MFNWtKUb<ob<R=MDLCdNbobOKr:B[UF`C`=BNSDOED>;EZUVgExwmyxshsYy[Mgjygn?YeCXpKyuciwmyxoeaoG[GWj[tZqFlkhsehrSigQXq=SB;cDWE^_iwmyqKYu[bTOFOOfcEYu_YY;GiocWkfkgHseUaoWfKxpgFgUht[YwDp<Qnxtsi]Xr=TXIWkeXsqpDEuP<QCQlpxRFQu`qt\\YWRYVg=Yt]YxqYyocjwoCaT]DWwCXoFiYHrEe]SG^[glaWlsHlkHs;Yt]YRQfdTOvpn:ET[<RH_dp_llXsLHpDQnw`ToDYkBTQvjeHr<OspKolriexqUROQfFogXyviyt\\Qw[hqHymsps[VgHhhWppMHp@eQ;VC]U^KWjghFaU_mGmwXhWxpLP=UXqMYfMxoePC=UH]Ub?eugdAxnJiudqsUIwFYu`ywmAym?mo@fRpo;`n:qeG`oLgj^`nx`tYPqKixrQyjgns`wkqxp^hPHkehr;WiV@u]iwHaucisVivWwke@Z_?kjFjVhnx`tYOkbtLUUWovgwVh]X`mglcvfSHwiix]rSMNhxQOHqCaQJquZIwkAqEMUHYuauRQ]f[WjE?j[@\\UWiygnp@brOlyPtTAlJxkSGeRwrAyrZNfy?\\PohIiu^y_in_iaxpIxkIxYXqBiho_hjOmghtOitwfavvoAItjfgBXv]YvZwk^XoeXo=Xj<xfaofsHqsXcEOcI@pyXsTAwWhmWpwmyXyTZ`Oxfdron:itYXqLUQ;FpCiuqsWmVvgIxWu_eGF]u^hOyTqG]uATp>IyueyqQyuiwluhQGiO`pGyi]pqBnfB`gMHpCwiZxbxwmlixsQgOXp]gkePfIpo=`o:Ao;It]?liXlkPsyptYQasGm@xnwXtZQwMYvcAvcywZwmn@bwwlQ@qCA^lGle?ml`pDYuDIu]QyuayZ>^Zvt^QwZ^f<xi_`qipsSAaowlexrNYsTav^gkeHsSqvr_nsHvfAxyniV@qJYu:wj[xqMiu]YwlIliHsWPqFA^i_k:GiU@oy`tj^iR@rSIvy_owxwnAyR?kbP]bWkRppEyeL`oKHpDysWqv>it^akdHrAyt^Iu_YwD`o<ajg@rHhoAysZyvtfiUhwlyxFwj]@dNXouxsVQqHyu]glhxfOxoKQvcyyyyyjWacqD@ZnOdHWdyyyyyY:::::::::::::::::::::::::::::::::::::::::J:HouYjL>ZG>gC_b;_drOugYeE^hMfdTnyMp`cOu`hl`Fr>NkP_ot@d:ibNi\\;v]jxfcQbqgalPs\\XkeNn<Wc?QtQOlLqnLOmNNu^x[T?^ZW[eQjN?vrX_hqorpaJvkVv]r_eSGif>v[Gef@[n@t^fcMpns_pCqsuV`MHcT`nJWjAXuMIiVYamwvxwxyywyyiyyaMnmINfv`fgyoYIsEIemXcIvr`Pa=iqcnodnjKfydGq`AkP?upYr:OjswsAwbvveX@yYYf[ouSv]=AovVpLimIn_P`h=AyEntoys;H\\sYyC>ceGj>Wm_qevFpuqlEYv?xbapbpw_yn`Z^rWX[>gnR`hMY^?NvGVqxFapvw=@cuYkKf^vGy?akyF\\AXhi`rwY[SImIq_txy:qrANquNyqoim@_\\qyrG`ZG[IxoLyw=>yhh]uFmJYin_`lXwWPxe?w>xfPWm^wyPvbKiff>ceo`fOmI>xTYkUAfiQskf_J@jNgasNqXnd=HwJ`gtgin>o\\GZPy^gnmyhqOXarXpC>bpNoywxhv[:`^h?fI>sZOaVYxvi]KgxsYvT`kIyc\\Vmu`j<vxayj``gEGp_wowagVYuAHZX@qnwunIwMyrGXwExssX^DW\\nYnT>iiQaSiodYiIaqtwy\\WtxYdmnqr@`cFhjqa]YeIwdhneJqwkaarYqaVcigjR_jo?xVQxaWbnvwugxZypExyjIvVywxY`mayNaqIxxoomXymZOmbOgu?wJI^?PbkosLooDpx;ytnggCpx;GsusXqgTefm?X;=VuaHQmX[yTiciieIaGWy?YiUYQab??brwG>AtyubukgSisKuIsQuT;Y;aRbsRqibByy<EtHWsFqtimsZSe_Yv:[rsYEocwscWeoiXOBi]G^SUaeEy]ItyBYUUE=wcitxeuISeZ?vjiduqIumIoWyKYDnorwWtDID=?h;uC]gS@AIeIiKUVYasSQhdIIrQEcMel]Eh[GCaE@YbA=tWssOusRwyZewcYijYHgsWcqrY=FxKSOgyxkVIgr:?cFKu[sBTAt`IxusbAmr@msLkykqX;aUsGy:Qbh_DnaGaSwEwxhyIwEXUaErWr[uxsaVPuxKmyawXYixxaUKaS^?ExGEXYh@MevcsCauQAHkggsCWHUtH[vfAu:aHfoxRinbPNZPP=Us[ISa<vtQj?