• No se han encontrado resultados

MA 1112 Mike Prepas pdf

N/A
N/A
Protected

Academic year: 2020

Share "MA 1112 Mike Prepas pdf"

Copied!
54
0
0

Texto completo

(1)Universidad Simón Bolívar Preparadurías de Matemáticas. CLASES DE PREPARADURIAS COMPLETA:. MATEMÁTICAS 2 TRIMESTRE. ENERO – MARZO 2012 Profesor asignado: Valera, Humberto.. Previo: Enero – Marzo 2011, Profesor asignado: Palma, Ligia. Enero – Marzo 2010, Profesor asignado: Núñez, Ynes. Enero – Marzo 2009, Profesor asignado:. .. Enero – Marzo 2008, Profesor asignado: Montezuma, Aida.. Preparador: Miguel Guzmán Ingeniería Mecánica 06” Sartenejas; Septiembre 2012.

(2) TEMARIO. Prepa del: Viernes 13 – 1 – 2012 • • • •. Anti derivada Anti derivada trigonométrica Integración (Método de completación de cuadrado) Área bajo curva (Riemann). Prepa del: Viernes 20 – 01 – 2012 • • • •. Integral definida U sustitución. Paridad e imparidad de funciones e integrales. Teorema de valor medio para. Prepa del: Viernes 27 – 01 – 2012 • • •. Área bajo la curva Solido en revolución. Método de Cascarones, Arandelas y Disco. Primer teorema fundamental del cálculo.. Prepa del: Viernes 10 – 02 – 2012 • •. Funciones Transcendentales. Derivación. Funciones Transcendentales. Integración.. Prepa del: Viernes 17 – 02 – 2012 • • • •. Integración por parte Formula de reducción. Sustitución variada. Ecuaciones de funciones transcendentales.. Prepa del: Viernes 24 – 02 – 2012 • • • • • • •. Integración, técnicas varias. Derivación logarítmica. Demostración de identidad. Ecuaciones de funciones transcendentales. EDO Bernoulli EDO cambio variable EDO Aplicaciones.

(3) Prepa del: Viernes 2 – 03 – 2012 • •. Integrales trigonométrica Sustitución trigonométrica.. Prepa del: Viernes 9 – 03 – 2012 •. Integrales por fracciones simples.. Prepa del: Viernes 16 – 03 – 2012 • • •. Nuevas Indeterminaciones Integrales Impropias Convergencia y divergencia de integrales. Prepa del: Viernes 23 – 03 – 2012 REPASO TERCER PARCIAL.. Preparado por: Miguel Guzmán.

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

(5) 89 5 6 7 0124 79  . 65567656669 79 !7 8 "#4567956978979  #$"# 5679 %. . & 4' 8 . 65(678 '#)*+,*- .#)*/+,0.8 12345#,0#$5#6,0 "#'4 8 #'45785 #7595 %#$"#75+7. % +7.. . 8 49 779989 8 . 65667665665:6;:!67 5# 789 #$5#979 5679  #$5#799  657 "#4558 #$"# 5 %#$"# 789 %. . < 4 =>989  . 6567?55 =99    4 "#4 > 8 =>998  #4@AAABA 8 >A8AAC >AAC @AAAABA DE. D-. ")#F)GH,,- !I67775!75# > 8#$5#J   ")#J455#$")#J95 %#$")#J9 > 8 %) LN98,  ! 7O55:6;:75#99 #$5#)GH),-9  K"8#F=L)MGH ,- .

(6) 01234576528 .       .     .             . ! ". #$% &' %  (. )!*+,$) ' %   (  % (-./01 23 % '4 % ' %  (& ' (= 779  % 7779 '77%78777 '&' %  ( '5&67'7777877 677 :;. :<. &( !>> !>' %  > ?@ *.A!.0*-@-B'C %DE3F 'GC%F D3H 2. JKLM. '& ( '$'& ( '& ( '& ( O '& ( NJKNL I ' C%F " '  "' ' ' " " '"  " CF  PKJ  '  NPKNJ.    (Q   &Q  @*Q @*G% H. @*G% H R S     !  '  %   2 ' ' . T$% &U2D( )!*+,$V.0 XWB0   ( (Y%  &%XW( &XZU%XW( G"'XZ3%"[XZUH "\XZ3%"[XZU.

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

(8)  8 998 8 8   8 8 9 98 01567 234 9 9   9  11 22 01! !"1#01$  %&2 * * , - ( * (- ( + 8 8 ( 01'+ ( ()(1', ( ()(!'+ ( ()(1      1./  , , 1#01"1#01$.  .   .

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

(10) 999 98 99 012 3 4 8  567 67 . . "  67  99  9! 9  9!9#9$#. %&'()'*+',-)-,.'+*. 234'.,5'6&'. //0$# #1. ; ; < " 7 .89:9 =7 .89:9>=7 ?).9:9 ; @,?&''A,)+B',8-'(+,C7 ?).9#":9 ;. . 4)&?D82 E'.,++),).'F+)B&?-)8)-,5'2?).9#"?)."9G?).990 79/.8"9G?).990:9791:9G7?).9:9/7.8"9:9 HA,&,).'8).I-'. ; ; ; C917 :9G7 ?).9:9/7 .8"9:991<G/<C$$<$ .  $23J8-'(+'. 9" :9 K2/7L M/9 N. 4)&?D82 4O,?').,.&.--&?D8P9:P$9":9F)+)6&' :P C97 9 :PC 97 9 :P C79$L M/P " $ MQ9/P" 9M Q9/RPS" M M T,?'8B)KUV:KWUV .

