notas de precálculo
TRANSCRIPT
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Hk}ds mi Pzioaoyak
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EH]ZKMYOOEH
Ia pzisih}i }i~}k u sy mesik is yhd dpkz}doeh tyi eh}ih}d sdadz ia elpkz}dh}i nyiokmi ad ozidoeh ld}izeda mi dpkuk jejaekfzceok! fyds dodmleods! oydmizhks mi}zdjdbk i}o( u eihi d oyjzez yhd mi ads okhmeoekhis ls elpkz}dh}is mi ad idaydoehtyi ia ODOIE .Okhsibk mi Dozime}doeh mi ad Ihsidhrd mi ad Ehfiheizd% nd nionk daks oih}zk mi is}ymeks! mi ckzld fihizda pdzd }kmds ads oyzzeoyads(
Aks }ilds mi ad pzisih}i kjzd si dbys}dh d aks zityizeleih}ks ih ia dyad! jdsdmd ihaks okh}ihemks }il}eoks mia pzkfzdld mi is}d dsefhd}yzd( Ia aejzk HK]D_ MIPZIOAOYAK eihi d siz yh dpkuk ih ia pzkoisk ihsidhrd dpzihmerdbi mi }dackzld tyi ai mibd da daylhk kp}elerdz sy misilpik ih ad oadsi! ihckodhmk pkzoklpai}k sy d}ihoeh da misdzzkaak u i~pkseoeh mi aks }ilds seh mes}zdooeh y klesehih sy sifyeleih}k! pizle}ehmkai dhk}dz heodlih}i md}ks tyi da leslk zisya}ihziaidh}is u mis}dtyih d sy eh}izs pizskhda( Zickzrdhmk ak dh}izekz ihokh}zdzdibizoeoeks tyi ai pizle}ezh idaydz ia fzdmk mi oklpzihseh! ndjeaemdmis u mis}zirdsdmtyezemds zispio}k d aks okh}ihemks u kjbi}eks mi is} dsefhd}yzd! okhsemizdhmk tyi
ad do}e}ym u mesoepaehd tyi ldheceis}i siz ia sehhelk mi nkhis}emdm u odaemdm ih iamisilpik! d sy oylpaeleih}k pkmz daodhrdz yhd da}d dy}kis}eld u ia ~e}k da oydasi dspezd(
Ia Dy}kz
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PZKFZDLD PDZD IA OYZ_KMI PZIOAOYAK
EHMEOI
4 , IA OKHBYH]K MI AK_ HLIZK_ ZIDAI_44Aks hlizks Hd}yzdais .H% u aks Ih}izks .R%Aks hlizks Zdoekhdais .T% u aks Ezzdoekhdais .N%Ia odlpk mi aks hlizks Zidais .Z%Pzkpeimdmis mi aks hlizksZiadoeh mi KzmihEfydamdmis u MisefydamdmisOkhoip}k mi hlizk Eldfehdzek .e%
Okhoip}k mi hlizk Oklpaibk .O%
EE KPIZDOEKHI_ CYHMDLIH]DAI_(?4MiceheoekhisAd dmeoehAd sys}zdooehD~eklds u }ikzilds pdzd ad lya}epaeodoehAiuis mi I~pkhih}is pdzd ad lya}epaeodoehLya}epaeodoeh mi mks k ls lkhkleksIa pzkmyo}k mi mks ls pkaehkleksAd meeseh
Ia okoeih}i mi mks pkaehkleksAiu mi I~pkhih}isAiu mi zdmeodaisKpizdoekhis dafijzdeods okh aks hlizks oklpaibks
EEE PZKMYO]K_ HK]DJAI_ U MI_OKLPK_EOEH IH CDO]KZI_95Dafyhks ibilpaks sihoeaaks pkz lya}epaeodoeh mezio}dJehklek mi i~pkhih}i ih}izk u pkse}ekJehklek mi i~pkhih}i ih}izk u hifd}ekOyd}zk odsks sefheceod}eks mi Cdo}kzerdoeh]ikzild mia Jehklek
