MATEMATICA APLICADA

HIRMHIRFNI I\AFNIBI IEIAF^F^ BMA \]ERO BM MY]FAF@PFO Fek% Mepfy}m Ri|fi ^%

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HIRMHÉRFNI I\AFNIBI% Ieéaf~f~ bma |}ero bm My}faf`pfo

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RI@AI BM NOERMEFBO4

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 IEÉAF^F^ BM \]ERO BM MY]FAF@PFO MY]FAF@PFO

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WHIRMHIRFNI I\AFNIBI X

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NI\FR]AO F   IEÉAF^F^ BM   IEÉAF^F^  BM \]ERO \]ERO BM  BM MY]FAF@PFO MY]FAF@PFO 9%9 FERPOB]NNFOE Robo kmpmerm emnm~fri ~i`mp |op ierfnf|ibo! ~f }e e}mso |pob}nro o }ei e}msi mh|pm~i! si i |pob}nfp }rfafbib o eo v me y}æ efsma bm inrfsfbib |pob}nrfsi nohfmeti m~i }rfafbib% \ipi bmrmphfeipao ~m |}mbm }rfaftip ma ieéaf~f~ bm |}ero bm my}faf`pfo% N}iebo ~m rfmeme m~ribo~ cfeienfmpo~ |povmnribo~ v robo~ ao~ pm~}aribo~ bm|mebme bm nfmpro eôhmpo bm sipfi`am~! ma |}ero bm my}faf`pfo m~ h}v cénfa bm nian}aip% \ipi mermebmp i ni`iafbib m~rm i~|mnro! m~ |pmnf~o bmcfefp iak}eo~ no~ro~! noe ai iv}bi bm ai ~fk}fmerm kpécfni4

KPICFNI 9%( NO^RO^ CFDO^! SIPFI@AM^ V RORIAM^

HIRMHÉRFNI I\AFNIBI% Ieéaf~f~ bma |}ero bm My}faf`pfo

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9%9%9 No~ro sipfi`am sipfi`am roria *NSR&

M~ iy}ma n}vo siaop m~ré bmrmphfeibo! me |po|opnfþe bfpmnri! |op ma soa}hme bm |pob}nnfþe! smeri~ o n}iay}fmp orpi hmbfbi bm inrfsfbib%

9%9%0 No~ro sipfi`am }efripfo *NS]& M~ ma siaop i~onfibo i nibi }efbib bm ao y}m ~m |pob}nm o bma bma ~mpsfnfo y}m ~m |pm~ri%

9%9%> No~ro Hipkfeia *NH& M~ ma no~ro bm |pob}nfp }ei } ei }efbib mzrpi bm }e `fme o ~mpsfnfo% Ma no~ro hipkfeia |}mbm ~mp ma no~ro sipfi`am }efripfo! ~fe mh`ipko! ~f ao~ no~ro~ sipfi`am~ }efripfo~ eo ~oe noe~rierm~ v jiv mnoeohèi~ bm m~niai! ma no~ro hipkfeia bm|mebmpé bma efsma bm o|mpinfþe me y}m ~m rpi`idm%

9%9%2 No~ro cfdo *NC& M~ iy}ma no~ro bm }ei bmrmphfeibi inrfsfbib y}m eo sipèi b}pierm }e nfmpro |mpèobo! febm|mebfmermhmerm bma soa}hme bm m~i inrfsfbib% ^m bm`me rmemp me n}meri ai~ ~fk}fmerm~ sipfi`am~4 nierfbib |pob}nfbi! |pmnfo bm smeri }efripfo! no~ro~ cfdo~ v no~ro~ sipfi`am~ }efripfo~% KPICFNI 0%( FEKPM^O^ HOEMRIPFO^ H OEMRIPFO^

WHIRMHIRFNI I\AFNIBI X

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9%0 NOH\PME^FOE BMA \]ERO BM MY]FAF@PFO Ma ieéaf~f~ bma \]ERO BM MY]FAF@PFO m~r}bfi ai pmainfþe y}m mzf~rm merpm no~ro~ v ki~ro~ cfdo~! no~ro~ v ki~ro~ sipfi`am~! soa}hme bm smeri~ v }rfafbibm~ o|mpinfoeiam~% ^m merfmebm |op \]ERO BM MY]FAF@PFO iy}ma efsma bm |pob}nnfþe v smeri~ y}m }ei mh|pm~i o emkonfo ianieti |ipi aokpip n}`pfp ao~ no~ro~ v ki~ro~ noe ~}~ fekpm~o~ o`rmefbo~% Me orpi~ |iai`pi~! |iai`pi~! i m~rm efsma bm bm |pob}nnfþe v smeri~ ai }rfafbib o|mpinfoeia m~ nmpo! o ~mi! y}m ao~ fekpm~o~ ~oe fk}iam~ i ai ~}hiropfi bm ao~ no~ro~ v ki~ro~ o|mpinfoeiam~% Rih`fæe ma |}ero bm bm my}faf`pfo ~m noe~fbmpi noho }ei jmppihfmeri ôrfa |ipi bmrmphfeip ma i|iaienihfmero o|mpirfso y}m |}mbm rmemp }ei mh|pm~i me }e hohmero bmrmphfeibo%