(11) 0134151 .  6789 88  76789457678945.   9 8 . 0!"4#5 041$1% !&4#51315'()"1  9 8  67*++8+,+ ++- *++8+,+++./. .0. 0134151)"16745 162134151"5%34478 7475$ !)"1 2 2 8 8 4 6 6275 4 47627582762778 2 5 8 )"115!"91 6794578 :.  ;<=1"131)"1!&"54#5'1&454'. >7 B53531. 2 @ 8 @ 8 ? A ?8? A ?8. 0!"4#5CDEDFGDHIEFGJFKLDFMKLNJOLFIGFNPLGQDLQIFGKFREJSIEDFTIEJUDTDFTIHIFGIEFVWFXKIYPFHKGNDSPGFZKIF[\]^_`VWF UIDSPGF]CPEFREJSIEFQIPEISDFMKLTDSILQDXFTIXFNaXNKXP_FF ^e gh bif b `VF [\]^_` beb gh^beif^ebfb]b_`bf^ e ^e bf^e c^d fb jKIYPFGIFNPLNXKkIFZKIF[]^_FIGFKLDFMKLNJOLFNPLGQDLQIlF. F F.

(12) 01245678976 9679 6    '(&' !"7#$% !96&''(&')*+', ''(&'-   .' )&&'-)&/'(.'-)-/'-)01'-)234567.'8943  <  ;  :=<  . !"7#$% >";6?";$#9 6@#99;#  9567";?A$"B69?C;  DEFB; GHDEF7#9".', .  )I45678997567"976 967 M JKJL  MJJ. X. T]^Q !"7#$% N96?";76O699 969JPQRSTUVW_YQQQQQQZZ[[QQQQQY\S _\ST]Y. `aQbcadaQefaQ. n Si_j kT SiYj TnkTVpQ q gVho kYlS m S lh m S VpQ Q gV YlS QgVkrsk^Q T n kYlST. n {cdiwj |mwQ tusQh}nvwxsywzliYlw TjT. `~f€cduQ‚~bƒ„~{QefaQa{QfdQcdba†ƒ~Q{c„‡bc€~PQadb~d€a{Q n n n {cdiwj gVh}nwxmwsyh}nwzmwlh}niYlw TjTmwV_l_l_V_Q ˆƒQefaQ‰iwjVwxVsiswxjVs‰iswjQQQgŠ‹ŒQŽQQ‰iwjVwzVsiswzjVs‰iswjQgŠ‹ŒQ {cdiwj ŽQQ‰iswjV {cdiswj Vs {cdiwj Vs‰iwjQgŠ‹ŒQ ‰iwjViYlw TjT iYliswjTjT iYlwTjT. Q.

(13) 0124567689 5!"!#!$%&'&()*+&)&*!#($ ,-./012034 5 %$6&)7)!!#$(8&6!'&9)*":$!;!<(=>?@)A7!)*(BC D("7'&9)C 5&'$%&E!6("&)%$F!"(C G?H-I01J/K-L30MG?N-I20J01K-L/0MG?O-I3J20K-LP. Q!6(#7)%(*$'R(?N-STM?O-USM?V-3 W":$!$:X-G?H=>?N@YG?N=>?O@YG?O=>?V@*()*=>?N@-NVZM=>?O@-OZSM=>?V@-L X-\PLPL[L]LCL\[ B($#7)%(&E^7&$*(?H-/M?N-STM?O-US W":$!$:X-G?H=>?H@YG?N=>?N@YG?O=>?O@*()*=>?H@-L X-/\[L2L2L]LC/23 W":$!$!"$: O _N>J?OY[?J3@`?-/P. \CaQ!)*("%($6!*F!"($6 *&(#!$!&)%b$!"R!"""F!"($6 *&(*"!+7)'&9) / )c>L3@ =>?@->?Y/ @O D("7'&9)C def#!$!&)%b$!". h. _i =>g@`g-=>j@>kJl@. O O / / _H >?Y/@O`?-=>j@>3JL@-mJ?Y/H-3=>j@-mJ/[Y/-3=>j@-m/[-=>j@. / -/-mjOY3jJ3-L-mj-J/no[ >jY/@O [ B($"('7!""!("7'&9)*)%$(*"&)%$F!"(j-J/Yo[.

(14) 01245657895 9 5 756 558  " #  !$%&'. (9 ) 457989* 77985765758  856 5  '$ +$,'$-'. ' &' / 89* 7'$ # # !$%&$,$%&$,$0.  +1)2(5 9 ' 69345678978:7;<75=5>?@:<:A34567BC7@<975DC75 FOP I E : B FGH F JKLMNLQR5 S3E5DC75E:BFGH JKTMQR5 5 U?EC8:V;W5 X35YC;8:V;57@5678978:7;<75EC7Z?45JKTM[JKT\]M45=5<3B^:_;57@5>?@:<:A357;<?;87@5 R`JKT\]M`JKTM5 a?957E5<7?97B3567538?<38:V;W5 g. U75<:7;75. bKcdeMfIh JKTMNTfiKcdeM5 FOP. FOP. RjKT\]MdTkfIF JKLMNLfJKTMjKT\]MdTk5Q[55RfIF JKLMNLfJKTM5 S?B3;6?5ElB:<7@455>?95<7?97B3567E57B>397636?W5 FOP. E:B IF JKLMNLQR5 FGH.