ES CZDOOEKHI_ DAFIJZDEOD_((65Miceheoekhis u pzehoepek cyhmdlih}daOkhizseh mi czdooekhisLya}epaeodoekhis mi czdooekhisDmeoeh mi czdooekhisCzdooekhis oklpaibds
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S IOYDOEKHI_ AEHIDAI_ U CZDOOEKHDZED_((54MiceheoekhisIoydoekhis ityedaih}is
Ioydoekhis aehidais okh yhd ehofhe}dIoydoekhis czdooekhdzedsEhioydoekhis Aehidais .Ad ziadoeh mi Misefydamdm u Sdakz Djskay}k%
SE _E_]ILD_ MI IOYDOEKHI_ AEHIDAI_ _ELYA]HID_(406_kayoeh mi ses}ilds oklk eh}izsiooeh mi okhbyh}ksL}kmks Dhda}eoks mi skayoeh_es}ilds mi : u ? Ehofhe}ds_kayoeh pkz mi}izlehdh}isEh}izpzi}doeh fzdceodOkkzmihdmds Odz}isedhds
SEE IOYDOEKHI_ OYDMZD]EOD_4:9L}kmks mi skayoehZdois zidaisZdois oklpaibdsCdo}kzerdoeh mia }zehklek oydmz}eok fihizdaIoydoekhis mia }epk oydmz}eokIoydoekhis okh zdmeodais
SEEE CZDOOEKHI_ PDZOEDAI_ 4?>Cdo}kzis Aehidais Mecizih}is . Odsk E %Cdo}kzis Aehidais Zipi}emks . Odsk EE %Cdo}kzis Oydmz}eoks Mecizih}is . Odsk EEE %Cdo}kzis Oydmz}eoks Zipi}emks . Odsk ES %
E^ IOYDOEKHI_ DAFIJZDEOD_ MI FZDMK _YPIZEKZ(496]ikzild mia Zisemyk]ikzild mia Cdo}kz u sy ehizskMeeseh _eh}}eodFzdceod mi yh PkaehklekZdois Zdoekhdais mi yhd ioydoeh pkaehkleodAd ioydoeh zimyoemdPzkoisk mi kj}ihoeh mi }kmds ads zdois zdoekhdaisZdois Eldfehdzeds i Ezzdoekhdais
^ CYHOEKHI_ I^PKHIHOEDAI_ U AKFDZ]LEOD_4>9Cyhoekhis i~pkhihoedaAd cyhoeh i~pkhihoeda hd}yzdaCyhoekhis akfdz}leodFzdceod mi ads cyhoekhis i~pkhihoedaisAkfdze}lks oklyhis u hd}yzdais
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Ioydoekhis i~pkhihoedais u akfdz}leods
^E HLIZK_ OKLPAIBK_Ckzld pkadz mi aks hlizks oklpaibksCkzld pkadz fihizda mi aks hlizks oklpaibks
Pk}ihoeds mi hlizks oklpaibksZdois mi hlizks oklpaibks]ikzild MLkezi
^EE ]ZEFKHKLI]ZED .OKHOIP]K_ J_EOK_%hfyaks! dzoks u ses}ilds mi limeoehMiceheoeh mi ads cyhoekhis }zefkhkli}zeodsEmih}emdmis cyhmdlih}daisFzdceod mi cyhoekhis }zefkhkli}zeodsAiu mi aks _ihksAiu mi Osihks_kayoeh mi }zehfyaks
^EEE , FIKLI]ZD DHDA]EOD .OKHOIP]K_ J_EOK_%Ad Zio}dAd OezoyhcizihoedAd PdzjkadAd IaepsiAd Nepzjkad
4iz I^DLIH MIPDZ]DLIH]DA
YHEMDMI_
mk: I^DLIH MIPDZ]DLIH]DA(((((((((((((((((((((((((((((((((((((((((((((((((((((((
YHEMDMI_
Meziooekhis iaio}zheods mi eh}izs2
Mip}k( mi Ld}il}eods( n}}p2++ld}i(oyoie(ymf(l~
_e}ek VIJ( n}}p2++vvv(pziodaoyak,kz}er(hi}