9%> BMB]NNFOE BM AI COPH]AI BMA \]ERO BM MY]FAF@PFO MY]FAF@PFO \ipi bmrmphfeip ma |}ero bm my}faf`pfo ~m rfmem y}m fk}iaip ao~ fekpm~o~ V! v ao~ no~ro~ N Me cophi hirmhérfni ~m rmebpé ao~ fekpm~o~ |op smeri noho4

Fekpm~o~ 8 \pmnfo bm Smeri ]efripfo Z Nierfbib Smebfbi *9& V 8 \S} z Y Boebm4 V 8 Fekpm~o~ |op ai Smeri \S} 8 \pmnfo bm Smeri Y8 Nierfbib smebfbi

Ma no~ro roria N hirmhérfnihmerm sfmem bibo |op ai mn}infþe4

HIRMHÉRFNI I\AFNIBI% Ieéaf~f~ bma |}ero bm My}faf`pfo

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No~ro roria 8 No~ro Cfdo ' No~ro Sipfi`am Roria *0&

N 8 NC ' NSR

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\ipi o`rmemp ma |}ero bm my}faf`pfo fk}iaiho~ ai mn}infþe4

*9& 8 *0& M~ bmnfp ao~ fekpm~o~ m~ fk}ia ia no~ro4

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KPICFNI>%( KPICFNI KPICFNI RF\O BMA \]ERO BM MY]FAF@PFO MY]FAF@PFO

WHIRMHIRFNI I\AFNIBI X

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M~ bmnfp ma |}ero bm my}faf`pfo m~ ma No~ro Cfdo bfsfbfbo merpm ai bfcmpmenfi bma |pmnfo bm smeri }efripfo hmeo~ ma No~ro Sipfi`am }efripfo% M~rm |}ero bm my}faf`pfo m~ iy}maai nierfbib y}m |pob}nfbi v smebfbi! |mphfrm pmn}|mpip mzinrihmerm ao~ no~ro~ sipfi`am~! hé~ ao~ no~ro~ cfd o~ i~onfibo~ i ai o|mpinfþe%

9%2 I\AFNINFOEM^ BMA \]ERO BM MY]FAF@PFO I noerfe}infþe ~m |pm~meri ai i|afninfþe bma |}ero bm my}faf`pfo noe }e mdmh|ao%

Mdmh|ao 94 Nian}ao bma |}ero bm my}faf`pfo me }efbibm~ bm ai |pob}nnfþe bm m~npfropfo~ bm ocfnfei%

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 ^oa}nfþe4 Ao~ fekpm~o~ ~oe4 V 8 9=< z Y Ao~ no~ro~ ~oe4 =<<<' ;= z Y Ma |}ero bm my}faf`pfo! boebm ao~ fekpm~o~ ~oe fk}iam~ i ao~ no~ro~! ~mpé4 Y 8 NC/ *\S} „ Ns}& / *9=<(;=& Y

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HIRMHÉRFNI I\AFNIBI% Ieéaf~f~ bma |}ero bm My}faf`pfo

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a no~ro N bm |pob}nnfþe |ipi }efbibm~ m~4

N 8 2!=<< ' ;=z3< N 8 6!<<< bþaipm~ M~ro y}fmpm bmnfp y}m ~f ~m ci`pfnie 3< }efbibm~! ma no~ro bm |pob}nnfþe m~ bm 6!<<< bþaipm~% V ~f ~m smebme 3< }efbibm~ i }e siaop bm smeri bm 9=< ~m o`rfmem 6!<<< bþaipm~ bm fekpm~o! ~m noena}vm y}m eo ~m o`rfmeme o`rfmem e kieienfi ef }rfafbib% M~ bmnfp! ao~ Fekpm~o~ ~oe fk}iam~ i ao~ no~ro~% V8N ] 8V ( N ] 8 6!<<< „ 6!<<< ]8< ^f ~m smebme hé~ bm 3< }efbibm~ ~m o`rfmem }rfafbib! nian}amho~ ma fekpm~o |ipi ;< }efbibm~ y}m m~ hivop y}m ai~ 3< }efbibm~ } efbibm~ bm m~npfropfo~ |pob}nfbo~4 V 8 9=< bþaipm~ z :< }efbibm~ 8 90!<<< bþaipm~ Ao~ no~ro~ |ipi ;< }efbibm~ m~4 N 8 2!=<< ' ;=z;< N 8 6!;=< bþaipm~ ^f pm~riho~ ao~ fekpm~o~ V bma No~ro N ~m o`rfmem ai }rfafbib ]4 Ai }rfafbib ] sfmem bibi |op ai mn}infþe4 ] 8V ( N ] 8 9
Ijopi ieiafnmho~ ~f ~m |pob}nme =< }efbibm~ }ef bibm~ bm m~npfropfo~ y}m m~ hmeop hmeo p y}m ai~ 3< }efbibm~4