(15) 0123456278762 1 2385 548587052874 84 8286 84 8286 8 83245146  !"#$%5&'" ()* 7 (+","-".*"),/"0)")1!2343 63 #"0"8*,",)#"#"!!#! 8!#*9:(. 6*)1!(. ")")1!0",)#"!8!#*:2;2<4=3;3< 7*!0"8!0!#>"0,/"0"/""0"!? 2@4$37634A2@4B4= ")")1!>, 24B3;$ G CH5D35637;B3;$EF34%$I. ("),"-".*">),/">0"0">( J(; K3435 LM34; L34. 6*)1!(. 4","-".*">),/">,". G. 94 CHGD35;;EF3. O G  3 94NI63P 4QI6R;QI;R HG 94.

(16) 1. 01245672894 7 86 9462 9468 !" 4 5 #6$*+%45 82&2824'()4 5 - 45 4 #6,. 8 /40 *+ 2 61. 8 23212. 82/3 #6.8..  /145!!56""77 78469279467 14:77;1 14:77<=1. 1 >=7!"71 9276756?75 7296  &7 .'&728'6  :77;8 5 #6$*-&927'2&75')7 :77<=1 A. C. #6$B@42%2@4()4 $A9242%2@4()4 !771 #6 98D. .

(17) 0124566776896 7 77775569576755597767777591 17 !"!"77 #96$ 1%679 &995577 577896 7776'(#)*  0. 0. +,10-7 ./-,107. / +-5 010 +-5" 5"  +2-5".   314.5!6277. #96$ 175976&997)8#)89*:%# . +,;2-4.5 / 979687 965756. .. +2-,;45</ >. +2-=<0? ;.      . +2-@"AB02CD0A-. .

(18) 0124567829 458 268 .  !!"!#"$%!"&! '()*+'),'-.)*+'),/ 0)*+12),3.4.50()+0-()+1-.4 6!%7#%%8989:;<= B >.2?@C)()*+'),/+'()+2-*-A) B. >.2?@C)(+0)*,12)+3-A) B. >.2?@C+0)B,12)*+3)A). B >.2?D+0')E,')B+32)*FC.2?GD+0'H1,'2/+323F+D+0','+32FI. >.1J? "!K!#"$"%"#!).LM%#!N!#O"!N%! UYZ[TU B TUVWX PQQQQQQQRQQQQQQQS P Q RQ S * >.2?@C (L+)-() +'),/+'()+2-*-A).2'?. ;\;M="!%%%!N!%#!!N%"%]^_`;a%%% :;`98_;< ;<. b!"!cd"!!%!!!$cO!e%!"O!$"#!$f"$#]%:&a. Hgh!*&%%O"!%$"!"O#!%!$"!"&!).*+0e ).+ ,e!O"!"!"%%"%!"#!).+'   z{| }~‚ƒ|€i z| }~‚ƒ|„|i jkllkmnoilkipqrstosuupvqiwsilkoixyqupnqsoisornisoisqi.   . . | {i. | €i.

(19) 2 10. 3 5 2. 4 6 6. 3. 14. 10. 12 746 89726 89. 3. 14. DEFGHIJKLFGMNOHPIQHKIMFPRFQLHINSIFTFIUVWIRFMHISHPIMNXJHPIPHKIOFXJXNINSIFTFIXFIMHLNQJYKZI [NXJHI\]^_[ZI kl 0m6162I [NXJHI\`a_[I kp 0m6215I. n o n o. DEFGHbIcHMIOdLHXHIXFI][]ae`D]fZIfFILJFKFII 2 2 0m6162 1 0m6215 q7rstu z v6 w 1x6 w2126 w5m4yI DEFGHISNIJKLFGMNSIgEFIFhRMFPNIFSIiHSEOFKjIfFMNI. n on o. 5 |}2 wI w 1x6 w2126 w5m4yu6z v5y{ }~ {wv6 2 14  %&'. n. o. . ()*+,! -*+.)/01/20.0)/3*!+,!  601!/) 789.   !"#$# &. 4 %&'  !"#$#     ! " # $ # 5   4 &. & %&'  !"#$#5 !:9;59 4 !"#$#5!<=>?@A<B>@C 4.

(20) 012341516789. ,-.    !"#$%&'(/ !"#)*+*(/ !"#)*+*01. 234!4356"781691:;98<1=36161>!7619;1?3"@!A"176<!:;7;B1 ,N.  N F F   CDE&GH &I&F !"IJFK !"#)FK%FL(/M !"#)*+*(/ !"#)*+*O1 ,N.   F  F D P  #  C E GH F !"I F K% '@8 )*M/ @8#)*N/01. 1. J ) & J CDEF&GHJFP !"IJFKF)IQRSIJFK%K11. TBU1V"46W<61 P XB1(Z[YJY+1. 2893@!A"B1 \!:!7!6"781691!"46<:;981>;<;176?!"!<19;1?3"@!A"1:;98<1;]89348B126146"7<^B1 P  P P  P    _H(Z[# J+%(# J+11H`11_HJ )a %')J011 Z[  _Hbb)IJ%)K%#c&Ib)bK111H`11_H))J1 gf  f% e dB1(' fe 0 +f1. 2893@!A"B1 \6;<<899;h81691"3h6<;78<1>8<1691><873@481"84;]96B1 ,  f%& f _H( fMi%fP+f111H`11_H(fZP%&fZ[i/%fZ[P/+f1 Z _Hf& )fZP)jfZkP%l1.

