('AD] " 34 s A r ' r B ≤ × ≤ D 9!× D 1 <m≤ 4 1 m< 2 1 m>− 2 1 − ≤m≤ 2 − 1 4 1 2 4 ≠B 2A6 PQ] $1 AK ErPsKL( 4 '4 4 4 4 B ! B L D 2A6 PQ%"5#] = ( x 2 + 20) =| x + 1 | +3 ∈I1( "'( 4 K! '4 KD 4 A 4 D 4 ! 2A6 PQ?D] 6 ( 10 AA K A3 K 4 K s B - 2$ 9 0 1 4 '4 4 4 4 KA KL KE KD KP 2A$ PQ?RD] ) x, se x ≥ 0 | x |= ® ¯− x, se x < 0 ( 2 = ( 5 2 § · 2 ¨ | x | + | x | + | x | + | x | + ¸ = 5 5 + 1 ¨ ¸ 5 5 5 5 © ¹ ( ) 4 '4 4 4 4 2A= UKππAU UK π πLT UKπL π T UKAπAπU UKπAπT PQ] "5 34 sr KK ( 4 TKAAU '4 UK∞AU 4 TBAU 4 TBr∞T 4 UBAU 2A) )PQ?2] ?5 # 2 JsJsK r# P , #( 4 4 2 '4 6 2 4 S 4 7 2 4 B 2A$ +PQ DD] ) 34 s A r r 4 $'34 = '4 ?sKL 1 34s A 2A 4 s− '4 sE ,PQ FD] $ )344 " 2 5 )344s I( 4 P '4 E 4 D 4 L 4 A 2AF .PQ] = I→I 34 s AKPrE22JB / 2 A L0 3 4s3A4s3L4s JB, rA rL( 4 P '4 ! 4 S 4 Q 2A= PQD] = ' )344sr AKAKEttE( 4 '4 4 4 4 4 2A) PQ?] $ 34 s r LK r 1 ' 8 4 tKL '4 KLttL 4 uL 4 tA 4 uKA 2A6 PQ?2] ) 34s K $ 4 '4 4 2AF PQ?]. " 2 4 1 3 x − 3 ≤ 6 5 4 ( '4 (2 3 4 (' 4 ( 4 ( ]−∞ , 2[ 2A6 PQF]. ?' 50 x − 2 − 2 x − 1 = −1 x ∈ R 0( 5 B 1 BA BL BD/ BE 2ABL PQ? D], ?5 f(x) = | x + 2 | e g(x) = 2 | x − 2 | 4 I f (x) = g(x) '4 ) h(x) =| x + 2 | −2 | x − 2 | 2A 4 3&&&'4 2 ½ V = ® , 6¾ ¯3 ¿ '4 )PQDD] ?3D4As P⋅A x ( 4 A! '4 D 4 1 2 4 4 4 − 1 27 2AF +PQDD] 5'+% 1' ! / C - C). J 5 YNLY ) YYL UT 'LR\UT 6\QLNQ*'YNNR ) ( 9 -' A≈BPQL≈ BE≈ P Q≈AQD ( 8 ' AB A 4 ABASAB Q '4 ABPSABDB 4 ABAAAB ! 4 ABAEAB S 4 ABE!ABAQ 2AF ,PQDD] ? 3 n +3 − 3.3 n −1 3.3 n + 2 '(0 4 3 n +1 − 1 9 '4 KLrA 4 L 4 26 4 27 16 9 2A= .PQ?2] ) A s BL V 1 AAKP⋅ArEsB( "γ' ( 4 7 3 '4 A 4 4 5 3 4 3 4 '4 BAD 4 B! 4 B D 4 D 4 2A$ PQ?D] > 11 SE m) 6 PE m) ? 11 ) s PB×AKBS× rAE * 11 O 4 BAE '4 BPS 4 AE 4 PPL 4 BB 2A) PQ?RD] ) ' ( +Nγ s # + ( N(9#γ " 0 / '- ' 2A6 PQ ?2] $ F 5 AB L ' 2' 2 '8 ) 8 ! BB 2 8 2 8 A ( 4 ABB '4 A!BB 4 ADLBB 4 S BB 4 ABBB 2A= PQ FD] $ / 3*4 3+4 *s rD⋅3BS4A+ , 6 ( + * = + ' Q −1 4 4 P = log 0,8 '4 § Q −1· P = log 0,8 ¨ ¸ © 8 ¹ ' 6 BB '- Q −1 4 4 P = 0,5 ⋅ 0,8 4 P = 0 ,8 4 §Q · P = 0,5 ⋅ log 0,8 ¨ − 1¸ ©4 ¹ Q −1 8 2A$ PQUD] ? I→I(34s LK '( 4 =34sI34sI '4 ( 4 (5'5 4 (5('5 4 34sIgr 2A) PQ?2] >B#5IDBBBBBB 9Ns' A ?EIAB BBBBB A 4 I QABBBB '4 I !PBBBB 4 I!PBBBB 4 IEABBBB 4 IDSABBB 2A) )PQ DD] $ - ' 2' LABBBB A ' 6 ( ' = )- @ ( - ^ + +3$++4 4 ) $++ '4 ? - N34 s NBAK NB ( ( *( 1 B` O >1 BA≈BLB 2A 4 3ADrπ4× BDA '4 ≈L B +PQD'(D("9W'%"'] ?' ' 2 1 2 log 1 a = log 1 b = 16 3 5 16 6 log 2 §¨ a 3 ⋅ 4 b 5 ·¸ ( © ¹ 4 P '4 E 4 KE 4 KP 4 K! 2A= ,PQ%"'9(D] " : ( :_ 6:sK T:_U>6M( :sL ( ' 1 C ' C : s 4 :_ C ( BB 1 '4 :_ C ( BBB 1 4 1 :_ ( BBB1 C 4 1 :_ ( L 1 C 4 :_ C(L1 2A$ .PQUD] " 5 2 § x 2 + 5x + 4 · ¸ f ( x ) = log x +5 ¨¨ 2 ¸ © x −1 ¹ ( 4 I '4 ∈IR≤KE≥ 4 ∈IR≤KEu 4 ∈IRKPt≤KE≥ 4 ∈IRKEttKDu 2A6 PQ%"<'F] )0 W 2 ( + s 3AA43DA43SA4e3 log 2n 2 4∈] *+ ( B W BA AW BL BD BE 1 n! 1 ( n − 1)! 1 2 n! 2ABL PQD'(D("9W'%"'] V A3r 4rA3KA4sA 4 '4 A 5 (B 4 A 5 ( 4 A 5 ( 4 2A6 PQ?D] ?' 3rL4 2 x −9 ArK s B( 4 1 '4 21(KL 4 1LKL 4 21KLB 4 1 2A6 PQDD] ? r Ar L r D s KAB ( 4 B '4 B 4 BB 4 BB 4 2A= PQ?F] $ AAKAQs 7 3log 2 2 7 ) 4 sKDS '4 sKA! 4 sA! 4 sLP 4 sDS 2A6 PQ FD] $ 34 s 3 A4K ) ' A3E4KA3L4 ( 4 BEB '4 B!E 4 BB 4 AE 4 EB 2AF )PQ FD] "2 D!K P!sB ( 4 '4 A 4 L 4 D 4 E 2AF +PQ?'!"@%'"!&!!F 9( D] "5:1!' AB L ?AB LABPB ' 8 M34s S⋅KBA )M34 s AB LsAABAP $AsB!Ls Es P sAD( MS 4 ABD! '4 ABEP 4 ABEA 4 ABDE 4 ABEQ 2A) ,PQ?D] " 2 , - ,34 s ,B Kλ ,B 2-sB λ$' B, ' ( QQ 3QQ41- + '4 4 , 4 $ 4 B,B. '4 2,B QQ . 4 03 RA4QQ (9!(9 $03 RA4- ( 2 - BAsBL. BEsB! 2A 4 B,BsP '4 ,Bs BP 4 RAsP .PQ ?] " 34s$3 KK#4≥B $#(1 1 / '1 8 / / " 34( 4 4 2A$ )PQ?D] > ? 0( (2 4 log 4 3h + 6 2 '4 3h + 4 log 4 2 4 3h + 2 log 4 2 4 3h + 2 log 4 4 4 3 h +1 log 4 2 2A) )PQFF] $ ' F ( / FB - § B M = log a ¨¨ © B0 B3A4 ≈ BLB B3L4 ≈ BDS B3E4 ≈ B!B · ¸ ; ¸ ¹ E' ( BB< , 0 A s BLB L s BDS 0 HFs A × BEFB( B K AQ BA K A! BL K AE BD K AL BE K A 2ABA )PQ DD] > ' 6 1 ' $ ' 13m)4 +34s⋅ B' ' $ ' ' ' H Temperatura Perda anual de (º C) 0 capacidade (%) 1,6 55 20,0 )'+34 ' 4 '' +34 ' sBsEE. '4 ' '? . 2A 4 '4 s P'sBBA )PQD] , I '53G4 6 s DD r EM 6 AB G QB I6' 4 T L DU '4 T ! SU 4 T B L B DU 4 T B ! B SU 4 T BEL BEDU 2A= )PQ?2] ?' '2 '( C 3(e[4e ( 2 '( 4 4 2' ? '( 2 5AB O>'' x log x 1 2 3 4 5 0 0,30 0,48 0,60 0,70 4 D '4 DL 4 DE 4 D! 4 DQ 2AF C-P($1$T0196(-) + 1 ' C +34 J s +34 & , ( 10 ' KE ( A! )PQF] "21 +34s TKEA!U( B 4 P BA4 E BL4 D BD4 L BE4 A 2ABA C-P($1$T0196(-)) > AB` " 5 1AB`$ 2 I BBBBBBB - ( 2s BBBBB⋅3BS4 "L ))PQ FD] + AE` ) A s BLB 4 L- '4 D- 4 P- 4 S- 4 B- 2A) C-P($1$T0196(-)+ , / ' ' " ' 3,434 ) 2 / ' EBBB' )+PQ FD] ? ,34 ' ' AS / A m 4 L AE '4 AEBB 4 S!E 4 AEB 4 PAE 2A= C-P($1$T019=-),L).L+ = K $ F K 1 ' ? ( $ ' F 6 RH $ F C,Cs L!m)CsAL!Dm)CsLL!Sm) 1 BD m) " $ ( ' s K S3C K 4 3C K 4 ≤ C ≤ F( RH $ 4 '4 4 4 BB B B AB AB BB 2A) ).PQ?] ? $ PSRH3t PS4'3:4 m) 4 '4 4 4 L!≤:tLQLQDtC≤D LS≤:tDBP LSt:tDB L!≤:tLSPLQStC≤D 2A= +PQ?] * $F ' ( 4 '4 4 4 LQAm) LSPm) LSm) DBm) 2A= D2M I 2I PQ DD] " 9 9 ( PB ( 3+$4 $ 9( ),PQ?] $ 0L!Sm)' 4 LBA '4 ABA 4 EA 4 LEA 2A) PQ] ?5 34 ( 2 5 (D1( ? AE ( 4 AD '4 AS 4 LA 4 LP 2A) PQ] ? / 2 A Lee ( ( 1 / J JA JLeJe J s ( 4 (51( '4 (51( 4 (51( 4 (51( 2A$ PQ?D] )/ 1 ( $ 2 QP_ ( 4 '4 4 4 4 2A) DE D! DQ EB EA PQ?D9 *("R] " / ( $ / / ( / EΩ 40 Ω 33 M0 2 / '(0 4 DE '4 SB 4 BE 4 AB 4 AE 2AF )PQD'(D("9W'%"'] ,(3 ALDE4 '0ArEsQLEKLs P 6 4 '4 4 4 4 a5 a2 21 8 15 7 13 5 11 4 10 3 2A= +PQFF] 6 / $ '' 9 ` AD` LS` / 3FI6q6I AB L !E4 ? 9 (8 2 9 PQDD] $ ' / , ' ( ' B PL` BA PE` BL P!` BD PQ` BE !A` 2ABD ,PQ DD] =1 / 2 3 A L D e4 ( C / 3 R RA RL RD e4 ( (3+$4 ) 1 H 1 1 AD!E ?' BB 'O ) 1 4 = C 3ARE DRQ}e4 '4 ?5' C N 'sAR3r4 2A 4 DRE '4 + C R R' R +$ $ .PQDD] = 5 > I EBBB / I EBB / I BBB/I EBB I EBB / $ 2 62 4 '4 4 4 4 2A$ 4 '4 4 4 4 AL AEA ALEEBA ALE!EA DA EBA DAEAEA 2A$ PQ?2] " 2 5 $ / 2 LB_5( 4 '4 4 4 4 2A= SBB SP SSD QBB QEB PQ] ?(AB L2 ( 4 '4 L 4 E 4 ! 2A$ PQ?'%9 '"%D] " ( 2 3 2 , 4 E '4 S 4 A 4 4 D 2A6 PQ] ) 34sAA K E?53 A L e4 ( 1L f (a 1 ) = 1 $ 8 ELs E! $ (( DE 3E4sAA N 33 4 3A4 3L4 e4 ( (1PD $'( 9 4 ? '4 ? N 4 ? 4 ? N 4 2AF PQ?D] $ 1 1 1 "( / / +7( > 2 / =- 3 m 4 AP :1 - A '( - =- 3 Lm 4 EAA :1' 6 2 5 1 / H 3 Bm 4 $ / 11( 4 2614 4 '4 26112 8 4 26110 4 4 2614 8 4 2614 12 2A= )PQ?2] ? ( ( ( AB ( ( (( 4 2 39 '4 2 41 4 2 43 4 2 55 4 3 39 2A= +PQ?F] >/ E ( AE 4 SB 4 QP 4 BB 2A) PQ?F] 6' !PSBB '( PBB ? EB` ( 4 D '4 E 4 P 4 ! 4 S 2A= PQ?2] 4 > ' $ C ' ;>' !E ( 6 , D 6 O '4 " ' 1 8 $ ;? ( L < G 2A 4 )D '4 S = a 1 = 3 = 6 + ( 4 AEEr 127 2 '4 AEPr 128 2 4 382 2 4 4 32 2 2 −1 127 2 − 1 2 −1 2A$ ,PQ22] "( ( / $ s ' 'A A e ' Fs' 'Ae'( ( ) s A e (?'0$ s KE PD KA LA e AB ( 4 EE '4 SE 4 LBB 4 A L 2A= .PQDD] $ ' 5- - $ F) s )= =6 s 6@ @7 s 7: : s G ) 9 1 $+ - 1− r 1 − 0,5 ? 9P ' 4 PE '4 !A PQR] 6 9 DB AEAB BE L , 0 . . . '02 $ 1 ( 1 )A Bs BBB2 5 ( 4 E '4 P 4 ! 4 S 2AF PQ%"'9(D] $ ' $ 6 ') 1 6A V I IA IL e 86 6A6Le+ 7( 3+74 1 1 2 ) 0 1 '( +751( 4 '4 4 2 2 1 2 1 4 4 2 4 4 2 8 2A= PQD] G ' 1 6 ' 1 , G ' 1 E A!BE 4 ?' G 1 -O $ 1 '4 , 1 62 ) ABPP! E 1 *O $ 1 4 '4 4 2A 4 0 ?Es A!BE s! sL sE >@- 4 + (s E '4 0 s! sABPP! E sL s >@- +( ABPP! E1 PQ 2] $ ' ' /9' ' BB 9 9 / 9 DEm ' , 0 5EB9 ' 9 ' 9 100 2 50 (2 − 1) 2 49 100 2 49 (2 − 1) 2 50 100 49 (2 − 1) 2 49 100 2 50 (2 − 1) 2 50 2A$ \ ? PQ DD] $1+ (ARQ? (EE+ 4 A '4 L 4 B 4 E 2A) PQ DD] >IABBBB/ 2 , / I QBB , / 1 I !BB , / I SBB ?' - ( 2 4 IPBB '4 51 4 51IPBB 4 IPEB 2A$ + PQ DD] ) ? ' 1 4 (1EB` '4 EB` 4 4 (1AE` 2A$ PQ?22] H $- 2 2= $ >? P! ' 6 A !