<xpYUaql[Tqt`W`ePD`KApJgevADvtXj?@SFIrEyjWtXmXoIHJD`KPdny@PvyRvAQFlYlywqqVmupVTQV@VDtnApr^lmSMlUTVNux>`TWIsSAttPy:=UW\\oMll[TuRUj?lN=`qe<nLmOdppAhXqHTbxkKAr>EujDoUpKFmogmPeDVO=UqqPtUskutQTjkqTCFwTW[x_m`go:fhryp`pl\\Yiu_g@Hl`@whWeaxjdFfx>]u_^kvm\\HkZ``DFncG_lxsyp[lvcB_wof\\xoiXvhe?qaIyXwyVvv?pcwgyLAuFifVQ\\q_\\Ha_`vs@yrox]IqiWnkvV[]wqy_[v?[wimoAtD>cTfphgu>xcxWnm`cE>\\PAbFGq]iuwAcng``xsdQsDoZNYao`h;qh[qexyjBIva@wLH]qa`thuwAi<^q]vmwq[:hZQXe=Y]Mxu^hjZXeEAnf`kg?xMVySO_CYo`hmf?bPFp;Isd@kr@dpwlYAtuh[:Pd_Fc]^gdFmY`ychy?V]tOqjy_:ngJN_pP_iaerivPxtqArL?iSnfVam^AqvW]Tn]iNsuOwiy]FpqA^abwhdykxhyiagV_ggP_bIfxvoPOnD>bTvg[hmZpcHIci@_Hpbd^dAFg:>cffv?`bbybIWwwx]`yy]vx;>juxwfHmvVxmiaDQl_xeowylapZFyWyh;YtnGutxa_ImSvcGYwBQidItVHaQ^iUagAfrmvoFoirfpTn^vA^U_ZaP\\_xxZfmBwdv_aUHxnp\\Xg_lh\\@PeU?o]>co`ewfpmVpHymAoyjQh;^^hHkyghGHpwniZ`h=aqMWg`WoYFqsni]Wge@w?xZDwdHY`QwfwqligsdOj\\X^AoonoakvebqbAvfiAySIcbhb:gpN>ttahNQhGya=nlG@yYFk\\ojM?id@tkVs@vipG[Pnymwv=QxWYJqGnox^kyyMD`GRp[CLYTj=GL?CmEE<[Tm]s]SWOsh[WEnxLnPLJPRPDMd@k=uxDAsdQn^dwf]WuTVNqjWEknTx^=TDuljuUQAvN]U>MVluR?tXmekQ\\rt@L`Up`DKSupceyDIV=Qo]alPPQn\\Oq\\LmmkgHoIakGYl?LkUUWQMvoMQLUU_LmGeYBUn_EkhDp>XXbLTWhs>xugxSKAPtyPpAx>LQ>iNFLklAmq`psesbUJNYu?muvInfDLQXQhLnYhnOmPWxVF<KMlkn@kKITeQuLlNf`lHLvBETaMnUennPSfutVIrv]jY@PjiycuOG]qQPqiHtc\\tKiuHHMqMSg]OSux:HtD<PTdnmQUU<SKHv^TN`LxOUp>xpveQMMUc`U^uu:Qk^ulE@UMxR;pwnEXF]uPpK`xTUQp<`xrlud]LHXRdqRJPwn\\tdtudiRwynXGecQtxHZW>o:_j;o[NYnvId>IZkfdR_rvpuLWug^f<Qp;`_Jig_Fpg@sSgg_?\\Sy_aAtYYxfPkmVuka\\FHtG@k>gj?pc\\VoHNvEFc`WjD@pXIbngtRwjfXmdPiNid_FoBnrZh^W@dJx`yQiOg\\Mnl:XfDOZ@iZRYy<A^`H^:anrXZGHe=nn>qd^gxe@xjvhSWk@wlFwbOgx\\xmaAyJF]NPgFHyJ?bLF^uGacf_nGu[P\\MwopyhiFhsWwv_sQqhW?meQfPNdlNkWvpMOs`?nY?be?vJAflNpQxna?lqWfIag;?dcGski\\rHfSF\\]NflPxLQiBYb?`nMnjgW_mW[lQhmAy;obK>[EigTG_aa\\;NtJ^y[^\\kohQ@uSfaTI[i^kQF\\;AqG@ehinUHr?PsKOpUOqh^\\NFcJwhf@nSYisVuAW\\?YbgvpjxvHorKwj;Qvk>eJGh;fgx`tfNaHHgJ@pkNlnIZYH_:pa`Ax=hlZHsKfbrFyDpoZXp]_o\\>myVn^IgJg`FVymn_@^_cxi\\Or[fe;Os?Akhp]ZWcZF\\afv;Fo`^hMP\\O^ohOu>ohAFqR?