(21) 0123456278762 1 2385 5485870528674 84 8286 84 8286 8 83245146  !"#$%&!'() '*!!+,-!+!+./ 0'1 2345 67898.. 6)(: '7,-!);2<=("!" >32345 67898.62345?8>3.@68>3.6A234516.B12345 345 B .B62121 345 6A . 61. C'1 .6D;EF989G();E#919!,(;E9H. 6)(: '. .B6DD;EF9();E989();E#989G;E#9#1I!,(;E9H8J9K98#9GL. 3 M'1 .69NO93. 6)(: ')!); <,!)'.69PQ9199R+,-!); .B6PQ98 9 19 S .B693TPQ98  19U . 99 9 9 9 9NO3. '*!-!),+!",!+V+!' Y?J923@ WZ #9 X9. 6)(: [",!);+V+!' 989 9   W #9 X96W #9 8$X96$G98$98\.

(22) 012342567936735 97 33. 974931232 9!23 $% )* "#&' (%. +634,- +92.$%).$%)* ). # ). 7922422243# )"  #&'.   /0.1    &"  $% 2!,7 456. 7#*,68*39:;<*)* @AB +634,- +92.*).*)*3=,68">@?CDA 9E:; B #,678.379:;8<..).39""39:;<.)",76788..).3#")" '"6 '37 8*6. * )* #F* *G. +634,- +92.F**G).G*)*2295H7I*JKG*FL F  G* )*# F )*U F#FG** *G)*FM#  F*OO **G *G NOO OPOOO OOQ NOFOOOOPOO OOOQ RS. J#)..3V.V63VF*GV6. RT. W2!2,65X392567,422!226YF0*Z$*[K1F0*$1ZK.

(23) 1 34. 0123445 671 2 4       $'    8793 4 !"#  %&(   )%&')(  *  +,-.+/0*12+,-.+/345 62 " * " " ". . 78797:;7</045 "4=1 =+,-.+/3"45 62 . 5>?-@AB0414 C@<D-EF/GH/HI@AJDH-@AB041KLMKNLO<DHP@ID<.EQ<E-+I@AQ@,>? '? ? 7> "> 4;7R>'?">?2 . >5AH-BS0414 C@<D-EF/C+THI@AJDHUAH-B041KLMKNLO<DHP@ "S 4 R 4 R>S? 4W>? ;">?4 70>?> S V?1S >? 3>?>? 6 7 R5 S "='5S=35"'62 750>? 1=0>? 1'2.      .

(24) 012456677689756 559 !" !"#        . $%&'()*)+(,(-&(.&/('&%()!+'0&(,'(1.!)2!(+('3*)+')!1'&)&# 789. ;'/'*()!+'0&(# $/(.(*'!3*)+'.      . 45:7896 <56=)!>? 4=)!@A")!@A"B=".

(25) 0123456278762 1 2385 5485870528674 84 8286 84 8286 8 83245146  !"#$%&'"()*. +,-./012342. 5(6 789":)#"!8;8. CD ? ;HA89;8ABHADI( 6*)<!(2!#:")<!=*:=":#>*!>?@A":)#"!8AB ;@AEFD G J J 8J ;8 789":)#"!8;8A8$":)#"!867LM$MMK8 MNMM9MMO PQ. ":"RE>S>*T"U:"))<!( 8 W;8A896!K89KX REA7V86K8 9   J 9 4!#*!)T RA8$":)#"!8K%!K8968%KX 9KZ Y(6 78!$8$98KZ ;8. 6*)<!(":T*S:*T=*:>*>!#:")<!=*:=":#T(7*!> @A!$89KZ AB ;@A$8%98KZ;8 ? ;HA$898KZ;8AB HA%!$89KZ 9KZ  8 [ \ $ 8 !9$89KZ6RKXAB RA!9$89KZKX  9 9  67 ; 8 KX AB RA RA%! $8 KZ LMMM$M8MNM 9KZ % % MMMMO P * RA!9$89KZKX. ](6 78J^_DG K_D`a;8 6*)<!(7T#:b*Tc#!*Td PQ. PG. effgf effgf J_DGfh J_D`fh ;8K78 ;8 78J^_DG K_D`a;8A78.

(26) 01214567189  12196145   012146!"217#!$ 2$12"%6%15&'()(5) 5 5 4&) *+&,)&) *+&)  5 -./0142&*+&3)+  . 4*,%!5675588 7#!4  11%%""7#!!5896%"! 2:; 4,%!5&675884,%!5&84,<%!5&8 0 2;1= 21$27 8 %1!"212$ 2$12"%%1> ?%!5&8(<?7%5&8&(< < %5&8 4<%!5&8*&, @AAA7ABA AAAC DE. F"21G$ 2$12"%$1214 H7%5&8(<H*%!5&8&(< 4<7%5&8*&,<%!5&8 %""I! %"! 2:; < !5&8K 4<%!5&8*&J<7%5&8*&, @AAA%ABA AAAC. L %$M1! . D. < 44<5%!5&8*&7%5&884N5%!5&8*&7%5&88 O 2%1! 7189  1219%" ! PRQSTUVSWVSQXYY*XZ1TSWVSQXYYY  .

(27) 01245667768569765 7567 5     . 96 1 5!965756 7 5"6579687!9#9 75 #9#571   $%  75&%%'&%0()%+*,*-%')%. $%./0. 7!9 75 950955!19785 5167&%%'&%0 $%./02345 68565!976967! 7 8%9:/023:4;/9/0234;%<2=/>2:. 2124566765!6577 7#975#55 3?@4A?. 96 1 B75 #9#57"75&%3?@4A%'&%C3?@4AD0??()%?%'?%) $%?3?@4A/C3?@4AD30?4? E1785!9F7?%3?@4/@"679 $%?3?@4A/0C3?@4ADG3?@4/@H? 3K?KKLK @K4KAKM ?/@3?@4AD?O $%?3?@4A/0CIJK N. $0C$%?3?@4A0C@3?@4AD?. . RSRHT RTSR P%QGQRTU URTGQRSRHTDUVQ.