` /AB A :5BO0 1!06B51'!dYNLZDL -0. = AB A 2A I/ P!ppppppp A !B` ppppppp BBBB` "'/0 s L! $ >? L!'AB L PQ?'%9 '"%D] M'5 ' AB` , 5 I 5 ' B`+ M I ASSB ' I I LPBB , ' I 5 M 8551 4 IAPB '4 IA B 4 I LB 4 I QB 4 IAQB 2A) )PQDD] > 2 '' ' 1 AB` ? ' ' ! '' ( 4 S!E '4 QLS 4 !DA 4 PQL 4 EP! 2A$ +PQ?D] > / I BBBBBBBB P` !E` $ ' +- I !ABBBBB 4 IABBBBBBB '4 I !EBBBBB 4 I EBBBBBB 4 I AEBBBBB 4 I BBBBBBB 2A$ , ,PQ?D] > 5 ' - $- ( 1 ( 1 ' ?'0 ' 5S`5 1 ( !(9 BSsBBL AsBLB Ms)⋅3 r4 4 B '4 E 4 AB 4 AE 4 LB 2A$ .PQ?2] 5 #` / PB` E ) ( # ( PQD'(D("9W'%"'] > 5 I BBBBBB 1LB PB I EEDLBB I BESBBB G 1 1+ 5 ?5 E` / '5 1O 4 IABBBBBB '4 IA ABBB 4 IA LABBB 4 IAAASBBB 4 IAASABBB 2A6 ZL PQ DD] §a ¨ ) 1 A = ¨ − 1 ¨ c © 1 1· ¸ 0 b ¸ − 2 0 ¸¹ '2 4 6 ' $sK$ '4 =s 'sK § x · §1· ¨ ¸ ¨ ¸ A¨ y ¸ = ¨ 1 ¸ ¨ z ¸ ¨d¸ © ¹ © ¹ O 4 S '4 Q 4 B 4 A 4 P 2A) 2A 4 sB'sAsK '4 sBsKD PQ FD] / $ ' . " J1= 1 2 '( ª5 5 3º « » y z ] ⋅ «6 3 3» = [96 105 79] «¬ 4 5 2»¼ ª x º ª5 5 3º ª 96 º » « » « » « « y » ⋅ «6 3 3» = «105» «¬ z »¼ «¬4 5 2»¼ «¬ 79 »¼ ª5 5 3º « » «6 3 3» ⋅ [x y z ] = [96 105 79] «¬4 5 2»¼ ª5 5 3º ª x º ª 96 º « » « » « » «6 3 3» ⋅ « y » = «105» «¬4 5 2»¼ «¬ z »¼ «¬ 79 »¼ ª x º ª 96 º ª5 5 3º « » « » « » « y » ⋅ «105» = «6 3 3» «¬ z »¼ «¬ 79 »¼ «¬ 4 5 2»¼ 4 [x '4 4 4 4 2A= PQDD] ) $rFYsYr A) 5 - ( 1 Y 1 $ 2( 4 FK≠"(1 " ( 1 '4 F5 4 F≠""(1 4 F K 5 ( 1 4 $)5 2A= PQ 2] ) $I→MA3I4 MA3I4(51 A A( t ) = t2 t −1 t + 1 2t − 1 = 4 0-.[0-oL. '4 0- . ( 1 4 0-o.[0-.o0-. 4 0-.(1 2AF PQ22] § − 1· §0· ¨ ¸ ¨ ¸ B = ¨ 0 ¸ C = ¨ 4 ¸ ¨1¸ ¨ 2¸ © ¹ © ¹ i + 2 j, se i ≠ j a ij ® ( ¯x, se i = j = 1 A = (a ij ) 3 x 3 2"$FK) 5( 4 ! '4 B 4 4 L 2A$ )PQD'(D("9W'%"'] = 1 ª a 1 − aº A=« » 0 ¼ ¬2a 2 1$AK$( 4 '4 Ar 4 AK 4 KAK 4 B 2A) +PQUD] ?1 1 x + y + z 3y − z + 2 º ª « » 4 5 −5 » « «¬ y − 2z + 3 »¼ z 0 ((( 4 B '4 4 P 4 L 4 KE 2A) ,PQ] ?5 Y 5 1 A×A $ $ 1 Y1 1 5Y $ 1 A×A 5Y N ? $ F Y $rF '( Y $'( 9 4 ?( '4 ? N 4 ? N 4 ?( 4 2AF .PQ%"<'F] $ 0 1 > ' 15 2 B B ' )0 ( 1Fs3'543'54s33PK544 B BA BL BD BE 2ABL PQ?2] ? M 1 MK M =M+ M ( 4 =s+ '4 M1 4 MK M 4 M 4 M⋅MK ( += 2A$ PQ] > 1 + s 354 ( ( 5 s 5 + 1 ª 2 − 3 5º « » «− 3 7 4» (( «¬ 5 4 1 »¼ ª x + y x − y xy º ?1 M = «« 1 y − x 2 y»» (( «¬ 6 x + 1 1 »¼ 0 M( 4 K '4 KA 4 4 A 2AF PQDD] =1 ( 8 1 ? ª2 1 º A=« » ¬0 − 1¼ ªx y º » 1 ¬z w¼ ªcos x −senxº A=« » ( ¬ senx cos x ¼ 4 ,1 '4 4 4 *1 4 ' 2 2A= PQ?D] ?5 2A Q )PQ?D] )1 2a + 1º ª a A=« » ¬a − 1 a + 1 ¼ (2?' $$K 5( ª2a − 1º « » ¬ −1 ¼ $K ( 4 '4 4 4 4 D$K 2A ª 5 −7º A −1 = « » ¬− 2 3 ¼ ª 20 −28º 4.A −1 = « » ¬− 8 12 ¼ ª 3 1º « » ¬11 4¼ r'rr rJr1r&( 4 B '4 4 KA 4 L 4 KD 2A$ PQ22] ª3 7 º A=« » ¬2 5¼ 1 B = « = 1 ªa b º « » ¬c d ¼ PQ ?] $ 1 5 (5 + '1 E P ! S Q 2A$ +PQDR] ª2 x $1 M = ««0 x «¬0 1 0º » x » x »¼ 4 '4 4 4 4 2A$ B BK K A AK ,PQ D] )1 ª 3 0º ª1 3º A=« » B = « » − 1 1 ¬ ¼ ¬ b 1¼ =$1$ $A 1 $⋅$ V 4 5 '∈I 0 ª 3 0º A ⋅ BT = « » ¬− 3 1¼ b= 3 2 1 $ r AF ( A B C D E F G H I Número 1 2 3 8 9 10 11 Letra L M N 4 O 5 6 P 7 Q R S J T K U Número 12 13 14 15 16 17 18 19 20 21 Letra Número V W 1 ª47 30 29º » ¬ 28 21 22¼ 4 ' s A# #∈] $ r AF( 4 5'∈I1$rAF 2A= .PQ?22] > ( 1 1 > 1 ( ' 2 8 ' Letra ª2 1º » ¬1 1¼ 10s « s « '4 '∈I03$rF43$K F4s$ArFA 4 + 1 1AADD ×0[;;( 1 -YpY. $ D '(0D× [D × 0×([( > X Y Z _ 22 23 24 25 26 27 + K ª S E Nº ª19 5 14º » s « » H A S ¬ ¼ ¬ 8 1 19¼ Ms « + 1 AA $ ( 1 ( 1 6 s $ × M ( $ ' '(' ) 1 D 2A ª 1 −1º B=« » ¬− 1 2 ¼ ª19 9 7 º ªS I G º F6s « » s « » 9 12 15 ¬ ¬ I L O¼ ¼ $(?7H" PQ?2] § 2 −1· ¸¸ A = ¨¨ ©1 1 ¹ ) 1 § x· §1· ¸¸ = ¨¨ ¸¸ © y¹ © 2¹ " A¨¨ 2 J 6234 s3$4 $10 BB( N ?D(10L D s det( B) = 1 ; ( 1 9 A ) 4 $N '4 $N 4 $ 4 $ 2A= PQ DD] 4 § 1 a 1· ¨ ¸ 1 a ¸ ' ¨ 1 b 1¸ © ¹ )1 M = ¨ b 2 + 4 1M( '4 M( 4 M(AK'A 4 1M(8 2AF PQDD] ? 1 x º ª3 « » 4 x + 1¼ ¬ 0 DQ > ( 4 E '4 KL 4 4 KD 4 A 2A= PQ ?2] "4 1 0 0 log x 16 log x 8 log x 4 = 1 ( 1 1 2 4 D '4 P 4 A 4 LA 4 S 2AF PQ] ?$$K ª2 3º » ¬ 4 8¼ 1 A = « 1Fs$KA $K ( '4 −111 2 −83 2 4 K PP 4 97 2 4 PA 2AF PQ] ?2J1& ( 1 ªx 1 M = ««m «¬ u y zº » n p» v w »¼ ( 4 '4 B 4 & 4 L 2AF )PQ?2] ?5 MLL ,DD 1 ' 52 ª 2a 2b 2i 2c º ªa b c º « » 0 0 2j 0 » « » M = «d e f » N = « «2d 2e 2a 2f » «¬g h i »¼ « » ¬«2g 2h 2c 2i »¼ ? M ( 2 # , 4 K P5# '4 P5# 4 KA5# 4 A5# 4 B 2A$ PQ?F] +PQD'(D("9W'%"'] ) 1 0 º ªx 5 « » A = «−1 4 1 » «¬ − 2 1 1 + x »¼ = 1$ s 2 ? ' 1 $sBu' b a F s 4 K '4 KA 4 KL 4 KD 4 KE 2A6 ,PQ ?2] " 1 ª1 « «0 «¬ x 0 x 0 -1 º » 0 » - 1»¼ ( 4 4gB '4 4g 4 4f 4 Bt4f 4 4fB4g 2A= .PQDD] = 1 ª2 1 −3º A=« » ¬0 − 1 2 ¼ ª4 1 º « » B = « 2 2 » 3$⋅F4( «¬ 3 − 1»¼ 4 '4 4 4 4 2A) AP K S KLA AS A §0 ¨ ¨ 3x ¨ ¨9 © 2 0 0 0 ·¸ 4 ¸ ¸ 2x ¸ ¹ § ¨ sen 3x cos 3x ¨ − cos 3x sen 3x ¨ ¨¨ 0 0 © · 0 ¸ 0 ¸ x ¸¸ ¸ 3− x ¹ 5 3$F4 ≤ B 3$F4 1 $F 2A "5 (UK∞BU ∪TALT∈.≤BA≤tL PQD2D] ?'1' ' ªa 1 3º ªa b c º » « » 2 5» Fs «2 4 8» «¬ c 4 1»¼ «¬3 5 1»¼ $s ««b 1 2 B $s F BA 3A$4sDF BD $sF BS §¨ B ·¸ s$ ©2¹ P $sKAF 2ABL PQ?2] ) 1 A § 1 0· §2 1· ¸¸ B = ¨¨ ¸¸ A = ¨¨ 2 1 © ¹ ©0 2¹ ?5Ms$⋅FF(1 F " 1 M( 4 RS '4 RP 4 RD 4 } 2A) PQD] " 1 ª 1 « «− 2 « « x ¬ 2 x 0 0º » 0» » x »¼ ( 4 uwD '4 tB 4 tA 4 twDuB 4 uwAtwP 2A= PQDF] ? §m n · ¸¸ A = ¨¨ © 2 − 10 ¹ 1 $K det A −1 = − 1 6 4 ErsKL '4 EKsL 4 ErsL 4 rs 4 KEsL 2A) PQD] ? $ ( 1 A A B?Fs0A$)sLF0 F0 ( 1 F )( 4 wPB '4 4 4 4 −3 20 −20 3 9 40 40 9 2A= )PQ?22] > 1 I !!BB $ I BBBB 0 I BBB " I!LBB/ I BBBIEBB /I BB" 0 ( 4 I BLBB '4 I B!BB 4 I LBB 4 I !BB 4 I ALBB 2AF +PQ DD] "(3((4 BB (!E#"( (QB#(PE# 4 * O '4 ? B ( !E # !A # * ( ( BO 2A 4 DB '4 BA# ,PQ%/$A"( 1$A"D] $ ( A *EB 4 AB '4 Q 4 S 4 A 4 AA 2AF .PQ?D] > '- 1 E B ) I !LEBB + I AAEBB ) ( 4 QEBB '4 LBB 4 SLBB 4 !EBB 4 QABB 2A) PQ DD] , 1 , + a / - J1 4 " 1 1 3x + y − z = 0,20 ° 2 y + z = 0,55 ® ° z = 0,25 ¯ )J '4 ? 1 AD` ≤ r J r 1 ≤ ED` ≥ B` J ≥ AB` 1 s B` ' 3J4 1 2A 4 sB Bs B`JsB Es E`1s BAEsAE` '4 + PQ?2] = -4e$ x + 3y − z = 9 ° ®2 x − y + z = −4 °− x + 11y − 5z = m ¯ ( 4 s B '4 5 4 ≠LE 4 sLE 4 5 2A$ PQDD] ax + 4 y = a 2 °̄x + ay = −2 " °® J( 4 ≠KA '4 ≠A 4 s±A 4 sKA 4 sA 2A= PQD] ) x − 2 y + az = 3 ° ®bx + 2 y − 2z = 0 °4 x − 2 y + 2 z = 6 ¯ ' $ ' '( 9( B ? 3 AL4 ( ( BA ? s ' s B ( BD 6 ' 3 B 4 ( BS ? s A ' s K ( P ? J s 1 ' s B ( 2A L PQD2D] $ B " 1 2 x + y = 3 (A ® ¯x − 2 y = −1 BA $ 1 2 x + y = 9 ( ® ¯x − 3y = −13 B BD + s KD 2 x − ay = 8 ® ¯x + 2 y = 4 ( ax + y = 1 ® ¯x + y = 2 ( BS + s P 2 x + 3 y − z = 0 " °®x + 2y + 4z = 0 ( °x − 14z = 1 ¯ 2AAB PQUD] " [ x − y + z = 2 ° ®3x + ky + z = 1 °− x + y + kz = 3 ¯ A (6 +$ ' 3 (( 4 S '4 B 4 A 4 D 4 P 2A$ C\ F PQ] ?Yn5P A 2 5 Y → n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s LE ) s )#A s L ( 2 4 !L '4 LA 4 LEP 4 PL 2A= PQ%"'9(D] 6 0 ( " 29 ( ( 4 A '4 S 4 P 4 AD 4 AB 2A6 ) PQ?2] $C ' / ' / I ' ' ( '' 5O 2A 2 3 PQ?D] N ' ?( $ )F )51 $ 5 ( 4 !` '4 !` B` 4 B` L` 4 L` P` 4 P` 2AF )PQ?22] $ 5 '' ' ' '9 ' / > 5 / )0 '' B5 ' A ' AA 0 '' XX 5 '9'0 4 '4 4 4 4 2A$ '''' '''' '''' '''' '''' +PQ?] > ( ! E = P / A A L /+1@ ) 0 D $0 ' - '' 5 ( (X"$!$%9 4 AP!` '4 ELL` 4 LS!` 4 D Q` 2A= ,PQDD] " P , 5 2 1 = D 5 5 5 "2 51 4 E '4 AB 4 S 4 P 4 A 2A) .PQ] >AEP ?'0 AS` L L$2 '( ) 5LBO 4 ASEPB '4 SE 4 LSBB 4 BAS PB 4 E BP 2A$ PQD] +52 A 510 ) " 2 ' 52 E( 4 C1530 ⋅ C 620 '4 A1530 ⋅ A 620 4 C1530 + C 620 4 A1530 + A 620 4 C 5021 2A$ PQ?F] 6 D F 'r 2' ' ) ' ( 4 sL '4 sD 4 sE 4 sP 4 s! 2AF PQDD] * 2 2AA B2 C-P($1$T0196(- F 3ILBPQ4 ' 1 =( F # H : q 3H:q4 " 2 ' =AB BAB H:q PAP` , - ' ' >? L 3I PPQP 4 3>I?