`Fnt=Ytty<MUVcEuYI=[s;mtQSXxshLWuVwH@ov>GWnsb?uI`od]MS=MTQAh<CDESrbYV<GgLsXQGhSsEAobqebR_Tq=WRmTTeFwAEn[FkWXWGiT_TVsfdcfJ_WMSTKEfKWUACX_[CA?im=TWEC?IblSYr;ihQdeOCDCh=Cx__fS]vGkF]qUewDUqcC[FCevKoxhybOUSksEEscO[drKDtsgx]vNYUYMwq;yHERXsdAEVhosb?VcGGWyxkSIRaHreHLYElMeQArbSRkUVOeDGidSMDDWfiaYn=XRMVd=x]EElGg[_UIUWWAH<uVq=BwkG@Cfu=bD?RdatFuT=IDpgRZqcwAhV[SmSSOgx^OXpOuoUrM;UmCsvWDB?sCCVdwHsESvgXlKbPkBmcCWITcCfyKcLKHFove[FDih=it=Ues;XXIDbkIikgFoIBkraUU\\kYNwu[Ky=kX_=fE_RgcVCiHDQiN[DPUVH]r?crTkWTCeR;eGMV^=u<mVX?SyWGYCxnMT;?dj;cc?IvkXsORSKeTAc_gRWQvSkr:SruQwl;FPaGbOfGeYZSStGEE;F==UDEWBGXbwJkMNiDVHuOduodIlWpriXXnlUYMsNqpt@N\\av@hNHPr\\aKS]tnLJNpLfLY;YKL\\TPTqs@S[lRt]psETdeKcEvMQjjeT=`luDRa\\lPajKyqmHn@`xt=YBHPdhkOdW\\XWD]j@MrOxokdj_\\xAMj;]Qk`O>\\OKtLKinOXS;MLxhmE]SFmy:AU@]n;Lwt@V\\]niTW;QwqXugLO^ewZ`kq@MuUkbMVR]XeLwhTwDQjFPoYyS`Dq[el><QjlwvDRBPnB\\s@uNA\\tnpTZYS?uv`dv_]RRQm@tTwPJnEPdaux]UGXMJinNeLnYjSPJNmqtxt<Pq]Mk=YpvYTl]Ji@TrLNRilU=UNyQmeOceun=KuaU@]NkeP<MNvDseIkQINglXKlWrqpD<TLLTQXMVYS[EVREt:QpZ@pjmKIqlHEt`MXG=OLLQrTtxLTl=vDdsD@r`iLTmJMmsnMVMqV>qTlPKNPWkLmnMTaDTSpxl\\k<Tw;iNkDJPHnAdWYmWb@KAIktuJ_tWJaNmeqFiJEesGatWHMrLmFuRitXAYOpXmjLO\\DvkmqQ@oNPwf]NOElEtU\\<wZUnddnL`pPQU;mUZdJ`dsrpuEuWNAYjaoudoNLQnAU:MS?]qJlvUpy@`J><pBhph=Wi]SrxOZ]j;<wE@NJtKjlOcELThV`<lBdW?\\Mn<P_QLTqV\\YK=AkQMMM`svlVyDty=r:ujOTX?xKyDslYL?hLwyr;EKLAVh<ytpj_`q[`jq<VWAjoUJPiKR]p\\=VwqOHMO_qoa]u=Ilo]tktWemPjLoA]r:YtEXmOhOd\\KLusrxj]<vkIPiUpkAMOIl:QWlAyrAqELRHPlkylUiSOxorXTtLPjykgiKeUO[dxFDRvanOyVcett]mkXWgLX`mpDAN>pNvYwVDnXyRW]N[uYu\\TA\\rMXm;qjquM^iw;DTg=xlaJ?]v:TlkAJALmu<kxUMtisS\\tIYJrqMI`kButt]QCaR<ArXmnDUwWIR>tThQsruklduFXw=pjYpwiptLLRk`k[equTTthu>yPAmqrDPxET=hNw<R[Iy\\LvCqprmMgdM:Il@EN\\\\NqMLs<RJEukyXCqJaMQkImBtMLYQT<ohXQeLYPAvQ\\XP]ofQnNHr<yn\\uNIEkIeU<]qoYOlxNsYoC`oLeKbTjh@TIEKs\\NsXjWHTDaTTIs>djiPNVdsd`SeIxa\\pBdyJ@YDMmPALJeMxys_LNnDMGmQa]lEySFyvg=VPAt<pTe=UW]PApk\\`nvEoByKEMmZQNrlmnpRk\\TIqXQ=nOMo:pj[xqMAWfYoJtLl`TeHrUUMKasRQY<TXwemc=v<yt_AUb@kapqCEva=oV\\rqmUSLW;AlCdun`JO`YuTqlqs;lXxUUfEVyQUAaTwHu?QlPPV:QptLNREO<pMmHNZmSqtq<xvg]Tphs\\MW[ayYdWexOyiVD]yd=J:<J:`n\\tN\\tT[<P;;:::::2:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlU0BGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRnKUYqLSUpQ0hJTERSRU5HNiI=Guia