(28) 012456676589 6577 977555 7 691 755 75755755 77 7595775!"7"#!"$%&7'75 ("7"#("5 )"57%$%&75 )"57%$%&77%* )"57%$%&+ --/ %712 ,--7-.0. )3$%&)"573$%&7 9:;<=83<%=9:;<=8?8 4"5678<%> <%>.  @127765957551 D * A1%E *3CB. "#!JK 69175!'""#F!!"565 5 G76H 71IJK J*"#!J* D F! D * !"#)"FL!%!36!3*MD )"E *3! !"#)"FE !%*3*3! & E )"FN*&%*36&O"#)"F6&%F&  . P1%%B*%&.

(29) 0123456780 24 51 5 28  254 1                 !"#$ %$&'  27&'!    !()*+,-$)(./$0$(.8           12 3 12 43 0 24 51 5 28$  $ $  8 $   4$  343  $34 $ $ !" 864 64 $ 3 5647  4$   8  64 497:567;!  64  4 8  4  64   <=>?!=@8  27A6B64 4 497:64567;!. /8 C6D6. 012345678E 51 5 28      H IJKFG   F G   H I J K F G  LM4NO3P27&'Q! PG4STRI6OSTRKPC63D6NU6ST627AST6B!. 8 KRG .V8G 0123456780 24 513W5188G  88P K G &8'85P887 P88F8 PL8O8PQ! G  PL8&P8OO'Q!  3O5R&G'G&P&G'O'7!.

(30) 01246785967 7   67. ! "#$7%&' 7(7 #)7* +  + 5  ,4 -*8 . ),*4 85 ),*4 ./ /5/ 85 - . ,*01/ 2/ /3 8545/6. . 7  7  9. 7  7848587 587 587. " 7 :(2993"%;4 <. ,49=2935874>9(3587497.?3 4 ,429.$97.' 9427 9 @:374 7 )9.358747)9.7/9.7)9.735/9.4)7 9.  9.587 5/9. 9. 9),2458 5 9),2982!394/6 ,245/9 . 5/9. 7 8!08 7 55/6 ,208587 587. *ABC! 37.824837/D43874. @::3E4 .82 .82 7.82)G 87 F7/D)G)7H=8D862>(077/D 53874)77/D 87)G 7.8287.8D7)27./D782G)785I62)JKLM8N86O . PABC.  . JQ . 32785437.85*4.

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

(32) 123495677899 19 9. 562 56662. 679 19 4975656778 5 5679 65!!6"5679  1"#$$ " 1"  4 5678 1"4 " 1" 475566778 " " " &&&( %&5&6&7&'& &&&( %&5&6&7&'& )*. )+. ,5678 7567567 " -, ./05!!61567 "  111" 67 11  /13567 5671 -/  /567 "3567 567567 " -/ /4135 1 26 5678 5675675679 567 5679 335678 567567 5679 5679 35678 567567 5679 -. 32456789:;<=>?<=;9=@6=;9A8B678<:=@<C6A8DE876=;9A8B9= , 9 $ FGJH39IK=. 562 565L!MNO5!6P!6M 567F I9G5679 3IQ56739IK 2R6 I1F3 IG5679 3I56739IKIGI3I I 3K F19 9/ Q 9 9 Q39I .5S I 1FT 9 V9W3 IG56G 9 KKIGI3I I KX 19 QU39I 9/ JH39I 9 9 339I.

(33) 012456 65. 89 .  1 !"#$ %#&'(  -.&/#$  -.".3#$ .  89)*+, . 0189)*+,) ) 2)*+, 0  81  189 4)*+,)56) 2'#7 1.  81295:;5<=>56?@5A=?@6@ 28D 7 C B 89) 4B8 ) ) EF6F;5G H H1.  1 -.#&&#( .'.&( $.#$.&.# *JK J *JK *+K J4*+K7  I  2I  28 I B8 ) 4 ) 7 C ) D9)  BI ) L ) M9. *+K *JK *+K *JK *+K *JK *+K  +  2I  J  BIJ  +  BIJ  J  I*BIJ*BIK2IJK I*BIJ* IKBIJK I*JK 9 9 ) B )  ) ) N &O.. P. 28D9 B 8 C ) 4B8 7 ) ) N#&##'.%&#Q.&/#( O. 28DR H H1S61IB89H8289H 4B8 C 7 ) ) ) ) -.".3#$ .'.. 90)889T.

(34) 0124156768949 149789  78977. 9199. 91991.  !"#87$27 %!9'4&'%(''')*+,-. 1469. ! 1 76'' 9784999567/:;451<=:5' 74689869. /48 '0/234 5 01241567 >&//0>&4/0>&448 ' . !"?@AB@CDE@FGB@F. 1469. !. 1H11H99HF. I72214471744 17271 L ML KOKMO KLKML KOKMO 11H99HJK K  NJ  NJ  NJ  N. P6489849 1 LKML KOKMO KLKML KOKMO K J  NJ  NJ  NJ  N LQOKLMOKOMLKMLQO KLQOKLMOKOMLKMLQO KLQOKMLQO K        01241567 11H99H1H.  .

(35) 012456758986 75557 1 8888. 87 1766 5! "#$###$#%&'('& )*8+7585 5857 56 ,-.%'& 4568956/8 /*/5 565865/5* 6 80  18" 2/8 5!/ 5 8 98:;345< # #"#"$ 3456778 " 76 86*=56 <"> ?/*@  58 65 87A5+75BCDEFGD 7 98*5!+757/8857 1   .