$ AB AFL4 >I?$FI$?H6I"i$$$d(Lm?(/! D1( ?+ 5AB AM6I)$="$ 3) 9' AB A4 PQFF] ? 5/ 1 ( , 2 ( B EA BA EP BL PB BD PD BE PS 2ABA ) C-P($1$T0196(- + , P? - 2 ' PQ] + ' ' ' / " 2 1 ( 4 P '4 AB 4 Q 4 A 4 S 2AF C-P($1$T0196(- \ "0 '9 5 : 3 14 5 EE > 1 ( $ 1 ''(. '9 3FI6q6IAB LPD4 PQFF] ) '- ( ' : '9LADA , ' 02 ( ( B Q BA B BL A BD D BE E 2ABL C^F PQDD] " ' § 11 · ¨¨ ¸¸ © 4x ¹ § x + 3y · ¨¨ ¸¸ © y ¹ 0 ? ( 4 PE '4 LLB 4 EE 4 DPA 4 2A$ PQ] + # u # §n· n! ¸¸ = Ws k k !( n - k)! © ¹ ¨¨ AL? § n · §n· ¸¸ = 3¨¨ ¸¸ © k + 1¹ © k ¹ # 1 ¨¨ 0 4 '4 4 4 2A) sD#r sD#rA sD#rL sD#rD ) PQ?2] " ( 0 9+ H HA HL A HD LL HE DPD HP E B BE ?5 + 2 9 + 34* 2 , P ( Q 4 '4 4 4 4 n 2 − 3n + 2 2(n − 2 ) ( 'C 7 $F , $rF( 4 4 A 4 1 1 1 1 + + + ... + 1⋅ 2 2 ⋅ 3 3 ⋅ 4 1 999 ⋅ 2 000 70x B 81 4 ) ( 4 2A) PQ?] ?5 21 !W s S3 K 4W K !AB 6 4 (2 '4 (2 4 ( 4 (2P 4 (2 B 2AF PQDD] ) 2 1 1 1 ≥ 0 = − n ⋅ (n + 1) n n + 1 § x2 −1 · ¨ ¸ ¨ 2 + Ax ¸ © ¹ '4 n 2 − 3n + 2 2n − 1 n 2 − 3n + 2 2(2n − 1) n 2 − 2n + 2 4n − 2 n 2 − 2n + 2 2n − 1 4 QQQE× BKL '4 QQE× BKA 4 QQQE× BKA 4 QQE× BK 4 QQQE× BK 2A6 )PQ?2] , 3 3 4 5 3 5 3 4 8 3 3 2 A 3 2A= +PQD2D] " ( 'C §¨ x m + © 1 · ¸ xm ¹ k (3# 214 ?' # B #(2 BA #(2Q BD #∈T BABU BS #t E P #(E 2AB! ,PQ] n ? §¨ 2x 2 + 1 ·¸ x¹ © Q( ! A 4 S '4 P 4 AD 4 LA 2AF .PQ?2] " §¨ x + © 1 · ¸ x3 ¹ PQDD] $ ' L ('' 12 ( 4 AP '4 PQ 4 AAB 4 ASB 4 L B 2A) PQDR] 60 ''$( 4 1 '4 4 4 4 § ,'C ¨¨ x 3 + © 1 · ¸ y 2 ¸¹ 24 ( LP J ( 4 K A '4 KAD 4 KP 4 K S 4 KD 2AF C \DFF PQ DD] >C' (ABEB, DBB'' 2( ( 4 RD '4 ARE 4 ARL 4 LRE 2AF 2 1 3 1 4 2 5 2 7 2AF PQ?2] =$F $ '' $(+3$4sBD'' $F(+3$∪F4sBS+0 ''F( 4 ERP '4 DRE 4 LRD 4 ARL 4 } 2A= PQ?22] + C ( = tRR'RRM>J"=$Ju $ BAB L ) + 5 $ s + 5$ = '' ( 4 '4 4 4 4 1 5 2 5 3 5 4 5 4 4 2A6 +PQD'(D("9W'%"'] G LB P 0 L - (''A 5O 4 '4 4 4 2AF PQ DD] > / 2 12 4 + / 2 (''O '4 ?/2I ABB 2O 1 10 1 7 4 190 203 184 203 92 145 90 140 85 140 2AF ,PQ%/$A"( 1$A"D] $ 2A 4 ≈BBBDE '4 AB )PQ?2] > 9 1 LB 1 L 1 LB"'0 - L '' 1( 4 '4 4 1 63 1 21 2 21 >1 π s L 5 '' ' 4 2− 3 2 '4 3− 3 2 4 2− 3 3 4 4− 3 3 4 3− 3 3 2A$ )) .PQ?'!"@%'"!&!!F 9( D] >F' ($ '2 (' 60 ?' '' )'( 4 2 '4 4 4 4 3 5 6 1 6 2 5 1 5 .E > G ( 2A+'- 1 5 + , G ?'0 5(11 '' 8 - + G( 4 1 '4 4 4 4 2AF PQ%"'9(D] >((- D$ 2 ( ' 6 D G + (? E +.EG 6 1 5 1 8 1 16 1 4 2A= PQ? D] 6 DB AP / 5 AA / /5 $ '' 5 ( 4 DE` '4 DS` 4 E ` 4 ED` 4 E!` 2A$ PQUD] 6 L? 2 ( '' 2( )+ 4 '4 4 4 4 1 2 3 4 7 8 2 3 5 8 =)' 11'' ( 4 5 '4 2AF PQ?D] 6 ( ' 5 ' > ' E` 1 1 L` 1 1 " '= PB` DB` 60 1 ' $ '' 1( 4 QED` '4 QEP` 4 QES` 4 QPB` 4 QPA` 2A) PQFF] 4 4 4 128 7 128 15 256 17 256 25 512 2ABA PQ?] > AB $ ' ' 2 , ( 4 EE`PE` '4 PE` 4 DE` 4 DE`EE` 2A= )PQ?2] 6'' ?' ' ('?' 1' ), ' (' "2' ( 4 '4 4 4 4 A LP D EP P 2A6 +PQ?2] > ( ' ADPS>'( 2( .'( $''(( 2 5 E( 4 '4 4 4 4 BLDE BLEE BLPE BL!E BLSE 2A= ,PQ?22] ) ( $F I ' /,'' 8 '( 4 '4 4 4 4 2AF 3 4 1 2 3 8 1 4 1 8 .PQ?2] > D D , ' + '0 )'' 4 . '4 / . 4 . 4 /. 4 2A 4 RAD '4 B 4 RD 4 RL 4 LRS PQD] " 5 0 = ' $ = O 4 DDB '4 QAB 4 AB P 4 DBLA 4 E!PB 2A6 ). PQDD] 6 AB ALB 6 / AB` ( B` = ' ' / ' $ '' ' 5 ( 4 '4 4 4 4 24 350 24 47 47 350 23 350 23 47 2A6 PQ?D] " ( 5 ' ' ( + F 2 5 5 ( 6 2 ( 8 ' .(' ' ? 5 '' 5 1 5( 4 '4 1 3 5 12 4 4 4 17 36 1 2 19 36 2A) PQ?D] =50 ' ? @ ' 8 34 @ ' 34 ' 34 / ' 4 * @ O '4 ) , 2 3 / '4 6 ,0' 4 ) + '' ' N + t REB ?) I2'@F K QSS@ ( / 2A 4 ,s!,sQ0s D?sD?sL '4 ,s)D.A⋅)Q.A⋅)!. ⋅)D. ⋅)L. ⋅L! ?,sAE⋅L ⋅! 4 8748 13585 C-P($1$T0196(- , ' BBBBB / ' L ( $F)$'' + ' embarques do mesmo passageiro 5 4 números de pessoas 1.000 1.500 3 3.000 2 10.000 1 60.000 G '1L ' 0'6 5 PQ FD] ? 5 ' PQ FD] ) + BBBB ' $ 12' + ' F 1' +1' V3?434 4 '4 4 4 4 2A$ C-P($1$T0196(- 6 5 - ) ( 1 5 1 ( 5 ? 9 ' ) / $ '' 5 ( ( 4 1 '4 4 4 4 2 5 8 2 3 3 4 5 6 2A) C E PQ?D] )( ' $ 2 ( ( + 4 EE!SQ B '4 DEP!SS 4 DEP!SQ 4 EEE!!Q 4 EE B B B B 2A= PQ?2] $ ( (P $ ' / ( (' 4 '4 5 ' 4 4 /-' 4 ' 2A= PQ?22] , 2 I2 / 9 =tR&&&u$ ! AB L $ 4 PA` '4 PL` 4 PD` 4 PE` 4 PP` 2A6 PQ?22] , F ) ( ( /' (( 2A )0 ( ( / '(0 $ S $ASLA $LS ! " ( ( (A PQ?22] $' F)0" m 5 P AB L =0 +%fWWWg fLTT T YNLZTNYT LMN YNLZ$ g0%YNYNLZ -0. + g+5 :5BO0 1!06B51'!YLYNLZL -0. = 4 ( )0" ( F '4 ?' ( / LBB BB ' )0 " 2A 4 $ APPDL! '4 = ( / ( LBB BB' BBBL` )0 )0" '(0 = AB L 8 C AB L 2A L!' +PQ?] +1 ' " ' ) $ M 7 M 7 ? 7 )PQ?22] " (CF AB L 34 1 4>>Q 34 5 + # LR \d 34 0 4 - . ) # LR LP $/'( 9'( 4 '4 4 4 2A$ N0N0N N0N0@ N0@0@ @0@KN + ,PQ22] > 5 ( A L e # "'(0 5 (MM 2 M M≠M≠M≠# ? 5 '' 4 M '4 M 4 # 4 M 2A= .PQD'(D("9W'%"'] = ' '34('' ' ?' µ σ0 4 µsDBB Btσt AB '4 µsDBB BBtσt B 4 µsD BQBtσt BB 4 µsD BSBtσtQB 4 µsDAB!BtσtSB 2A) PQD'(D("9W'%"'] > S 5 ' ' ' 8 ' ''"5 $F)=6@7: ? ' "( 4 QBBB.Q E.QEBB '4 QB B.Q AB. BBBB 4 QBLB.Q AB. BBBB 4 Q AE.QAEB. BBBB 4 Q AE. BBBB.QSBB 2A= PQ%"'9(D] > M ( ' 6 AS ( ( !B $- BB DB I ( ('0 4 '4 B` 4 AB` 4 B` 4 AB` 2A$ PQD'(D("9W'%"'] > $ F ) = 6 " 2 ' + "( ( 4 LAB '4 LLB 4 LEB 4 DBB 4 DEB 2A6 PQ?D] " ' * ( O 4 LEB '4 LSB 4 LQB 4 D B 4 DDB 2A= PQFF] $5' )6,>If,M9$;9"'' @=?+ABBP SL = ( 5 ( B BQL BA B BL BQ BD ! BE AE 2ABD PQD] $ ( ' 1 2 ' , ' ' 0 " ( 4 PP '4 !D 4 SE 4 Q! 4 A A 2AF C 2 D PQDD] ,-''0 $F)=F)@69 + P A B A " -( 4 SL '4 BL 4 AL 4 PL 4 ADL 2A) PQDD] > 5 ( ' 0 ' L ?' LAD L 4 LPB '4 LES 4 A!D 4 APS 4 AEA 2A6 PQ?22] " 5 ( ' ' $5( '''0 $ ' (8'0 ) ' ( - B`' ' 0 ' 2A $ AD BEPL PQ FD] > ' 05 9 $ 05 P '( P $ 05 ' $ A ( 4 72(3 + 3 ) '4 36(6 + 5 ) 4 108(2 + 5 ) 4 27 (8 + 7 ) 4 54(4 + 7 ) 2A6 +) PQ%"5#] > ( 1 - s DB DB$' 9 9 ' ?' s BBB L s AB 3 = 1,73 ( '( 4 EP '4 ED 4 LA! 4 E! 4 LAD 2A) )PQ?D] $ 9$F)=6@7:$Fs A$=s S $@ s Q 6 DE 8 ?' 96@+5- =*F):6+7 L ( 4 DSS '4 ELA 4 !AB 4 E!P 4 DEP 2A= +PQD] $ 1 ( ' 8 '/ ( ' 1 ' ( 3$)+I'M$ M KA 6K?+6 H@AB 4 > L P A ' @ RR&&&'RRRRp =' ' ' ? NL ' ND ' NP' ( 3$ 3 s !4 ++ 4 NLtNPtND '4 NLtNDtNP 4 NDtNLtNP 4 NPtNLtND 4 NPtNDtNL 2AF ,PQ] > ' - 9 A B D ( LB ' ? 2 ! Q A AB ' 4 DSBA '4 BDA 4 L!PA 4 DSSA 4 D PA 2A$ .PQ?2] > ' ' ' ' ? ' 4 BL# '4 BA# 4 B# 4 # 4 BB 2A$ PQ?2] > 1 9 B E A6( 1 E BBB $- / 4 AE '4 A!E 4 LB 4 LAE 4 LE 2A6 PQ ?D] > 0 $ ' B '6 ' 5 F+ ' )' (F * 9 5$(FO +, 4 AB '4 10 + 10 2 4 LB 4 10 + 2 10 4 10 2 + 2 10 2AF PQ?D] / ' ('( $ 1 '( 4 1 '4 4 4 4 8 1 6 2 9 1 4 1 3 $ " "Nα ' 2AF PQ] ?5Yn]/ + ( 9 5 ' ( 9Yn]5 ( L L " 5 + ( 4 '4 4 4 2A) PQR] > $F)= " ' α 6 ( "N F) ) $F)= "N . "N ( Bt≤ π . 2 9 "Nα. 9$F)=N 2'(J " J9L 9 ( 4 '4 +. 4 4 , 2A$ PQD] $95 1 @ -=:- 9 9 3$)+I'M$ M KA 6K?+6 H@AB 4 ) 9 ' 5 A : :- ? ? 9( 4 ?s3r43K4 '4 ?s3r43K4 4 ?s3r4A 4 ?s3K4A 4 ?sA⋅A 2AF )PQ?] ?'0 ' 9 ( $F)= 5 ' 24 2 ?'0 '( 9 ( N ' P $ 9 A ( 4 QPB '4 LAP 4 B!P 4 ELP 4 E!P 2A= +PQ?F] 6 9 -5'( A ?( DABL 9 4 PBL '4 DBL 4 A BL 4 LLBL 4 DABL 2A$ ,PQ?2] =50 - 9 ' $ ' - AL - ) 3 = 1,7 -( 4 AEEBB '4 AAQEB 4 !SEB 4 ELBB 4 !PEB 2A) .PQR] > - - A "( )1- 2A 1 4 PQ?D] 6 9 ( 5( 4 a 3 '4 a 2 4 a 3 2 4 a 2 2 4 a 2 4 2A= PQ?D] $ ' !0D ( 0D " α?'0 5 (! α α BC ( AD $(D! ( 9 - ' BC 5 α9 θ B t θ t πRA ? !D s " 2 / 2 " θ 4 !0D. '4 9 0!D AB . 4 9 0! AD 2A 4 '4 4 l 3senθ 6 l sen 2 θ + 1 2 l ⋅ 4 cos θ + 5 2 PQ ?] > ' @1 '9 '" DAL LBL ) ( A ( , PQ] $ $ 'N$ F'AA NF 5 9?