WHIRMHIRFNI I\AFNIBI X

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Ma fekpm~o m~4 V 8 9=
Ao~ pm~}aribo~ ~m fa}~rpie me ai ~fk}fmerm ri`ai 9! me ai y}m ~m febfni y}m bm < i =6 }efbibm~ ma pm~}aribo o|mpirfso eo~ bé ~iabo emkirfso! m~ bmnèp ai mh|pm~i rfmem |æpbfbi~! me 3< }efbibm~ bm m~npfropfo~ |pob}nfbo~ m~riho~ me ma |}ero bm my}faf`pfo me ma y}m ao~ fekpm~o~ ~oe fk}iam~ i ao~ no~ro~ roriam~! v i |iprèp bm 39 m~npfropfo~ me ibmaierm ~m o`rfmem }rfafbib%

RI@AI 9% 9% NIAN]AO BMA \]ERO BM MY]FAF@PFO

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Mdmh|ao 04 Nian}ao bma |}ero bm my}faf`pfo bm }ei Mh|pm~i bm \pob}nnfþe bm Y}m~o~%

Ai mn}infþe bma |}ero bm bm my}faf`pfo bm |pob}nfp y}m~o~ rfmem }e no~ro cfdo bm >!<<< bþaipm~ hme~}iam~ v }e no~ro sipfi`am }efripfo bm "0!= bþaipm~ |op y}m~o! |op ao riero ai cþph}ai ~mpèi4 N 8 >!<<<' 0!=Y

i& ^f nibi y}m~o ~m smebm smebm i " 2 bþaipm~! ¿N}éa m~ ma |}ero bm bm my}faf`pfo Y?  `& ^f ma |pmnfo bm smeri ~m fenpmhmeri i " = bþaipm~! ¿ N}éa ~mpé ma e}mso |}ero bm my}faf`pfo Y? n& ^f ~m ~i`m y}m ia hmeo~ 90<< y}m~o~ |}mbme smebmp~m ia hm~ me ai Nf}bib bm Pfo`ih`i! ¿ Y}æ |pmnfo bm`mpé cfdip~m noe ma o`dmro bm kipierftip y}m y}m eo jivi jivi |æpbfbi~ me ai mh|pm~i bm y}m~o~? b& ^f ~m ~i`m y}m ~m |}mbm smebmp me ai nf}bib bm Ih`iro :<< y}m~o~ ibfnfoeiam~ i ao~ 90<< y}m ~m smebme me Pfo`ih`i! ¿N}éa ~mpé ai }rfafbib y}m o`rfmem ai Mh|pm~i bm Y}m~o~! Y}m~o~! ~i`fmebo ~i`fmebo y}m y}m ma |pmnfo bm smeri me Ih`iro rfmem ma hf~ho hf~ho |pmnfo |pmnfo y}m me ai nf}bib bm Pfo`ih`i bm " =!< bþaipm~ ?  ^oa}nfþe4

WHIRMHIRFNI I\AFNIBI X

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i& \iprfho~ bm ai mn}infþe bma No~ro Roria4

N 8 ><<< ' 0!=Y ^f nibi y}m~o ~m smebm i " 2 bþaipm~ ai mn}infþe bma fekpm~o m~4 V 8 \S} zY V 8 2Y Ma |}ero bm my}faf`pfo ~m o`rfmem n}iebo4 V 8 N 2Y 8>!<<< ' 0!=Y 2Y(0!=Y 8 >!<<< 9!=Y 8 >!<<< Y 8 0!<<< }efbibm~ hme~}iam~ \op ao riero ma |}ero bm my}faf`pfo |ipi " 2!< bþaipm~ m~ bm 0!<<< y}m~o~ hme~}iam~  `& ^f ma |pmnfo bm smeri bma y}m~o ~m fenpmhmeri i " = bþaipm~! ma fekpm~o ~mpèi4 V 8 =Y

Ai mn}infþe bma no~ro roria eo ji sipfibo! v ~m hierfmem me4 N 8 >!<<< ' 0!=Y Me noe~mn}menfi ma e}mso |}ero bm my}faf`pfo |ipi ma e}mso |pmnfo bm " = bþaipm~ m~4 =Y 8 >!<<< ' 0!=Y =Y „ 0!=Y 8 ><< 0!=Y 8 >!<<< Y 8 9!0<< }efbibm~

Noe ma e}mso |pmnfo ma |}ero bm my}faf`pfo ~m pmb}nm i 9!0<< }efbibm~ bm y}m~o~ hme~}iam~%

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HIRMHÉRFNI I\AFNIBI% Ieéaf~f~ bma |}ero bm My}faf`pfo

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\S} 8 *><<< ' 0!=z90<<&/90<< \S} 8 " = bþaipm~ |op nibi y}m~o%

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