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

(37) 012456789 5678. . 675676 56789 5678 589 !589 !!"775 #4858$ 58% &5678$$ 5678%% ' ( )*#5678+% 5678,$ ( . -458 . 676.6.7/*7670751 58  4& 58 528 ' 34 58 #45 455565 28557; 6728 56728 728557 45 4556565 <#2"=528 = >?@AB8 >?@AB8 ( <#C"D6E6DF5678 GF58  #C4F2 FF ( )*#58 >?@AB8 ( . +H5E567*5 A4 2 2 2 J  8A I 2. 89. 8:. 67D6E6D6*7K6LM58N G LM58N 78N N #AI4 58N 78N J NAI4IJ58N7J8N78N NAI2457288NN NAI245675288NN N I28528N !2 #AI2O5678N P ("D5*5E6D8 *.D6E6D.

(38) 1234567897 31456789 78489869      . 3!"#$ %&2'(% 13()*() +746,746-.3(%/!)20(*!(/2+12( 87467 87  7 7  8 185 234586274878'(#4967 8781234969 74 868123496 971234969712349697 7#4:414968;4966 7-' 123496 (#496<2=*21(% 1((0(*!(/2 *!=!#(46 '(#496788 7 '(#4967 8    123496788-7 1234967  8    7#  8  8 . #496314969 1 1!3 1496. 3!"#<2(!>(% 123(%/!)20(*!(/2+?7314967 ?71!#4969 ? ?7 7  ?7 74#4?6?6 7? ? 7#413:496631496.

(39) 9 9 012456728 9. !"#$%&'()*+,-&./%&'(!)+,-/,. 7+,--(7 9 ( ( 9 ' + 4 564 5) * 1 !)+,-/,&.0&21931)+*!8)+,+-,--!)+,-/,&.0&2173)!*)8++,,--/, 0&23 18 8 28)*+,:$!);*:!!)<;*!*)=$>!*!?=$)@:!"!)=*$A; 9 0&4253BCD,E'+,-)7+,-/,FB,GHICJ&BD,E+,-&./J&6)7+,-/,  9 9 9 9 9 0&42536J'/J&.0&425K6JLMNO&.0&425K6BCDPL+,-MNO Q>$)!)!"#$F )*+,-&21%. . . 9 T456U%7 9 2 0&6RSK 2% M NO.

(40) '2"$*'. 0123456278762 1 2385 5485870528674 84 8286 84 8286 8 83245146  !" #$%& #'() . / 10.0 +', -..10. 0.102.. 6)(3"')* 4)45*#(()"66 7686$" ./0.10.09:.0;0<.0= .10.10 .10 .10 7)"4:98;98=98<9 .@0< >9-?.1.00.10@2. 9A >9".100B # * ( $ # "?  B 1,.0D  . C', -..,.,E2.. 6)(3"')* F$)4)45*#(()"66 766$" .1,.0D 9:0 ; 0 < ..,.,E . ., .,E 7)"4:9HG1 I;9,H/J I<91KG 2. 0D- 2. 9A >9 D".,%".,0D".,E0< >9D-2..,%-., E .,E   E N L', -M,OMM,M0O N0NM0PN QM 6)(3"'. F$)4)45*#(()"66 76'. .1,.0 9 : 0 ;.0< 0 =.0S .,.10.0R11 ., 1.10.0R .101.0R1 .,. 0.0R0=.0S., 9:. 0.0R 0;.0< 1 . 0.0R1.,. 9:.K0./0R.10./0E.10.0R.10R0;.0<./0.10R.,.1,.,R0=.1,=.0S.,S 9:.K0E./0E.10.0R0;.K0;./0;.1,R;.0<./0<.10<.,R<0=.1,=.0S.,S.

(41) 01231456708496016408494 6016405 84 49460126408394 3460164083 36. 056 8497 8494 706 84 4947506 583 94 3473506 83 37506 056797380606067 73806060677 83506 060606067753806 060606060678483835484 835757875 9735 73773 2 5 1 3 5 0146 145 13 1 013516013145 24146217 24" 14 14 135 !""#" "$!"""""1"#" """"$ !""0"1"2"4 "#" """6"2"$ %&. %'. *  -.  )*7+, .3*. /0127135727 1 556013564 4 3475 2275560264 7!""""#""""$  789:;<=>?4. *  0.4A6 -. )@73+, .@[email protected] 14 173 5  144 1 355124 5 12414 14 14 14  1 F 7355C!""""#""""$ 2 4"14 1 414 !""1"2"#" ""$ %D. %E. 14 1 37124 14 GHI271241472701461 601""2"4 14 7 227560264 75!" ""#" ""64 """$2. 3S7 124114  . JKLMNOPQR2. %(.

(42) 01234567891 79791                           !"#$%  7 678&'%(  )******+******, -./012345(. :;<7 ?; 6789;==;> = B D  <  <  A A A A @C BC   <D  I ABE)*****+*****,   C A)****+****, C FG. FH. JK5L7MN8  A&<O'  A&<B' P <B <D A  A A A @    C   QR C  %U   <ST  <)*** **+* ****, C -./012345V.     QW C 01234567891 79791X     678Y5YY  5Y Y 5YY   1YY 1YY Z67  @ 8Y[ B 5VY @ BYBM8Y%R.