$?F 4 '4 4 4 4 P ! S Q B 2AF , PQ22] > " $- RL 0 2 $( S ,( A SB 4 '4 4 4 '4 4 4 2A$ PQ ?D] > 1 ( 5 ' = 2' 1 3$πsL D4 4 '4 4 4 4 2A) L DB LLDP LDED LE A LS P VB ' / V A 4 4 1 4 1 2 1 4 1 2 1 2 1 8 1 6 1 6 1 2 1 4 2A$ )PQD] , + 2' ( 5 (EL` 5 / 6 5 G( / L ? G( DB` = 1,4 = 1,183 4 S` '4 DB` 4 SL` 4 PBB` 4 ! A` 2A) +PQ?'%9 '"%D] $ ' B A 9 A * 91 Pπ A ?' 0 3 4 4 AB` '4 AE` 4 LE` 4 LB` 4 DB` 2A$ ,PQ?2] " $F)= P 6 LPBm ( AB " - L( 4 DPπ '4 DSπ 4 EBπ 4 EDπ 4 EPπ 2A= .PQ ?] + ( / ?'0 (L( 4 E '4 P 4 S 4 Q 4 A 2A= PQUD] + " Is P 0 9 θ s AAEm 6 0 s +10' AC BD " ' $( , 4 2 39 cm '4 15 39 cm 8 4 55 cm 8 4 2 55 cm 4 15 55 cm 8 , 2A6 PQ?D] > ( L ' '( C 6 H'0 "' ( ' " 1 BB(L 4 E!DBBπ '4 EPABBπ 4 EDSBBπ 4 DSPBBπ 4 DEDBBπ 2AF PQ?'!"@%'"!&!!F 9( D] > 'S9 P (( B )πsL( L ( 4 D A '4 PEL 4 !DP 4 QLE 4 S!A 2A= PQD] > 1 ' ' C ?' LP ( DS 9 ( O =1( $ 1 2A V (9 9 ) 1340 =0 ( 8 '0 B RL BP RL !( 3 3 ≈ 1,44 3 5 ≈ 1,71 + 1 ( PB ?' 1 ( ' 1 0 '1 1 ) A1 NA 1 N )( 0 + 303 4 cm ( PQ?22] > /ABAB 9 ' ( ' , 4 ES P '4 SA SB 4 SD PS 4 SQ EB 4 QB SB 2A) PQ?2] >C( (:=50 :' C $ $- ( 4 '4 4 4 4 H 4 H 6 H 8 H 12 H 24 2A6 )PQ?22] =50 A ' ' ( 9 ' $( ' H'0 ?'' πRP 2ADIDIPI +PQ] > I 9 N ? ( EB` ( 4 BBB` '4 AEB` 4 A EB` 4 AL!E` 2A= ,PQ?2] > 3 4 L 34'( L? ? SB` ) 2AQP .PQR] >$L (α >10 @ @ $ "' )(@5'( ' 5 ' ? 8 ( 9 FT, 4 B '4 Q 4 S 4 ! 2A) PQ?RD] > / '- C 5 ( 34 ?'0C 34 ' 3I4 ) C ( ' " - ) ' ( h2 R2 ( ,) 4 A '4 D 4 S 4 8 4 3 4 3 2A) PQ?D] ) P 3 4 P 3A4 'P3L4 -5 ' 3D4 BB - / ( ARL AA LL 1 (2 DD ( ' 2ANN@@N PQ%/$A"( 1$A"D] > E P 9 " 2 9 >1 π s L 2 ( 4 S D '4 !BA 4 LQP 4 EBB 4 P S 2AF PQFF] ?'( ( EBB $ / 8 . '( ( 3 '( (4 3FI6q6I AB L !P4 )0 ' π s L 0 / B AB BA AE BL LB BD LE BE DB 2ABL C-P($1$T019=-L $ (( ,+ " L " / $ F 8 1 PQ FD] = 5 4 L '4 LE 4 D 4 DE 4 E 2A= PQ FD] > ( " 4 (ABAEπL '4 (ABAEπL 4 ABAEπLDBEπL 4 (DBEπL 4 DBEπLPB!EπL 2A$ C 2 PQ FD] ,'+*I? / ( / α β Btαtβtπ ?'αsBS0 β( 4 KBS '4 BS 4 KBP 4 BP 4 KBA 2A) PQ] ? I → I ( 34 s A r ( 4 DE '4 LB 4 E 4 B 2A$ PQUD] ?534sArβrβ?34sB 3π β= 2 ,, 4 '4 K 4 K B 4 K 4 B 2A= PQDD] " 5 3?4 A⋅A r 3A4 u A B t t π ( 4 π 5π ½ S = ® x ∈ (0, π) | 0 < x < ou < x < π¾ 6 6 ¯ ¿ '4 π 2π ½ S = ®x ∈ (0, π) | < x < ¾ 3 3 ¿ ¯ 4 π 2π ½ S = ®x ∈ (0, π) | 0 < x < ou < x < π¾ 3 3 ¯ ¿ 4 π 5π ½ S = ®x ∈ (0, π) | < x < ¾ 6 6 ¿ ¯ 4 ?s∈3Bπ4 +PQ FD] $ 34s3r4DK3K4D ,. " '( 4 5π 2A$ '4 PQ DD] ?5s" ( 4 '4 4 4 2A) )PQUD] 6I sen 2 x senx 4 4 ( 3 − 1)/ 2 (1 − 3 )/ 2 ( 5 − 1)/ 2 (1 − 5 )/ 2 f (x) = 4 12 4π 9 3π 8 5π 6 2π 3 2A$ ,PQ ?] > 5 0 ' $J θ ( ( 4 ∈IR≠#π#∈] '4 ∈IRA#πttπrA#π#∈] 4 ∈IR π rA#π≤≤ 3π rA#π#∈] 2 2 4 ∈IRA#πt≤ rA#π∨ 3π rA#π π 2 2 ≤tAπrA#π#∈] 4 ∈IRA#π≤≤ π rA#π∨ 3π rA#π 2 ≤tAπrA#π#∈] 2A= 2 4 '4 4 4 4 2A= JsAθ JsAθrA JsθrA JsAθ JsAθrA .PQ?] ) '5 1 ' @- + / $ 8E3sB4 - § πt π · T ( t ) = 24 + 3 cos¨ + ¸ © 6 3¹ 34 - 34 3m)4 " ' 4 PAEEm) B '4 AA!m) B 4 AA!m) E 4 PAEEm) E 2A) PQ?2] , '0 J s KD K > (' ( 4 J≤Kπ≤D '4 J≤Krπ≤KD 4 D≤J≤Kπ 4 KD≤J≤Krπ 4 KD≤J≤KKπ 2A= PQ D] $ - J s 34 ?' ( 4 s πRD ∈] '4 Lπ(1 4 34sAK 4 π 4 34sAK 2A= PQ?22] 6 5 ( . ?'0 (AA 9θ( !( ρs RL s × BE,RA s BRA 4 LRE '4 LRD 4 BR 4 DRL 4 ERL 2AF PQDD] > , S # 9 +' 9 PBm 9LBm ' $ 4 SB#R '4 ADB#R 4 AB#R 4 EB#R 4 ABB#R 2AF PQD] $ $ ' ( 2'$ $ F , ( 3$F,4 ' C ' 6 5 1E`SLL`> E` 1 'BBEI ) '0 A ? $F, E` 4 E '4 AB 4 2 + 1 20 4 401 − 2 4 4,01 + 3 2A= PQ ?2] " π 7π π 7π ( y = sen − cos + sec + tg 1 20 4 3 +1 2 '4 3 −1 2 4 4 4 2A6 3 +3 3 −1 3 +1 6 3 4 . )PQ DD] > 2' 1 ( ( 3 a 0 4 ' 0 9 θ ' ' . 3&&&'$4 4 ? ( 9θ '4 ) 3θ4s RD B t θ t πRA ( %3Aθ4K%3Aθ4 2A 4 1 '4 2 7 17 +PQDD] $ ' ' L +( +** 1( ' ' A 6 1 = α s BS + 9( 4 DS '4 EB 4 LS 4 DD 4 DB 2A) ,PQFF] $ 1 9 6 ' N " ( 9(2 /$F , 2 A $F ? 9 $0 ( B 1 + cos θ 1 − cos θ BA 1 − cos θ 1 + cos θ BL 1 − senθ 1 + cos θ BD 1 + senθ 1 − senθ BE 1 − senθ 1 + senθ PQ?22] "' 99 . 2AB .PQ?] 6 M0GM- 3 SQL0 QSL4 $ " ( PB B $ 'S $ 9 9 '5 O " I 3 DLP0 D!P4 C ' D! ' / "' + * ' " 9 α /8 (8 ) 9 ") ' GM- "9α 4 4 3 −3 10 '4 4− 3 10 4 4−3 3 10 4 4+3 3 10 4 4 3 +3 10 2A$ PQ?22] H " ! % ' 9 + 1 9/ ( 9 +% fWWW)T)T)TNdLLLN)g0 %MYNLY]0b > 9 / E (BSS ) ' 2A A 4 9 . '4 1 0 1 ( AAEBEPAP#R = 2 ≈ 1,41 3 ≈ 1,73 2A 4 senβ = PQ FD] , 34s 34s 0,26 ≈ 0,29 0,88 . '4 ≈ Q!D !!!#R PQ] ? ( D−Ds 1 ( 2 4 '4 3 2 4 3 3 4 3 $( cos( 2senx ) = 2A= PQ?] > ' SB / 9 AEm 1 ) EB 8 /0'9EBm ' 2 2 4 BA '4 BL 4 BD 4 BE 4 BP 2A) PQ?D] = '0 520 § p+q· § p−q · sen p + sen q = 2 ⋅ sen ¨ ¸ ⋅ cos¨ ¸ © 2 ¹ © 2 ¹ ?'AEm(BDA AEm ( BQ ( 4 '4 4 4 4 DD. DA. DB. LS. LP 2A) H⋅Q(/ 4 BrS '4 A⋅3PrA4 4 A⋅3 BrS4 4 4 2A6 1 2 1 2 ⋅3PrA4 ⋅3 BrS4 \ PQ? 6 1 6 ' 0 - 0 ' ' $ ' 8 * ;<O 4 "' ' '4 $'1 1 ' 4 " ' ( 0 4 $ ' 1 ( 8 4 + ' ' ' ( PQD (C 0 5 1 " 1 ( ( 1 $ 1 1 . 3RR'$4 $ ' 1 + 1 0 1 8 + 1 0 18 , 1 8 1 - 1 N ,1 6 4 '4 4 4 4 N N N PQ? $ 1 4 $1 ( '4 " 1 ( 2 ( 4 ,1 / ( ' 4 $- 1 4 $ 1 1 0 ( PQ FR > ' 1 ( 1 $ "'0 ' ' $)"II6$? 4 '4 4 4 4 , .) PQD @ALI'?( Q!BI 34 DE!A DE!7H?>36>$4 $'( 3@AL41' C;< 6 I 3@ AD4 6 1 ' '' 6 ( $ ( 5- 23@AE4 ?'0 @ADMC;< $1 /' $ ' ' ( @AE)(2 )'ADAE ' 9 $ ( ( ? - ( ( 5- AE ( 2 " I ( N , AE ( 1 (-' $ 4 ? '4 ? N 4 ? N 4 ? 4 ? N )PQR /6 6A6L 6A 6 6L? ( 9 $ ( / $ 6 6A. - ( , ( 6 6A '6L +PQ = rD r 19 6 1 8rD0 1r O 4 ARL '4 LRA 4 ERD 4 RL 4 LRD ,PQ * ( r rA rL rD ( $ 0 )5 B ( ( $ - ( ( 4 1 q 4πe 0 d 2 '4 2 q πe 0 d 2 4 1 q πe 0 d 2 4 4 q πe 0 d 2 .PQD > 1 ( u B + .+ BD " ( 0 D( BS G ' 1 - 0 ' ( 5 9 0 ( ( AB P , ( - '(3 04 '- (D ( -68 =9 θ 8 0 3 4 ( + ) , ' 4 '4 4 4 4 3⋅r⋅64⋅θ 3⋅0⋅6⋅ 2 4⋅θ 3⋅r⋅64⋅θ⋅θ 3⋅r⋅64⋅θ ⋅r⋅6⋅θ PQD G( 0 ' 1 ' ( 0D. ( 9 SBm$( ( D ' ( 0 ( H0 '( 9( B " (5(0 BA ? G ( 5 0 - ( 0 ( (1 PQ?22 > =,$ + 0 () ' 9 + 1 1 ' 8 → → F res = −b v $ 1 $- 0 > 1 0 AB N ) DB '0 ., "( ( 6 s AB BD,R) 9 (s!B) ( 5 ' (- P BK Q )Q BKL # , ( 4 ( . '4 . 4 1 ( PQUD > BE A ' 5 8 ( & ) | g |= 10m / s 2 0 1 , - ( R 8 ( 4 '4 4 4 4 LP BL LP BP EB BP !B BP AP B0P PQ?2 $ ( /$F) $ $ ) ( 8 4 B× B A ( 2- '4 PD× B A - 2( 4 B× B A - 2( 4 PD× B A ( 2- 4 ( ( PQ?F V 4 $F/( ) '4 $F/( ) 4 $)/( F 4 ($F ) N$tNFtN) 4 ($F ) N$uNFuN) PQ?22 )08 B 18 .. ' r ? -( 1/ /( 4 T = 2 π L g '4 T = 2 π mL qE 4 T = 1 2π mL qE 4 T = 1 2π mL qE + mg 4 T = 2 π mL qE + mg )PQ?F $ H@ ( +PQD >B # BKP ) ( - BE ,R) =1 / B RA 4 SRA BRA '4 QRA BRA 4 SRA ARA 4 QRA RA 4 SRAQRA ,PQD V ( ( 6 ( 1 ( * - ( -1 0 1 9 / ( ( (!s εB( ( =10 0-sA × B0A!#(sA× B0 Q) ' ( s D × B Q ,R) 1 1 = 1 A( 4 " ( ( '4 $ ( @ 5- ' 8 4 $ '( 4 $ (( 4 " ' ( ' ( 1 2e 2 a 2 4πİ0 3c 3 0 E $9(sD× B ( ( 1 - 9(Cs B0 Q 4 ) / ( ! s α A α s 2 1 2e 4πİ0 3c 3 sP× B0EAj⋅$ '4 ) - $ .PQUD > @ ;,3#s Q BQ ,AR)A4 * 8 9 = ( LPB ,R) ( SBN <$ 4 ADµ) '4 Bµ) 4 LB) 4 S) 4 B) PQD $'( 9( B ) ( ' ( 0 ( BA ) ( ' (0 BD H ( 8 BS $ ( 0 P 6 ( ' 1 5- PQ * uA uLuD , 5 ' ( $ ( 4 '4 A 4 L 4 D PQ? ) 1 , ' 4 ( ( '4 ( 9 8 4 ( ( 8 4 ' ( 1 4 - ( 9 8 PQD2D ) 0 D Z 9 0 ( D 4 " 4 ? ' ( Z $ - ( ) B 0 D 1 BA $0 3 *D 4 9 * 4 BD " ( 0 ( ( D BS " ( 0 D P $ PQD ) ( ( I '( 9( B + t I (( BA + = u I ( =(=A BD $ ( Q 2 4 πR BS " ( Ns kQ tI 2 (# 27Q2 16d PQ? 6 =6I$, (' ' ( , ( <3 + ' # '# '1+ ;# ' = , +?9AER? +$FI$M6KABBE d P $ ( ( ( )PQ "' ) 9 ' / 2?' ( 0 $ '( 9 5 4 $5 '4 $ ' 4 '4 4 4 s3≠B4 sA sRA ssB +PQ > 9 C/?' ( ( 0 4 ( - ( '4 ( ( 4 ( 4 ( - ( ,PQ? , 9) s B@)AsLB@* s ) *A s L ) $ 9 ( s $- - LPBBB#R 9 d ?' 4 9 . '4 * . 4 9 )A - '. 4 9) A` ? tt 1 1 A ≈ 1 + x 2 4 2 2 1− x .PQ?F = ' ' > " ' ' ;6 '- 9 ) s PBµ@ (' ABN( ABN 0 ' 0 9 )A s DBµ@ + ? 