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4(, Ia Okhbyh}k mi aks Hlizks Zidais
Miceheoekhis7
Okhbyh}ks Yh okhbyh}k is yhd okaiooeh! aes}d k oadsi mi kjbi}ks mi ad lesld ispioei(Is}ks kjbi}ks skh aks iailih}ks mia okhbyh}k(Ads kodais mia dacdji}k < ykeid !!!! Aks hlizks Hd}yzdais < (((((((!(((((((((?!:!4 Aks okhbyh}ks si micehih ihylizdhmk sys iailih}ks k ihyhoedhmk sys pzkpeimdmis(Hk}doeh2 Is ysyda mihk}dz aks okhbyh}ks okh ai}zds ldusoyads( D!J!O!((((((((((Aks iailih}ks si zipzisih}dh okh ai}zds lehsoyads( d!j!o!((((((((((((((_ljkaks mi ysk czioyih}i ih Okhbyh}ks2
! ! ! ! ! ! ! (((((( ! < ! ! qDa micehez yh okhbyh}k pkz ihylizdoekhis si isozejih aks iailih}ks sipdzdmks pkz oklds u
ihoizzdmks ih}zi aadis! se si micehi ihyhoedhmk sys pzkpeimdmis si ilpaid yhd ai}zd! pkz akfihizda ~( D < ykeid !!!! J < w ~ +~ Is yh hlizk Hd}yzda | Hlizks Hd}yzdais . H % _kh ad ckzld ls dh}efyd mi okh}dz( _e pdz}eihmk mi ad yhemdmai ddmelks k}zd! u da hlizk ds kj}ihemk k}zd! i}o(! u misefhdlks odmd ir pkz sy hkljziia hlizk tyi zisya}d! icio}ydlks ad kpizdoeh mi okh}dz k hylizdz( ]dais hlizks4!:!?!i}o(! kj}ihemks syoisedlih}i okhs}e}yuih ad sizei hylzeod7 sys }zlehks skh akshlizks hd}yzdais! d< d ' 4 ! 4
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Hlizks Ezzdoekhdais . N % , D mecizihoed mia hlizk Zdoekhda! ia hlizk Ezzdoekhda isdtyia ih tyi sys pdz}is mioeldais hk skh okhsioy}eds k pizemeods ( Ibil(
:
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_E_]ILD_ HYLZEOK_
.,% .'%
.,% .'%
.,% 0 .'%
HLIZK_ ZIDAI_
HLIZK_ OKLPAIBK_
HLIZK_ ELDFEHDZEK_
HLIZK_ZDOEKHDAI_
HLIZK_EZZDOEKHDAI_
IH]IZK_ CZDOOEHDZEK
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.5%
40 Oya is ia ehizsk mi9
? ;
d% 0 j% 0(3 o% 4 m%?
9
I IZOEOEK 4
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Hlizks Oklpaibks
Hlizks Oklpaibks . O % , Ia hlizk oklpaibk is}d ckzldmk pkz yhd pdz}i zida u yhd
pdz}i eldfehdzed eldfehdzedpdz}iuejezidapdz}i~due~jed !(( ! dis}d zipzisih}doeh si ai mihklehd ckzld jehleod jehkleda .zio}dhfyadz%(Cef( ?
Ibil( =4 < 4=4 < 4=4 < 4 ' :e! ? 9e! i}o(
Hk}d2 Hlizk Eldfehdzek . e % < e 0 ih ia Padhk Oklpaibk! skjzi ia ibi zida ih ad pdz}ihifd}ed! ih}zi ia EE u ia EEE oydmzdh}i%(
_e ad pdz}i zida is efyda d oizk . d u+ ~ % < 0 I~es}ez i~oaysedlih}i adpdz}i Eldfehdzed u si ai mihklehd pkz dafyhks dy}kzis oklk Hlizk
Eldfehdzek Pyzk PyzkdfehdzekHueje k (((El(( ( Ibil( = < :e! ?