(43) 123456786494 37 4 6275792 2957894.   $  %&$    !"#!"#$ )  ( )$$  %&$$$ '(-.............../...............0 *$+  *$+, "# 123456789$:. #  ?$ ;<'(*"# *=#,   > "#. #  ;<'(*"# (#>  @"# %A$$ BC$DC$C$EF$GFF$HIF$ *  ( # ;'>DJ(K(,DJ"#K(> (   "# >  #  (@"# %$ LCF$HIF$  (>$  ( #$  $ (*$"# @#" # @ "# @ "# (M $ '@$(# "#$ BC$DC$ID$EF$GFF$ O RSJT(OK( O RSWTUUTXY( Z [\]^[_TO ( O  XTO` a$ N'PQ OUV ZU U ZU TUUTX $ $. >+b$cDDF$D$GFdD$$. "JK(K J K J E G   > C E eCEJKJCE"JKCEfJKKg$.

(44) 52   68              2 3 !2"2" #556286$3!82%4   &' ( ) * &' (+,) *       &'( -&')(* &   4 31 &' ( 4 $ 36857/86! : . 82486! 36/4332$23682622&')  5( 6482&372 8' 8* 48) 9 4 10 (* &       9    389  (    3 8   9       38;52;38;52;952( 123456789 1.

(45) 0123456278762 1 2385 5485870528674 84 8286 84 8286 8 83245146  !" #$%& #'()  '7$* ")+ $+ .  ,'- ./0  1234. 5670. 6)(8"'89(# )+"9*#")'":;3"<2.=>;? :;@.AB<CDFE> 7#G)#H#I"(8"J9)""(#+()"$"K# 4.; :;@F/0 ALM .AB<CD.=>N+$"H   2 1 ./0 3 ./0 4 567'P Q 3 "1 2 O;  ./0 3  <- => W  3 W 2  "< 2 >  ; ;?  :;@= 3 3 O;  V ; R   ;  ./0  STU./0 -  ./0 2 ./0 3 3 3= . [\7] YZ2@ C X'- ./0  3. 6)(8"'3# )+H^_#)*$"#"$*# 9*)9#N`#H")()")( )+""K" G)9#*#"$*#* )a+*_# )+#*!I(#G#I"(8"N#G !+ $#"I"$)+' 5()*G#"G)H#"$*#+!*#a#b)#(*_#N9)G )+()"(*H" c $"I"$)!*#+*!"I"$#')*)$#"$) . 2@[\7]efe YZ Z2@[.; Z C g ; d     ./0 3 STU ./0  O; 69)G )+"$*#*N`G#*! + )*+$#G)' =i 7h ;? 6*## )+h=;2@[\ ;? h7h;-@[\7];?7];C[i E h= 7h ;? jC;"1h24-h ;?jC;"lZ2@[\2m-n2@[\ jC;k-h = h- Z2@[\-.

(46) 7 7 4  0120789 456 4  7  .   78 456  !"#7$%&'().  *+4,-5. /+606+1232450+56226+17,2489:  !"#<;$4#=7$. /+606+14>656256226+17,2  4%&'( 4#78 ?%@9$4 5 6 78 4#$   # =$ 9  $   9 4   # # $     4#78 ?%@9$4 56 BAD 4 58 6   4 56  F78 ?%@9  78 7 78 4#$ CE #=$ . . '78 456G8608:48158:::%&'( =.  *+4,-5. /226+1405H2624650-5. %&'(I26+ -21 )O) L%&8:-+18: 8 8 : : 8 8 : : 4 1 5  4 L % &  456 J  K4 56 PA 456 (  78G= 78G= MN&8: CQE78G= -1-=8: 608:. .     78 456  48:.  *+4,-5. /226+1%&'I26+ -21  )O) )O) 8 : 4  8 :    ? &    456 48:78 456 8:48: PA 78 456 PA 78 456 78 CQE C Q E 48: . #$ FR  =  .

(47) 012456677685697657567951   1  . 96 1! 7975965756 7" 5  $%  $(% 0 $%55)*+$(#$%55&'+ #$  &'%  % 0 0 0 0 ,-957856597696. 7 9 5 #/$012 6 3: 56478 ;912 <=> ?@ABCDEBFAG@HIBCDEBFJKLH;M8 R  N1Q OPO QP. UP $T VW $T UZ $55)[*+ 96 1S79687965756 7" 5#/$TVWRV XW VYWR/ ZYR/ \856597696. 7 : 45 9 45 ]  BCDEBFJ_9LIBCDEBFJ?L #$]1^2 6 3a _`7_ 7< = > 3 ^` 912 : _`7_^`;6 ]1 Q 55)%*55bO c6 012 #$d0. P O e1Q/OP% /. 96 1,79 96575679555856979767856976. 71  P / P #$Q/OPO% OPO% S79687965756 7" 5 P #/$OPO%$[[$6)[*+$6)OP%*+ \856597696. 7 9 _` f _` 3 4 5 7< = > 3 =>J<FJ_9I?LI<FJ_^fI?LL7< =>ghiJ_I?LI<Fg_aI?jj #$6  01: ^f_`I? a1: a _`I?45;< 91: a1: #$k.  .

(48) 01245789 59 !"!#"$"%&$'#(7 )5* ()55( / 8 + , -.0 789123459 6(755(* 5(((7 ,4 5898: ; 75<)7((= 789 -1. >?@ABC?DEF ; G7 9585759 (HIJ85K985: / / T V148L23W0X +8, -.0 14123459-.0 148L23 59MN91OPQRS,+8, -TU, T Y1W8L23 UTZ +8, -TU, [5K79855658TU, \-],]T T ^QPQ,]T +8, -,UT.  _Èa9 (bJ58 / d g h5d .0 cdefTU0dfT b98:a958 9(b:. >?@ABC?DEF i 9758 / g h5d-./V d X5dUg./c T h5d .0 cdedfTU0dfT 0 defT 0 0dfT jklmknkopk wdefT x M-Tqrn8defT UgT0rn80dfT -rnVsdefTXUrnVus80dfTtX-rnvus8 0dfTt yz{rp{|}~knr}~r|mlk~ efT W wdefT x U wd gSN-rnvus80dfTtx -rnvus8 0dfTt €W 0 .