0 ?A M ) ' ) 0 ) 9 ( 1 , W< " 1 ' '- '( ' ' ) '- (6s §¨ 1 ·¸ )>A ©2¹ 9)s q U + $@ ( @A ' , ( U 1 BB PAG6B( B9 LBm U ( ?'0 L Ω B (DLAG" ( • • • • ) . . . @ PQD > C I s BΩ ( 9 E µ@ 6 5 ( ' AN1 1/ s AΩ ) ' 5 '( 9( B $ ( I( $ BA $ ( ( BD $ I( BN BS $ ( P $( (AEBµG PQ R 4 '4 4 4 4 LEB DDB ELB PAB ! B 3 3 3 3 3 PQ?D " ( ' ( -$ ' ( 2 ( ' " ' ( 9 8's S , 4 0 ( 0 3)04 3)Ar4 . '4 ( '. 4 :) : ( )0 )Ar '. 4 ( ' ( 9 A@ ,"66$="6 )(s0 P B0 Q) @s B0 A@ s B0Q [R2 C-P($1$T0196(- * ( / * ( ' ( ( ( @ 1 C 0Y PQ R > $ 1 ( 4 1 '4 ( 4 4 9 4 1 PQ DD + 0sEB× BK D A9s AB ( s 2 2 C = ε 0 A εB≈ d QB× B PQ D >$ 9L / $ ) 9 ) 9 )B 4 '4 4 4 4 )s)B )uD)B Bt)t)B )Bt)tA)B A)Bt)tD)B K A C Vm , s DE× BKQ)( 4 A× BAN '4 EB× BKDN 4 AB× BLN 4 B× BKABN C-P($1$T019=-)L+L, !( $ $] =2L)#]'$ +(LX]$ ) [ a ]π πε a . .LX $ ] )PQ?D " / ( 9 8 = (=/ . +PQ?D µ0a_L /(0a0)µ µ 0 a 0 L µ $ 9 ! a L '$ ) - ( 1 A]$ ,PQ?D , I) ' ) ' ( a $ )(( ) ( $b 2A= 2A$ )2A 6 ( - 6 6A * r *A s P µ) *a *aA 5*a s*aAsSµ) +2A$ ,2AF .2A= 2A A 2A 4 ( sP2 R $ ( 8 5 '4 N vT(M) = PAE× BwLR N vT(N) sEB× BwLR 4 $- 0 s F C s B ( ( s2T + V [ C → d 2F \ - 2AF 2A= 2A) QM vTM ǻZ M 15 = = = QN vTN ǻZ N 12 QN QM 2A$ 2A= 2A) N s vTM vT = Q d ⋅b = = cte. vT V s AE ǻZ N 12 = sBS ǻZ M 15 ) 2A6 )2A$ +2A= ,2A 4 $ ( s!C + / ( - ( ' :[ :[ 14 × 1019 C ⋅ N C ⋅ Kg 2 × 10 −27 s eE s 2 × 10 mp −19 s D× BA!TA $( A s α C s P × A A 0 Q B0EA U ⋅ 3 D × BA! T 4 B s !P× B0 !@s !P× B0 D@≅ A× B0 D@ '4 $ - ( ' , - ' ( ( 8 0 Q ⋅ D× B Q⋅D× B0 E s sA× B N s A× B0 E@s A× B0 L@ C $( s 1 Ar 2 2 ( E pot − Eirr ) mp [ s s 2 (1,12 × 10 −13 − 1,2 × 10 −14 ) m / s 2 × 10 −27 10 27 (1,12 × 10 −13 − 0,12 × 10 −13 ) m / s s 10 27 × 10 −13 (1,12 − 0,12) m / s 7 s B! (1,12 − 0,12) m / s = 1,0 ×10 m / s s B!R .2A6 2AAQ 2A= 2A) 2AA! 2AF 2AA )2A$ +2A$ ,2A 4 )sDB: '4 > sB 2 4 )Ad≅LBT r 1 18 ⋅3 B0D4AU: 4 ≅PBB⋅ B!R .2A $() - ABN(s) >(sP⋅ B0P⋅ As!A⋅ B0 P ) $- = '(0)s) r )A s P⋅ B0P r D⋅ B0P s B⋅ B0P ( ) s q U >s q C = 72 ⋅10 −6 10 ⋅10 −6 s!AN + $ ( 1 ) 6 s 1 ) 2 >A s 1 P⋅ 2 B0P⋅ AA s L⋅ DD⋅ B0P s DLA⋅ B0PsDLA⋅ B0DG , '(0 6s6 r6As 1 C1U12 r 1 )A U 22 2 2 M> s>As!AN $'(0 6 s 6 r 6A s 1 P⋅ B0P⋅!AA r 1 D⋅ B0P⋅!AA s 2 2 E⋅E SD⋅ B0PsAEQ⋅ B0PsAEQ⋅ B0DG ∆6s6K6sK !ASµG "'06(6 ) 0 9 $ ( ( ( G '( ( 8 2AAL 2A= 2A 4 "( ( " (( '4 6sS⋅ BPNR 4 • + − @)s AS⋅ B− A, • + Yo @)sAEP⋅ B− A, 4 *s!PS⋅ B− L) 2A$ 2A6 2A) )2A*sE) +2A6sBNR ,2AsNIRIsE$ c PQD $ ' 0 C $ ' 1 BBB$3$4 ?'0(( PB × B0 Q 2 (( ' 4 BPA× B0 S '4 PB× B0 P 4 E!P× B L 4 LPB× BA 4 AAE× BAA PQ?D $ ' ( / ( , / L (3$4QQBq QSB q 9 H HA PB q ,( (DDBBq A+ , ( D ( 8 (O M M G A $ Y I*( ( $ )=O $s) r= $s) 0= $s=0) G L $ C I " ( ( ( O M M 4 #q L. '4 ( ' . 4 ( ' ,"66$="6 $ ( B N AABN "'• PQ?2 $ 9 / 8 ' )/( 1 ' 9 , F L ( /$2( +. $ C I6?+",=$$ G PQ ? 60 ' ' - ' ' ' '5 ' ' ' 6 ' + ' . ?' - ' ?' ' ' ' ) )A )L + ( 1 4 '4 4 4 4 PQ?D , (/ ' 1 0 $ 5 AE$ $ $ ? ) )A $ / ( 9 BBΩ " ( N ? ' LB$ V 4 '4 4 4 4 N N )PQ ) / I IA $ / ( I IA ( 1 / $ ( 0 4 I sIA '4 I sDIA 4 I s 1 IA 4 4 I sAIA +PQ ) / / 6 ( 9 $ / ( 9( 4 LRA '4 L 4 A 4 ARL ,PQ?D $ ' ( , 1I IA ) 1/I s IAsL? 5 CB =50 5 ( C ) / 5 DB` 5 DB` / 0 $ ∆ 4 ∆t = '4 ∆t = 4 ∆t = 4 ∆t = 4 ∆t = 40 Rmc∆T ε2 60Rmc∆T ε2 45Rmc∆T 16ε 2 30Rmc∆T 4ε 2 15Rmc∆T 8ε 2 .PQ?2 > / Ω BB N " 0 H 3 DA BL GR# m) 1 AAPB BL GR#4 $ 8 AB m) ) 8 1 0 BBm)( 4 S LP '4 AAPB 4 LLP 4 AEQP PQ? > / 0 ' @10 / 0 ' ( ( ' 1 / ( ( / I + ( 4 I+ '4 I+ 4 I+ 4 I+34 4 I34+ PQ? H-' $ $/ 6 36$ K e ; 0 e4 / EL` ABBS ABLE = ( ' - 3- 4 $( ' - 0( $ - ( ' $RR&&&RJJR OsL LBAB'AB $)"II6$ 4 $ ( 1 ( 9 ( ( ' ' '4 $ 1 ( ' ( 0 1 4 $ 1 ( ? ( ( 1 4 $ ( 1 ( ' ' 3 -4 ( 0 4 $ - 1 ( PQD2 > ( 1 3 0'4( 8 ' N$F s AN 0 EB $ " / s BA Ω / ' 0 3 G4 1 $ ( 9 V 4 $/2(EE& '4 " (PBG 4 $ / ' (Eq 4 $/5( EB` / ' PQDDD :5 ( / 3 N 4 > 01 BB N * AB N / DB q , / 4 '4 4 4 4 AB LB EB B AB PQD > ( '' ( / EB*( AAB N ' DB $ $ ' '( 9( B $ 1 (ABBN BA$ / (SSBq BD$ / (SBq BS$ / ( !A` / P?8(AAB N // 1 PQ?2 " ' 1 364 AN/34A Ω 0 1364SN/ 34DΩ 4 ) '4 , ' O )PQD > ( ' AAB N ( ( B $ $ / ( 2 ( ABBB q $ 8 1 8 / ( 4 ABB.A.BSB '4 ABB.A.BQ 4 DBB.D. 4 DBB.D.BSB 4 DBB.D. E +PQ $ 1 !EBBBBN ( 9( 4 1( '4 1' 4 1 G 4 /'1 ,PQ > ∆2s2$K2F( 0D Cs Ω)'∆2 (( 4 '4 4 4 .PQ? " ( ( C / ' 1 6 + 5 (( ' ( 8 , 4 ( ( '4 ( 8 ( 34 /( PQD = 5 ( > ' ? ( ' / ( 4 RD '4 RA 4 4 A 4 D PQUD , ( ' 1 ( / ( 1 $9/ 1 3 q7 B N4 $- 0 a 4 '4 4 4 4 EB$ AEN AE$ AEN EB$AEBN AE$AEBN !E$EBBN PQ D $ 1 ' q ? 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'4 (9 I@sLIHs PQ ? $51 ( > ( ( 9 5 () ' ( 1 6 ( 5 ( 0 ,f? $ H a ,- 1 ( ,f ( ,fN5 ' T$ RR&&&''RR'R5QABQ U + ( ' / BB N /AB" + 6 H '( 4 $H) M '4 $H) 6 4 $ H ) M H 4 $ H ) M $ 4 $H) ) PQ$'$ "( 1 ' + (2 2 8 2 " ( 2 / " F ( ( ( ' h/3PB:14( / 6 A, i 2 11 8 = A, i 2 11 10 = A, i 2 11 12 = A, i 2 11 14 = A, i 2 11 4 i1 = '4 i1 4 i1 4 i1 4 i1 24 A i 3 11 27 = A i 3 11 30 = A i 3 11 33 = A i 3 11 36 = A i 3 11 = = = = = = 30 A 11 35 A 11 40 A 11 45 A 11 50 A 11 PQD >( 6 s6As DN /I s BIAsLB I s B $ $ I P$ " IA( $/IA Aq + N " I(' * s B RA πsL 6 4 '4 4 4 4 N N N N C-P($1$T0196(- = N1LB BSR $ BRA PQ DD 1 11 C > ( ( 1 = 9 , 0 × 10 9 Nm 2 /C 2 4 πε 0 ) BRm) ) EDB R PQ?D " ' ' / $ ) ' B q ( BP $ = ' C-P($1$T0196(- 6 ' C - 6 @ M - 4 " ( ( ' F ' $ ( 0 [ BAE A F / - ) 5 '5 '4 " ( > ' 6 s P N /sA #Ω ? ( ' 0 , C-P($1$T019=-)L+ > ( 9 )' K(1 ( B$. K1( ABN. K ' 9 /PBq )PQR $ / S9( 4 LB '4 PB 4 AB 4 ADB +PQR " 2 9 4 B '4 E 4 AB 4 LB C-P($1$T0196(-, !( $ $] =2L)#]'$ +(LX]$ ) [ a ]π πε a . .LX $ ] ,PQ?D " 3;4 ( 5 <16( 8 ( ( " (;-( L[R]Q[# ( , [R][# >1 ( d # ; " 1 = 9 1 ? ( ' ; =/ #1%!( C-P($1$T019=-.L , SBB$ N 1 1 ( N 6 1' '' 2 $ N ( 1'1 = RR&#R&#R+p pN $BA'AB .PQ 2 + A N 1 . ' 8(1 ( 6 0 4 $ ( '4 j 1 4 j / 4 $ / PQ 2 > - ( (LNV / # ( ' - $ / -)s B RA 4 B '4 BL 4 B! 4 BQ C-)P($1$T0196(- (176( ! (5L 1 01%!( %'; "(- • $ s B R A . =ρs BRLs BBB #RL • N 1 s LB× BS R •)+#sPPL× BKLDG×s D D× BK EN×. •)πsL D PQ?R?2 > ' - 1εs AN/ 6 ' ( ( ' -,@'( / 2 + ' ( 4 =0 ' / 2 G '4 ) / ' 4 ) / I / 4 ?' / η ' ( 1 N ' 1 ε / ' / 4 @ 'G C-+P($1$T0196(- + ( 2 2 1 / ( ( 2 ; 5 1 ( 1 ) 1 - $( 5 +6 G 0 / d ' '# " SB` ' I$M$H:"G@. @6II$I",;. ?"$I6?+$"@@? +ML QDABBQ 3;>M$Io6?AB 4 ;>M$Ic6??+)N)/:5 =t RR&&&5'R 'R'RAB RBERu$ A!5AB PQ%"< "'IAsIL s AI $ N $ $F' PB 4 '4 4 4 4 EN3LRI 4$ LBN3LRI 4$ LBN3LRAI 4$ LBN3ARLI 4$ PBN3ARLI 4$ C-,P($1$T0196(- ) ABBS '- 5 1 ) 6 @1'2'= M?2$(( PQF > ( / EDBBBq d AB ) (LS)' ? 1 (0 - A! ) ( LS ) EDBBBq '1 /q B DDBBB BA LLBBB BL AABBB BD BBB BE BBBB 2F c - 2A6 2A 4 ! E#q '4 , H sAQ$ ,A9 $ AsLB$ 4 s $ 2A $ 9F ) ( (( ( ? F ) ( F ( 8 () A$s)r= $$3$4( ( ' 6 9 ( )= =$s)r= L ) / ( / ( $)$ $ ) ( 5 ( ) ( $ 2A-$ 2AF )2A$ +2A= ,2A6 .2A= 2A) 2A6 2A$ 2A= 2ABL 2A 4 i = 2 A ≅BP!$ 3 '4 ; ηG = 8 ≅BSQ 9 I ηR = 3 4 ≅B!E )2AF +2A) ,2A) .2A 4 "( ( ( G ( 8 ' 5 '4 " ( ( / / ( 3+ s N4 = / ( 3N4 /( 2A$ 2A) 2A) 2AF 2A$ 2A) )2AF +2A) ,2A$ .2A6 2A 4 IHsDSDΩ '4 ≈BLA0 2A6 2A) 2A6 2A B 2A 4 AB BD,RA '4 AN )2A$ +2A) ,2AQA .2A= 2AF 2A 4 6 0 / ( ( / /(( = '4 4 4 4 [LYN0![!4([ dN0 sB Ω IsB Ω ηsEB` $'( 2 ×' ' 2A) 2ABA 2 PQ? N( ( ' '2 ' '- @' '2 ( $ 1 ( 1 ( ) '2 ( = ' ( 1 ' '2 ( PQ = 1("" @E$" " 4 4 '4 4 ) ' ( 1 " " 1 4 4 PQ? " 9 ( 9( ' (/ 82 ' j ( 5 ,1 A ( 1 ' j A ( ( N " ( ( 8 LRD 8 A 6 ( 0 1; C4 hTY 3' 4 ) - .*' ) $ (! '( 9 4 '4 4 4 0 0 0 00 4 ? '4 ? 4 ? 4 ? 4 ?N PQ ?D >''5 5 ) '' '/IsSΩP B( '4 " ( 4 $ $= ( 8 4 $ $F )= 1 8 '" 4 $ $= F) / DE B0A, 1 0' " / AΩ 1EBN ( '' = µ s D π ⋅ BK! R$ 3'(4 4 '4 4 4 4 Aπ⋅ Dπ⋅ Pπ⋅ Sπ⋅ Qπ⋅ BKE BKE BKE BKE BKE PQ?F > ( ' ( ( - ( ( >10 ' ' $ ( ?'0- ( ( BBE (( E$10 ( 4 $ $= F) /1 )PQD2D 6 S Q:)"' ( ( ( $ ' H " ( ) B $ ( ( / / BA " ( ( ' FsA µ 0 i π d BD " ( 9 8 Fs µ 0 i 4π d BS " ( 98A Fs µ 0 i 4π d P " 5(@s µ 0 i1 ⋅ i 2 ⋅ ⋅ L 2π d +PQ R ,PQ?2 $ ' ' ( ' ' ( $ ( 1/0 $ ( - F " (3M 4 3MA ML4 $ ( ?'0 (' M ( $ ( ' ( !( • )H • I/I • MM • )M # • )MAML A# • M-(F • $ + 0 ' C ( 4 nY '4 Y n 4 Yn 4 n Y .PQ?D 6'- "$ 1 '5 ( ( " N' 4 '4 4 4 4 I3M04RHF I3M0A4RHFA I3M0A4RDHFA 3M04RAIHF 3M0A4RAIHF ) 4 $ -/5- 4 = - / 5- 4 , - 5- $ F ' 1 $ - = 2 (N 4 ( ( '4 ( ( 4 ( ( 4 ( ( 4 ( ( ( PQ ? " 2 C + - ? <H:) 3H : )4W - e$f e0f ) M( > ( " ) M( 1 8 + ( PQD >M( *( 1 ( E ' , '( ( H = '( 9( B "- '(*3:r64 BA + 5- ( - 5Bs E H BD , 5- ( ' BS $ ( P $ ( ( 4 M/ - 5- '4 M/ - 5- PQD >''(C '' , ( 4 C( 8 '' + '4 '' 0 C ( (('' 4 '' ( C (('' 4 8 '' C ( (( '' 4 '' C ( ( ( ''( PQ?2 = ( ' 1 , . 0 ( 0 + (0 4 5 ( 2 '4 5 ( 0 4 ' 4 PQ?2 N / 5 ' ) ' 0 $- 0 1 0 + 10 0 ' 4 '4 4 4 4 '- PQ *' ( O 4 @ '4 = ? 4 : 4 " 4 " )PQ $5-/ V0 ( B ( 4 '4 4 4 '- , ) +PQ?F 4 " ( 2 '4 " ' 1 ('( 1 4 $ / ( 8 4 "- ( ' ( 2D 4 " 5- ((8 = AsA AsD >3NFK N$4 @ ( B 3 4 9QBm B , 1 • • B 5 66 6? 6? . 5- B ,PQ $ @ D ( D > ( 2 .PQ22 >( ( e ' + ( ( D 4 ( J *(F( 4 5- (' ( '4 5- ( ' ( . 4 ( 5-5( [-.T-D. 4 ( 0 ( - 5- [-.T-D. PQ ?2 , ' ( ( B = 5- $ ( F ( PRA ) ' ' ( ( ( 4 '4 4 4 4 8 @J 8 )' G $ ) PQD >/ ( ( / $ - D ( 8 ?'((Q ⋅ B KL # 5- ( LB ⋅ BL R - ' (- ' $F =[ P⋅ BK Q) 4 DD⋅ BK SGDL!⋅ BKLAG '4 DD⋅ BKLAGBG 4 BGDL!⋅ BKL G 4 BGBG 4 DD⋅ B SGDL!⋅ BLAG PQD 6 ( - ( ( ' " 9 9 ( ( ,∆s ) 1$ PQD " ( ( ( $ / ( , ' 5 8 , A ''58 ( 8 ( 1 '' PQ "' $ ' , '/ = '( 9 ) ( (1 ' ' ' ' (( 4 '4 4 4 4 4 $ ' '4 " ' ( 4 "( ' 4 6' 1 ' 4 "- ' PQ $ @ S ' 1 > / ( I s BB P Ω 6 ' ( 1 H s B 6 / - BB > ( F s BS ( ' 3 4 sDG $ 2 1 B m) 4 '4 4 4 4 LBR ABR BR SBR BER C-P($1$T0196(-) !( $ $] =2L)#]'$ +(LX]$ ) [ a ]π πε a . .LX $ ] )PQ?D > ( " & ( B ( , BB 6' 5 ' ( (. B 6' 5 ( ' (. BA 6' 5 ' ( 5- . BL 6' 5 ' ' 1 . BD $9 8 2F 2 - 2A= 2A= 2A= 2A) 2A6 )2AL +2AF ,2AF .2A$ 2A$ 2A L 2AF 2AF 2A) 2A$ )2A$ +2A • $ 1 ( v1 = 2 v2 • $1( R 1 ,2AF .2A) 2A) 2A$ R2 = 1 2 2A εs − ∆Φ .∆Φ=Φ)0Φ. I 66, C M0MJ 1 SS! ' $' 6 ' QBE $ ' M0MJ ( < -/W ∆t ΦsD0. 2 Φ)sD0)sDπ a 4 A ΦsD0sDπ ∆Φ=Φ)0Φs −3 DπA 4 ∆s + ) ' @ ε= 3 DπAR 4 $1 ♦ . ♦ 0 / '7<(W 7 I6 s ε 3 Bπa 2 = R 4 R R 2A$ 2AF 2A) )2A@N@N@ ?E PQ?F +'' M9 ,& 6) PQD $ ' '( 9( B " I I 1 / BA > ( / ' 2 +# BD $-'( '2C ( 1 BS " C ( 0 ( P $ 0 ( - PQ?2 " A L D ( ' 6 DH ( ?' 0 $ H ( 0 $ ( / 0 D ' 6)"II6$? 4 '4 4 4 PQR > / G AB 1 - / + 1 '' 8 $ 0 ( 9 - 18 )EL LL1 A 0AB $- BB 4 PAE '4 AE 4 AEB 4 EBB PQ?D $ 6?$=$")"MFIR 0 E ' AB Cm6;5 0 C ) *) 4 :U ) + A $ LZP + LL ' $ 6 + 0 /4Y:U *' LZL YNN +7 ? P AB ' 0 L FRL M0 ( 2 $ 0 0 L (S 4 BB '4 EB 4 AE 4 AE 4 PA C-P($1$T0196(-) !( $ $] =2L)#]'$ +(LX]$ ) [ a ]π πε a .LX.$] )PQ?D ) 8 C BB $ 1 1 B $ $ 2 C ' BA V ( / BL , F / ( -' ( -' ( ( 2 +# BD +1/ ( ( 2 0 BN C-P($1$T019=-+L, $ ' ABBA !e h 1 ' ' ? ' ( ' 6 I 1 ' $ ' 5 $ $ ( 8 8 ' - 6I Q C ( = tRR&&&'RR DARRBPR pBPBQu 34$BA'AB +PQ 2 $ I 0 $ 5 4 " ( 1 2 8 '4 "(1 2 8 ( 4 $ 2 ( - 2 4 , ( 2 ( 0 ( 2 8 ,PQ 2 $ ' 2 8 0 4 "( / '4 " ( - 2 +# 4 $( '( ( / 4 $ C-P($1$T0196(-. (176( ! (5L 1 01%!( %'; "(- • $ s B R A . =ρs BRLs BBB #RL • N 1 s LB× BS R •)+#sPPL× BKLDG×s D D× BK EN×. •)πsL D .PQ?R?2 > 1 λ s DBB s DBB× BKQ s BB q R A = 6 QBE C ( 1 ( - > ' 91 4 -1 '4 ' A B 4 2 - C-P($1$T0196(- ? -s P× BK Q ). - s !× BKA! #. s BRA. s!P:.1s L× BSR PQ D ) 9 s BγsBγ 6sBγAB( γ = 1 / 1 − v 2 / c 2 ( H1 = 6A K AA s 3BA4A ' < 51W 2F ?E - 2A ♦ , 1 ( - 6 '5 < (W <(W ( 314 $' ( 1 3 4 / ' -60 5 / ♦ , 5/ ) 66 / ( 6 ( <2W 3 - 9 C (4 $ 6 2A D 2A= 2A$ 2A= )2AN@N@@ +2A) ,2A= .2A 4 εsDQ!× BK QG '4 sBB G 4 sAB × B P- 2A 6 $ 6 A G< 51 W= + s $ s B 6 s s PQDD] ><C " ' W'-6 1 3N4" ?'0 ' 1 $0 ' '( )?"D'0 $0' (-' '(/ 10 N 02'( 3 4 3) A:AA" 4 0 - 6 O 4 '4 N 4 4 N 4 N PQ%"'9(D] > <W-( 4 '4 ( 4 ' 4 2 4 5- PQ?] ,00C C @C ( GC '9 * ( CO 4 @ '4 *- ' 4 ?' , 4 )' - 1 4 @ PQD] " 1 >( '(1 (> ( (5 ( " ( ( - $ ( 4 V'- (' '4 $-' ' 4 $/ ((/1 ' 4 * 5 4 $((∆: PQ22] $( " '9 C$'' Espécie química Fenômeno Dióxido de carbono Formação do diamante Ozônio Água Queda de uma fruta Cozimento de um alimento Nitrogênio Surgimento de queimada Cloro Quebra de grafite =' 4 -('9 '4 C )PQ?] $ M G M '/0 '( - 1 / , 4 $' A34 '4 $ . 4 " 4 " +PQ DD] > ' / 1 > - (' / - $ ' ' / 4 H0(C 5O '4 + 5 ' ( = 5 ,PQ?2D] " 0 '9 ( 2 1 )/'9 3+q$#! ++6F#L_ABBP4 V'LEm)'('9 0 4 '4 4 4 4 - - - .PQ ?2] "' ?">]$M1!%7!9!(<>"'(= tRR&R01R R00000Ru $L AB LT$U V 4 ' '9 9 '4 -' ( 4 ( 9 1 4 ( 1/ 4 ' PQ] $ 3QEE` r DE` 4 ( 5 $ 8 +'0SEm) pppppppppppppppp $ 4 '4 4 4 4 -K K K K K PQ?F] " $ ( 1 > 4 $8' 8 '4 "(( 4 $ ( '9 4 $ BB)' 4 "(B) (('9 PQ?D] , '- ' $ '0 '9 " ' 1$ BB , ' B ,' BA $' BL )' ( ' ( BD ,' 2 h PQ ?D] $ ' 4 (' '4 ( 4 5 2 4 2(('10 4 ( PQD] $'( 9( B " ( '( BA $ - - - ... BD $-(' BS " 1 P @1 ' PQUD] 6 ) J $ * 0 4)J 7 < =*A 0 5 7 )*A J $ - J . ) $C $ " <=7 " 5 <= " H) $ J " ' 4 + J RR&&&A'RRRpp ppp )'( 4 '4 4 4 4 (' (-' (-'0 A (( 0 )PQ] ?<;(A OW)$'?' 0 )/ :5 < ( ' ( '?''' ?'(W ?''2 4 $-' '4 "(' '1 4 $' A 4 $2''(( +PQ?22] " 3 - '4 ( / 8 ' ' 1 3A`4 6 ' 61$' )' 4 '1 ( =/. '4 /-' ,PQ ?] "(,2(1' , ( 'MV '$ AAB A 4 '4 4 4 4 1 ' ' .PQD2] "' N , ^ $ 4 '4 4 4 "/ $ "N( $ PQ?DF] , ( 1' "'(( ( '( ( $ '55 = tRR'R&RAB ARBLR#0J00J0u$ EAB A = ' ( ( 4 '4 4 4 4 "-' $ '( "-' "('9 "'('' PQD] $3434'( 934 B $(C'9 BA ?'9-/ BD $()")"A)"LAK'9- BS " ' ' - ' 'A'L P "-"A(1C ((9 PQ%"'9(D] ) ' ' - ?/ 4 '4 4 4 4 ' ' ' - '- PQ?2D] 6 '- '8''9 , 2 4 '4 4 4 4 A.. L... L... D.... D.... PQ?2D] $ ( '9 $ '9 '9 // 4 ^ '4 ^ 4 $ 4 $ 4 $ PQD2D] = ' ' ) B " ('9 BA "AD/ BD " A L D A D /L(/ BS "LD P " A 10 )PQ DD] )5O<>/ / ( ' )0 SBBB '9-'$:DBDE DE`3R4W ?'5 4 2 '(DE '4 -'( DE 4 2-' (DE 4 ' (DE BB +PQD2D] )' Vinagre Acetona Grafite Gasolina comum Água potável Gás carbônico Ar atmosférico não poluído Hidrogênio gasoso B ;'C'9 BA N( BD :/('9 BS ^'C/ ,PQD] )('''AEm) '( 9( B $(/' - (/ + BA " / 0'(/ BD 3$F)=64'9 BS $$=/ 5( P $$)(( / .PQ? DD] >''' '- / J A L '9 6J ' 6JA/ 6JL'1 )/ ?-J / A "JAL L $J A/ 63434 4 '4 A 4 L 4 L 4 AL PQ?D] $('1'( 1 > " '9 - $ L)3":4Ar$A3?"D4L→L)?"DrA$3":4L $( 4 '4 4 4 4 , PQ?'%9 '"%D] " 3$$?4 ( $ '- ( 9 ( " $$? ( ' $ $$? ( 1 $- $$? 1 ( - 3&&&'$4 " 1 1 $$? 4 '4 4 4 4 1 ' 1 ' PQ?22] > - 0 +'91/ 3( 4-' '9 )' 4 ( 1'9. '4 ( 1'9( 1'9 PQ] = '8/ 1- 4 '4 4 4 = ( ? ( = H ( . PQ?'%/$A"( 1$A"D] $ 5 ⋅!$*'% 9P\nYN ⋅*'%*') F 4 #F*' ⋅1*' ⋅(% )#9 ⋅! %4 ⋅1%)*' )+# ⋅(*'%$ #J 32# BB!AB L$4 6 5 4 '4 4 4 4 1 1 PQ] 6 1 BBHEBH / ( BB H ,) $- 3&&&'$4 "( 4 '4 4 4 4 P ` LQ` AS` AA` ` )PQ ?D] "-((-0 4 '4 4 4 4 +PQ?2] $ BBLRH BLBRH > ' 5 2 >'5 > $RH 4 QBBK BBK BBL '4 BBBK BBBK BBB 4 BSBK BBK BLB 4 BBKQEBK BAB ,PQ R] ><$W5 ((QE`E` '( ><FW5 ((QE` E`'(A6AE) ''( '6 0''"O 4 , 5 ' 8 '4 , 5 ' 8 4 $' ' 8 / 4 " ' ' '( 8 4 " ' ' '( A 8 .PQD] $ 0 ' " '( + BBH BBH '0 Em) " ( ,( QDHABBH $(BSBRH( BBRH8' )'( 4 '4 4 4 4 1( BBRH (EB` (/1 BBH QB ( PQ ?] $'-3#434 34G' 3H43H4M/ (V '9( ( 4 '4 ( 4 4 4 PQ?22] > 2' ' ' )0'AE 1 AE0 4 '4 4 4 4 + $ + $ ) PQ?D] $($ - * BB0 ) ^ BBRL ;BQARL 4 '4 4 4 4 QAL DEL BQL QPL QAL PQ2] $6 8'0 ' "- 4 '4 4 4 ( ( PQ] $2210 ('( ' $ ' ( @A"LrL)"→A@rL)"A !