(49) 01213457518979 74 181 77713174151  !"01211#5$   3   074%91&911$43774%91517115747774155$$415137$1177'(5&1537)4 %911437114374)1'3$151*+1797411487$3451*,-77741531415 7143719317444$7$413$151*-179741487$345137$11-77.!/ 5113777'()4251 7345            !12 3  ! !  3 ! 1 2   3   3  0  345  345 6  7  8  !   3     991847$1874 181)59'3$115:!,774$474181;.  <;=01$131575$187154 1814181;  7 $7  >;,:!?A  @. B49C ; D17(73457$1871E7  @J!, :A!?7 $7@!FGH>I!7 $7@J!@!F@I!    @ :A!,7 $7?KLLLLML  LLLN OP Q77RS77345E7 4 155315 :!?TUV @ 04 1TU!+T!V!+U!, :!?,@!F:!,SV!F:!67V Q44%91 :A!,7 $767V W734577$187347 3 ?AX7 $7@ :!X .

(50) 01234561789 376    6 5  2 6 1   !   1!" #  6526$1$1$$ %&1'  ()66178*23 %&'1'. +, -"./01. 2831, 436361234561735176. "./0'6. 43676178612345685886. 9. :" ./01 9. ;8< 376. =./0'>"9 # 9 ./9?'./"@ 9 232313 161732351631 D ?' A9  .9 ECBFG 9 .9H I858 3 @./"  J, :M K@1 L. 2831, 238N<35)6 38656"L373181678518<37351398858 361234563<85886 " L 1 L 1 :M K@:" K@ L 4367617861234561735176    ":K@1 # "'@L6 43676178612345685886 9 1 L   "P:9 K@1  "O :M K@ 9L. 43<3)6. 9L. 'Q "O @?L "P&@?LR # '& # STU VWXY 9L 9 L.

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

(52) 01324567893 3  32437 23 732437  389 7 8999!89  ' 334889 "3#$%7#&22$$'()7  . *(5. 67$ +, $ -. /9081* 2394546478098:9: ;$76<+=,$;$<(+=, .5 $76+=,$( $76+=,75+=,$( $76+=,(+=,7 2349:9: >?5.> 67$+=,$>?@(A+=, $73BC.>>?(+=> D737+=.##+ EFEEE!9>?- (+=> D73449*G998049H: D73 I ( 6 K    ( >?- +> >?- +> . -J-. &' $' +*(5N L 3($ O ' M$. /9081* /9H80&30H9:9:96:9980 29H9454. P $'  Q 5N L 3($ ' M$ P?&'. $' $ .5L 3($ ' M.

(53) 01242565787698  58   "#$%!+ "#$+ ,-#$  ! $ &'()"#$* ! /0 ./0+1!)2 $.  3.45.-6-7-"#,.45-7"6858"- 9 ! ! )(@ABCDEC 7"6; <1!)2$=  7"6; 1!)? $ 9:%$ 9:%$ . >. K. FG)LKHIJI2. M7N"O# P5"6.5QN.,RR.S"#"6.7T-75-U7N,. >. V. J2 H  LVHLJ2/WX XZ >XYX. M"5.7T.6]( P57QN.]R"T.54.. . [\. 7"6HJ^>+@ABCDEC ^:V. J  a%b > _G)J:> 7"6` 2$bb. M7N"# j M".T-7N-67-T-5"-U7.c.#7-SN#"O#.,.#R5deaj%fg>hifkf>> P57QN.8R.6-87"-57-5.47-R.lmn8",-7 J%b bbo 7"6 %22 7"6 2K a > 7 " 6 $ ` J:> 2 >p>J:>` !2 J:>` !%2 .

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c 9 ` a b$ ^ d _$;T, $0 ]I[\5LeZ\75[95LJ5895fIK5]e &'()*+1, g+123/.'0,-/'-.,. ;T$ i T,qpalmn0o, _$ hi! jkalmn$0o+j 0 pp ,8,,hi! +j_q0n;q0 or d. s+.)2,=(2,-./.,at9,uhvwxyw,z,{q|q,,a9,,a}~vwxyw,.,h+n,0o,.

(55)

Referencias

Documento similar

Como esta distribución es simétrica el área bajo la curva y a la izquierda de la media es 0.50 y el área bajo la curva y a la derecha de la media es 0.50 6.- Los porcentajes de

Por lo tanto se introducirán en el programa los valores de la primera derivada (en caso de condiciones de contorno de primer tipo) de la segunda derivada para segundo

Relación con la derivada... Página

La derivada como razón de

 Gráficamente, la integral es el área bajo la curva... Sumas

La derivada de una suma algebraica de funciones es igual a la derivada de cada uno de los sumandos respetando sus signos... Early Trascendentals, Sixth

Thus, this study was performed to determine the anti- allodynic and anti-hyperalgesic effects and the synergistic anti- nociceptive interaction of morphine and gabapentin,

The anti-hepatitis B surface antigen (anti-HBs) and anti-hepatitis A virus (anti-HAV) antibody titres observed following a primary vaccination course with Ambirix are in the range