(6 3∆O4AEm)#GR $ 3O4AEm)( 4 '4 4 4 4 ADS#GR KADS#GR ED A#GR KED A#GR LASA#GR PQ DD] 6 / ' ? @ ? ? ) " 1 BC $ 'D ( C - /6'AB Lq6> $( '9 1 4 ) ' ( C '4 = #GK '9 C 30LPP4 - / 3SA4 30ADA4 ( ( (O G )PQ?'%9 '"%D] , '- )' $'#GR( 4 '4 4 4 4 KE! rA ! K!SQ KA ! rE! +PQ%"'9(D] AM34r"A34→AM"34 6 :msKPB P#G + ( 4 (( '4 M34r 1 "A34→M"34∆:msKPB P#G 2 4 M34r"A34rLBBS#G→M"34 4 AM34r"A34rPB P#G→AM"34 4 ,PQ%"<'F] = ( ' ? ( ( 1 V' $ ('1 6 8'?$ ( 5 " ( 'DE- 3M$)6=". ,";>6I$AB A. AP0 AS4 M$)6="=.,";>6I$9 :?+$'AAS!DELSAB A )0 8'( B $1' BA $ 0'( BL " ( 1 ' BD $1'9 BE " ' ' ' .PQD] $3434'( 934 B *(8 '' BA "∆: BD "∆: BS $ ' ' ' ' P ? )K)(LDS#GR )≡)( BDD #GR PQD2D] ) :A"34→:A"34→:A"34 B $( :A"34t:A"34t:A"34 BA $1 ( BD , ( BS , '∆:tB P $1 (3∆:uB4 PQ?] @'>"H Q'AB L' 1''<]b1 >N / )" J )$ *' ]qb= !()' 3)A:P"344 5K LPS#GR) AR.: R." PR @RR'R0'R0RR AB LRBQR QR100000000 ''01,sDBDR BRAB L F (X'9( 4 $ ' E ' ' 3 -4LDAB#G '4 " 0'(2 4 "' 4 ,(' (S PQ?'%/$A"( 1$A"D] $ -' )P: A"P34rP"A34→P)"A34rP:A"34 B !(∆: 'sKASBA!#GR ) BB3)P: A"P45 ( 4 L #G' '4 L #G' 4 E#G' 4 E#G' 4 PA#G' ) PQ?'" "9(!( ('AD] ;+'< 3RR1''RR4 $( AB L LE1 EBB#(( ?' / ' / K A P' )P: A"P1 P!B#1 4 AD '4 LE 4 SB 4 ADB 4 LPB PQD] ) '314 /( 13 C 4 H10(g ) + O 2( g ) → 4CO 2( g ) + 5H 2 O (l) 2 =3)s A."s P:s K 4 ?''' N N $ (( $ (( ?ES')"A1(DPBH3),+4 ?'QB`)"A1SBPDH3),+4 $ '' $(( 4 '4 4 4 4 N NN N NN PQ] = ):D34rA"A34→A:A"34r)"A34.∆:sKAAB#R0 4 '4 4 4 4 'LA'DDB# 'DS'PPB# 'LAA"A34 ' PB'AAB# (( + )PQ22] $ ' (9' + 0 >( 5 5 H H C H C + H H Metal H H C C H H H H H C C = +146.0 kcal.mol-1 C H = +100.0 kcal.mol-1 C C = +82.9 kcal.mol-1 H H = +104.2 kcal.mol-1 )0 0 #K ( 4 PB '4 LL 4 DLL 4 P! +PQ?F] Ligação química Energia de ligação H−I (kJmol −1 ) 300 Cl − Cl 243 H − Cl 433 I−I 152 A:34r)A34→A:)34rA34 $ (' 6 ;'< ( 0 * ( ;'0<$ '9 '(0 ' $ ' ( 4 $(:34((A34 '4 $ (DDL#G 4 $ ( LLQ#GK 4 $ ' !E#G 4 " ' B S#G , ,PQ?2] . $ '0 )K )!Q #@$H?$ 4 '4 4 4 $ )K:( QQB#K $ :K::A( BDA#K $ '9(KABL#K $' AB'( ! !#K .PQ?] ) '∆:s0 ED#GR )(- )s)( '( 9 =+ 3(4 )K)ADL#GR)K)LD!#GR)K)LL #GR 4 '4 4 4 !PP#GR APE#GR PQD#GR P A#GR )PQ?22] $' +(' 3#R4 ( 4 '4 4 4 4 SP DED PPS LDD PPS LD !!S LDD !!S LD )PQ] 6'2 " - $ )L:E,L"Q34 ( ,A34 )"A34 :A"34 "A34 $ ' $ ( $ ∆:uB $ ( $'( 9 4 ?( '4 ?( 4 ?( 4 ? 4 ? )PQ?2] $ M o34( 024( M o34r4:A"34→TM3:A"44U o34 )01 0ar34MAr34)r34 / ( 4 MAr34tar34t)r34 '4 MAr34t)r34tar34 4 ar34t)r34tMAr34 4 )r34tar34tMAr34 )PQ?2D] " ( ( 6 ( C'(- "):@L(1 ):D34rL@A34→):@L34rL:@34 ) !( ∆H 0f ( kJ ⋅ mol −1 ) − 1437 CHF3 (g ) CH 4 (g ) HF(g ) − 75 − 271 $0 #GK ( 4 '4 4 4 4 K PLL KA !E KALAE r PLL rA !E )PQ] , ' ' 6 ( ) 4 '4 4 4 :A34r}"A34→:A"34KPSL# :A"34KPSL#→:A34r}"A34 :A"34→:A34r}"A34rPSL# :A34r}"A34→:A"34rPSL# )PQUD] "' ' ' 1 ) ' ( ) 4 )"A34→)34r"A34 '4 4 4 4 1 CO ( g ) + O 2(g ) → CO 2 ( g ) 2 1 C (graf) + O 2( g ) → CO ( g ) 2 1 CO 2 ( g ) → CO ( g ) + O 2 ( g ) 2 C ( graf ) + O 2 ( g ) → CO 2( g ) ∆:srLQD:GR ∆H° = −284 KJ / mol ∆H° = +110KJ/mol ∆H° = +284KJ/mol ∆H° = −394KJ / mol ) ))PQDD] "CF0 :'"F0:' 3a)4 $(,)"II6" 4 '4 4 4 4 ' (SQ#GR )0)(ADD#GR a)34(K! !#GR 1 a34(D S#GR (( )+PQ?F] $91 ( " -234 > 4 $ -234(KQB#GK '4 $:34"A341 B:"34 4 $ -234 (8 '9 4 $' -234( ' - 4 $ ),PQD2D] =7710 ( + ( 1 - ( /" (') B $ ((( BA $ (∆:s−SB#R BD "Y BS $ M34:A"34FM3":4A34:A34 P $ $F' ).PQ?22] $ 3∆:4 ( 1 8 $ . )L:S34rE"A34→L)"A34rD:A"34∆:msKAAAB#G . )34r"A34→)"A34∆:msKLQD#G . :A34r}"A34→:A"34∆:msKASP#G $ ' +PQUD] "3#4( (2 ('("' ( '0' R > ( ) 34 ) A:AP34→)P: D34rA)L:P34 ? ' 0 / ' ) A:AP34r 37 "A34→ A)"A34r L:A"34∆:m)sK!E LB#GR 2 )P: D34r 19 "A34→P)"A34r!:A"34∆:m)sKD PLB#GR 2 9 )L:P34r "A34→L)"A34rL:A"34∆:m)sKAAABB#GR 2 >1 H : 0 0 4 '4 4 4 4 K LSQPB#GR K LBB#GR r BQBB#GR r LBB#GR r LSQPB#GR +PQ] ) #GR )"34r:A34→)34r:A"34∆:sK EB#GR )"34r}"A34→)"A34∆:sKA!L#GR :A34r}"A34→:A"34∆:sKAL #GR +0 ' )34 )"A34( 4 '4 4 4 4 KPED#GR KEBD#GR rEBD#GR rPED#GR KLED#GR +PQ ?2] " ' 34 ( '9 -V21 'N5 +'34r)A34→+')A34∆:sKLEQD# ∆:sKLAQL# +'34rA)A34→+')D34 V ∆:B +'34rA)A34→+')D34( ) 4 '4 4 4 4 KLB #G rLB #G KPBA#G rPSS!#G KPSS!#G +PQ ?] = ∆:sKE! E#G A:A34r"A34→A:A"34. ,A"E34r:A"34→A:,"L34. ∆:sK!PP#G },A34rLRA"A34r}:A34→:,"L34.∆:sK !D#G $ ∆: A,A34rE"A34→A,A"E34 4 KLP!#G '4 KAS!#G 4 rLP!#G 4 rAS!#G 4 rLSL#G +PQD] ) '3AEm) 4'( 9( ?34r"A34→?"A34∆:sKAQ!#GR )34r"A34→)"A34∆:sKLQD#GR )34rA?34→)?A34∆:srSS#GR B $ '(K B!P#GR )?A34rL"A34→)"A34rA?"A34 BA $ '(( )"A34rA?"A34→)?A34rL"A34 BD $ )"A34 ' ?"A34 BS $ A )"A34 /(!SS#GR P $ )?A34(( +PQR] $ ' / :A"34r)34→)"34r:A34 , AE) ) :A34r 1 "A34→:A"34∆:msKADAB#G 2 )34r"A34→)"A34∆:msKLQLE#G "A34rA)"34→A)"A34∆:msKD!!B#G )5 #/ +)PQ?22] " ( ' 5 6 ( ' 2 6'8 ( ( ? 2 ? 2 )' 4 /(3"4#Ω) $s BKL$ N $K s Ω '4 '1 ' ++PQ ?2] 6 3'14('( 9( 4 ''1L '4 "' ALAL 4 ''1A 4 ''1 4 "'(LA +,PQ?D] "'/' LA6' 'C'1 )) 2 9 $ 9C )+ $ ' ' C $'''A A $'''A L $' 2 ' ' 'L D "2'''L( P $ 4 '4 4 4 4 ? L ?AD ?ALD ? AL $ ALD +.PQ?] " - ' 1 ' $ '1 '( 4 A '4 LA 4 L 4 A 4 L ,PQ?] $' ?' 4 '4 4 4 4 $ δ)K)(AKL $ δ)K:(LK $ δ)K:(LKA $ π)K)(K $ π)K:(AK ,PQ] ;*"9(*'<$ ( $' 4 @ '(L '4 "'(' 4 $ 4 H0 / ,PQD] $'( 9( B )'//9 BA $ '1 ( 1 ' BD , ' ( ' BS ,(' P "'C ,PQ?] $ ' 1 $1C ' O 34 ( ( 5 ou $(( 4 '4 4 4 4 + +-)E:P ,''1 ,/ +''1L ,PQ ?2] $( '( 9'C ):L):):L):A)): ), 4 '4 4 4 4 ,PQDR] I 5 F 5 6 > -'1 =0'1 4 '4 4 4 4 -)Q: ,L"A' -)Q:Q,L"A' -)Q: L,L"A/' 3π4 3σ4 3π41 3σ4 ,)PQ] $ ( ' 5- 9>(,a O O ):$,6$>?:">IGM/R(1 %(< #%"' /$"9 4PSALABBL34 6,a'O ). 4 '4 4 4 4 M )' - $'C +( ,+PQ?D9 *("R] $( )10 ' 9 ('6 1 $' 9 4 *'9 O '4 *( ('O ,,PQ] > q1 ' ' C '( OH H H H O TESTOSTERONA ) 8(0 4 '4 4 4 P' 'C(/ ' (C-) !:AD"A + ,.PQ] + SES SP @ $ a#( $' ? ) $ M F / ' 9 $ ' 0 9)' 9 9 29 4 $/ '4 + 4 ) ' 4 6/ 4 F' .PQ] = AB A '1 L ' ?' ' 1 ( APD , .(18' C(161'( 1, 1(3(4 C3'4'1C3'4 ,8 4 "( (DB` '4 "( 4 "9'1 4 "'1('1 .PQ] "( V1 O H 3C O NH HO CAPSAICINA ? 9 4 '4 4 4 '( ( ( ( + .PQ] , ( N ) :- ( '6-( 1 " M( ?( 6 $ " 0 '( ' ' 6 (5' O OH O O $ 9 4 '4 4 4 4 '( ( ( .PQ] $-('9 " ' ' 6 ' ' > F > '( 3):L)""4A+'rA):L)")→+')ArAY ) 0Y( 4 '4 ( 4 ( 4 ' .PQD] $ $'('- 1 9 $ 00 2 F ( ' 0 '( N 1e 11 6 / - + $( 6 8 ( + 4 ('-): '4 (-5- - 4 'C 4 '1 E-' A 4 (''3AEBR4 .PQ%"< ] " - 5 + 3B)) 4 ( '$A3+H$A4=(/ - , ( 9 4 '4 4 4 4 '( '( '( '( (( .)PQ 2] $((( *90 HO O O CH3 O 4 '4 4 4 '( '( .+PQR] " - ( ( - O H + " - ( ( - .,PQ?2D] + 1 / 1 ( "' $-1 ' ( 4 '4 4 4 4 A L D E ..PQ?] ) -/ A,A"E34→D,"A34r"A34 )-/5P× BKL HKK'( 9( ,"AHKK 4 S× BKL '4 AD× BKL 4 P× BKL 4 A× BKL PQ?D] 0 / M :)> :) - 1 ' ( J - /' - / 1 ' "'''' ' 4 $ ' * :A6 6 M ' 0 '9 '4 ,'''1 M + PQ?2] ) ( $ F )=, BPB $ PB F $- F DB)AB='DB$ $ ' ( 4 $rF→)r= '4 $rLF→A)r= 4 A$rLF→A)r= 4 L$rLF→A)r= PQ%"'9(D] ) A,"A34→A,"34r"A34 ) 1 -/LA× BKLR,( /R( 4 P× BKL '4 DS× BKL 4 LA× BKL 4 PD× BKL 4 BA× BKL PQD] + 1 5 " 15'1 1$ '314 /( C 4 H10(g ) + 13 O 2( g ) → 4CO 2( g ) + 5H 2 O (l) 2 "' 'RH [C 4 H10 ](mol/L) 22,4 20,8 18,2 16,6 15,4 14,9 Tempo(horas) 0 1 2 3 4 5 $(1BE L 4 K ERHKA RH '4 ERHA RH 4 ERHKA RH 4 A RH ERH 4 K ERHA RH +) PQ DD] *''-QB`(' 6 ( '1 ? ( " ' ( - ALD 4 = D - '1 ' O6 '4 >'C1- BB Q) G =$ 34(ALBB 3$q#@ )!U DE3L4AB!0AAD Q!!4 PQD] " -( 1 1 - 1 $ 1 ( ' / $ ( )A:E?:34r:A34→)A:P34r:A?34 4 ? 1 5 1 '- / Experiências [Etanotiol] [Hidrogênio] Velocidade inicial 1 (mol/L) 2 (mol/L) 1 (mol/min) 4 2 2 2 8 3 3 6 8 4 6 6 16 )'' '4 ) ( 1 ( BR R ++ )PQ] > 1 LDD H ),+ , -'' ( 4 PB(R '4 PBA BAL(R 4 SDR 4 AADHR 4 PBR +PQ?D] >29 1 " ( $ArFA→A$F $ 4 '4 4 4 4 (∆:sK B#G (∆:sr B#G (LB#G (LB#G (DB#G ,PQ22] = $ 8 "' ( $F8 )= +, )' 0 4 '4 4 4 ( E#G (DB#G (( (0LB#G .PQ22] "/ ):D34rA"A34→)"A34rA:A"34 = 'C ( +. PQ%"$(%92] $ 11 ) / 4 '4 4 4 $1 1 ,1 $ ≥ $ 1 PQ R] " ' 1 6 ) '( 4 '4 4 4 $ ' $A ' $ 6 r6L $ A ' (6Ar6L 4 $ ' (6 PQ2] $ , 3∆:4 4 '4 4 4 . . '. '. , PQ?D] > ' + S ' EB H :) 6 ' 1 ' $ ' C -( ,": " ' BB H " ' Volume de Volume Volume de Temperatura de H 2 O 1 2 HCl (aq) (mL) 50 50 (mL) 50 45 NaOH (aq) (mL) 0 5 máxima ( º C) 23,0 24,4 3 4 5 6 50 50 50 50 40 35 30 25 10 15 20 25 25,8 27,2 28,6 30,0 7 8 50 50 20 15 30 35 30,0 30,0 Tubo 4 ) ' ,": '4 $ '''OG ' 4 ) H0 :)' ,":1ABH0 PQ] )('@? :) @34rA:)34→@)A34r:A34 $@$ ( 4 KK '4 KK 4 KK 4 KK 4 KK , PQ R] ) +$rF)→$)rF ?$)r=→$r)= "( ' = ( 4 3A43L4 F '4 3 4 4 3D40000000000 4 3E4(2 4 ( )PQ?2D] " -' ' ? ($rF→ )r= / 6 8 ( 4 ' '4 ' , 4 ' 4 ' 4 ' +PQUD] > (0 0 -''-$1 ( $- ' C ' ( '' Método 1 2 3 4 Estado do Temperatura Tempo Comprimido da água de reação Inteiro 10º C 50 s Triturado 60º C 15 s Inteiro 60º C 25 s Triturado 10º C 30 s = ' ' 1 $ ( 3 4 $ 15 $/(/ = (1 4 '4 4 4 4 ,PQ] " - / ," ,"A - ' 1C" 6 "Lr,"→"Ar,"A 6A,"Ar"L→A"Ar," 6 "%'( 9 , 4 '4 4 4 4 ","( ""A( 1C ",","A 0/ " C-P($1$T0196(-. , (#1$($9!( = 0 5 ' 1 $ 8 D BB':5- (C ( > ( )/ F- > @ M 7 '$( $,N?$@=$6> = BB'9''- 511 $ '9 H - ( - 3$I75AB AB4 .PQD$D] V'9 4 '4 2 4 1 4 -5 4 - C-P($1$T0196(- "/ / ( 1 ' 6 ' PQ?'!"@%'"!&!!F 9(D] ) RA,A34r RA"A34→,"34∆:srQB#GR," $ ( 4 '4 4 4 4 ,A34r"A34→A,"34rQB#G RA,A34r RA"A34→,"34r SB#G ,A34r"A34rQB#G→A,"34 ,A34r"A34r SB#G→A,"34 ,A34r"A34→A,"34r SB#G C-P($1$T0196(- $ / , 1 0 / $F?+ 3&&&'$4 PQ?'!"@%'"!&!!F 9(D] ' ( 4 '4 4 4 4 C-P($1$T0196(- " / ' +-0 '' ( + / ''5 ( ' 1 / ) :A 1 ' :L)0):A0":34rA:A"34r}"A34→E:A34rA)"A34 PQ?2D] ) ∆:')A:E":sK LPS#GK ∆: :A"sKASP#GK , +0 / #G( 4 '4 4 4 4 rPA r PED KPA K BSA KA!QS ,) C-P($1$T0196(- =t&&& 'RR BSALB 000000u $AQ'AB A PQ?D9 *("R] = ' 5( $ 4 ( '4 1 - ( 4 - ( 4 ' ( 4 ( C-)P($1$T0196(- 0*+ 0 ) 63;0(! 6:!0 ) / *)5*) J + # )$ //O# 7)/ 35"92"1'AB AAD4 PQD$D] "**+ SSLB#GR#($' ' )A:P" 3 s AQ PDB #GR#4( 4 LE '4 !A 4 BB 4 AS 4 EB C-+P($1$T0196(- 0 / )$#) (J > 5'' '? # )$ wz ' 5 ' $ $ ( ' )0 $ *7 ) *' 35"92"1'AB A!!4 =I ') *' ) A:AA" r:A"→D)A:E":rD)"Ar QP#G PQD$D] +') *' 4 ' DQ#G '4 ' QS#G 4 ' QP#G 4 ' DQ#G 4 ' QP#G C-,P($1$T0196(-) "( '$( ( ' ' $ '0 $ - ( '- 'C $ 0 ( 1 '1 =( 1 '( ' 9 $ ' ( - 3)P: B"E434r:A"34→)P: A"P34 - 5 1 $ A Em)' 2BD`/ G- ,+ 1 QB`( ' ( ' ' 3?6H67:M.+"Ha$I+"NAB ADB0DE4 ?6H67:M+.+"Ha$I+"N= '"%9"<"'$ "'%F " ?+= BAB A )PQFF] " ' ' 9' )0 B!P#RH B!QRLABm) ( A× BKL)K 1 (B!DDMGRH ? 34 $(AEm)PS!m) 34 $ABm)( !!× BA#RL 34 >PB'EBB ABm) ? ( LEm) ' ' 34 " BL!DD× BPG1 $/'( B NNN@ BA NN@N BL @@@N BD @NN@ BE @@N@ C-.P($1$T019=-+L, $' ,, +PQ%"'9(D] ? ( 4 1 -- '4 1 -- 4 1 -- 4 1 -1 -- 4 -1 ,PQ%"'9(D] $ ---3-4 ( 4 ∆:EK∆:AK∆: '4 ∆: r∆:Ar∆:Lr∆:D 4 ∆:EK∆:LK∆:D 4 ∆:Er∆:Lr∆:D 4 ∆: r∆:Lr∆:D C-P($1$T0196(-. f / ( $ '(( " '( '-5 O H 2C O C C17H31 O HC O C C17H33 etanol O H 2C O C C17H31 O etanol glicerina + 2 CH3CH2-O-C-C17H31 + éster do ácido linoleico O + CH3CH2-O-C-C17H33 éster do ácido oleico .PQ?2] H'C8'(( , H'(2 'C ,. C-P($1$T0196(- + ( K A 1 '9 aA?A"S 1 aA?A"L1 $ (' 0176(76( aA?A"S34rAa34→AaA?"D34rA34 AaA?A"L34rA34→aA?D"P34rAa34 PQ?2] )0 '0((CD H ' C-P($1$T0196(- ) ''- -' 6 MD BAR ' B-YN.*' *' % /NY\ +LB - $G //+). 3&&&''4 PQ?RD] $'C'- 4 ( '4 ' . 4 ( 4 (' 4 C-P($1$T0196(- = AB ! - ? + I M- F 3IMF4 8 - '( F > - - 0AD ' 6 -20AL! @0AD ' )?2+3)"?+$4 $ ' ->"A>@P >"A34rD:@34→>@D34rA:A"34 >@D34r@A34→>@P34 3$&&&''R00RAB ARBAR 0000'000 00AB !:F"= +6,R),6,ABBQ&&&'4 PQ?2D] )' Substância ∆H of (kJ ⋅ mol −1 ) − 1100 UO 2 (s) UF4 (s) UF6 (g ) − 1900 − 2150 HF(g ) H 2 O (g ) − 270 − 242 " ' >@P #G⋅K ( 4 4 4 4 4 KDED K!PD K APD rDED r APD C-P($1$T0196(- " ( 9 $ '1 . ):L0):A0":34rL"A34→A)"A34rL:A"34∆:sK LPPS#G pppppppppppppppppppppppppppppppppppppppppppppp CH 3 CH 3 C CH 3 CH2 CH CH3(l) rAERA"A34→S)"A34rQ:A"34∆:sKEDP B#G CH3 PQ?D] = )"A34∆:sKLQL#GR :A"34∆:sKASP#GR 0 ' (#GR 4 K B!E '4 r B!E 4 KA!!A 4 rA!!A 4 rPS!! C-P($1$T0196(- 2" LNN + ) / G 1 * G $ )$ " 5 + ' + 0 *' *' *'% O CH2 O C R O CH O C R + 2H2O lipase O CH2 O C R triacilglicerol CH 2 OH O lipase CH O CH 2 OH C O R + 2R C OH monoacilglicerol 3=$>#+" 7 QQA$4 . PQ?D] , 0pppppppp pppppppp pppppppp $ 4 1KK '4 KK 4 1KK 4 1KK 4 KK C-)P($1$T0196(- 5 4" ) !e LPYY 0 LPP\ B 4 ) A *'3 $ +4" Ld5 LP5 LR5 3 4 ) 9 4" ) G -5Y. + 1' 7*A4" 3 *' 5Y 3RR'$4 PQ?'%/$A"( 1$A"D] 6' 0"A 8'" 1 3&&&4 " Am) AAm) ( 4 '4 4 4 4 / Am)(BBSH"AR /(5 /AAm) B / ( ( B 1 ( . C-+P($1$T0196(-) $ 3)P:E,:A4 (0 2 /' '1 D)P:E,"ArQ@rD:A"→D)P:E,:ArL@L"DrEDB#G )PQ?'!"@%'"!&!!F 9(D] $ '∆:#G( 4 K PSB '4 K LE 4 rA PB 4 KA PB 4 r LE 6Y" S0)8 L! >1 ''- +PQ%"'9(D] ) ' ,( 4 //' '4 4 ' 4 ' / 4 C-.P($1$T0196(-, 2- 9-3"A4' ( !B` "A - ( ' 8 / . - "A34r)34→34r)"A34∆: srEEB#G⋅K 9 34rA)A34→)D34∆: sKSBD#G⋅K 9/ )D34r"A34→"A34rA)A34∆: sK DB#G⋅K ,PQDD] )( )D34"A34( 4 '4 4 4 4 (' LED#G (' AED#G (' AED#G (' LED#G (' SBD#G C-P($1$T0196(-. = ( ( ( + ( 1 2 9 ( 2 '' $ ' 33ABBL$4 .PQ?'%9 '"%D] ) 2 # s DA #G ( (1 29 ABBB# 4 '4 4 4 4 ` A` L` D` E` . C-P($1$T0196(- " ' $ ' 2 ' )P: A"P34rP"A34→P)"A34rP:A"34r $' H H O C C OH C O HO C H H H C OH HO C H H C OH H C OH H C OH H C OH CH2OH CH 2OH d-frutose d-glicose $'1 $ '''1 C'0 H CH 2OH O OH O C OH OH CH2OH H C OH HO C H H C OH H C OH O OH OH OH CH2OH α-d-glicose OH β-d-glicose d-glicose PQ?] 6 3OB)4AEm) composto ǻH 0 f (kJ/mol) C 6 H12 O 6 (s) − 1.271 CO 2 (g) H 2 O(l) − 393,5 − 285,8 )' ' 'AEm) 4 '4 4 4 KAABQ#GR KAPBD#GR KASBE#GR K EBS#GR .) 2F HE - 2A6 2AF 2A$ 2A$ 2A 4 "L s 1C. ,A s / )A s '4 @ 1 )2A= +2A 4 $ - ( ' 6 / - '4 $ 5 - d - ,2A$ .2AF 2AF 2A= 2A@NN@@ 2A$ 2A L 2A) )2A) +2A 4 .+ '4 $( '( -' ,2A$ .2A$ 2A) 2A ! 2AF 2AF 2A= 2AAL )2AF +2AB! ,2AAD .2A) 2A) 2A) 2A 4 = '4 = ,). = 0 2AF 2AF 2A= )2AF +2A= ,2A6 .2A) 2A) 2A6 2A) 2AF 2AF 2A 4 $ (C( ,:D,"L→,A"rA:A" '4 $ ( ∆:sΣ:KΣ: ,:D,"L→,A"rA:A" KLPPrSAA3KADA4. ∆:sKDSDrSArLPPsKLP#GK ) ( 0 ( )2A$ +2AF ,2ABA .2AB! 2AA! 2AF 2A= 2AF 2A6 2A$ )2AF +2A= ,2A$ .2A= )2A= )2A$ )2A= )2AF )2A= )2A) ))2A) )+2A$ ),2AL ).2A + ' ' 0 ' ( 1 5 2 +0 ' 4 )L:S34rE"A34→L)"A34rD:A"34 ∆:msKAAAB#G 3 ∆:m4 Q# _ KQ → K,Q# _ Q#∆ ∆Ka_[R ., 4 )34 r "A34 → )"A34 ∆:m s K LQD#G 3 L4 Q# <"9_Q#→ →Q#∆ ∆K aXQK.[RaK,[R 4 :A34r}"A34→:A"34∆:msKASP #G 3 D4 KQ#_Q#→ →KQ∆ ∆Ka XQK,)[RaK[R ?0 =: Q# _ KQ → K,Q# _ Q# ∆Ka_[R ∆KaK Q# <"9_Q#→ →Q#∆ ,[R KQ# _ Q# → KQ ∆K a K [R ggggggggggggggggggggggggggggggggggg →K,Q#∆ ∆KaK Q# <"9_KQ#→ )[R +2A) +2A6 +2AF +2A= +2AA +2ADLE× BD#G )' +)2A 4 Is × BEΩ BB#Ω " I '( ' 1 '4 $ ' 1 / ' > 1 ( / 2 '1 (A ++2A6 +,2AF +.2A) ,2A= ,2A) ,2AAS ,2A) ,2A= ,2A= ,)2A$ ,+2A 4 9 A L . L '4 ( / 'C ,,2A) ,.2A6 .2AF .2A= .2A$ .2A$ QD47'- .2A) .)2A= .. .+2A $ '1 ( ' '4 ) O OH .,2A) ..2A= 2A 4 )' ' ( 6 B K E L K BLs EL s ∆V ∆t = 15 L )s3ALBB×BB Q4sDL! "'0 3A.DL!4 - L R KALPLKA! LsQL sQLR '4 2AF 2A$ 2AF 2A 4 $ ( 8 D $ - '1 ' $ ' '1 2A 4 $ ( s # ⋅ T6U⋅T:AU ( A '4 JsLDBR:A? )2A6 +2A= ,2A= .2A$ 2A) 2A6 2A= 2A 4 '4 $ ' ' 3(4 8 1 4 RH 2AF 2A) )2A= +2AF ,2AF .2A$ 2A= 2AF 2A$ 2A= 2AF 2A= )2ABD +2A= ,2A$ .2A " ( 'C " 2 ( "( 'C " 2 ( 2A , 8 1 $ 1 / , 1 2A6 2A$ 2A) 2A= 2A$ )2AF +2A= ,2AF .2A$ 2A)