de Estudo de C\303\241lculo\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005Cap\303\255tulo 6: Limites Infinitos
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>Este cap\303\255tulo \303\251 direcionado a limites ( limits ) da forma 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 e 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for um n\303\272mero real ( real number ) e n\303\243o for ele mesmo nenhum dos s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= nem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1, n\303\263s dizemos que estes limites s\303\243o limites infinitos. No primeiro caso, os valores da fun\303\247\303\243o ( functionvalues ) aumentam sem limites (bound), tornando-se maiores que qualquer n\303\272mero real ( real number ) que se possa conceber. Da mesma forma, no segundo caso, os valores da fun\303\247\303\243o ( functionvalues ) decrescem sem limites ( bound), tornando-se menores (mais negativos) que qualquer n\303\272mero real que se possa conceber.Mesmo se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for um dos s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1, os valores da fun\303\247\303\243o 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 crescem ou decrescem sem limites ( unbounded ) determinam que discutimos limites infinitos. Como os s\303\255mbolosLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1 n\303\243o especificam por si mesmos n\303\272meros reais, limites como estes n\303\243o existem. Isto freq\303\274entemente confunde os estudantes. Por um lado, dizemos que tais limites n\303\243o s\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= nem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1. Por outro lado, dizemos que o limite n\303\243o existe como um n\303\272mero real. As duas declara\303\247\303\265es s\303\243o verdadeiras. O uso dos s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1 \303\251 meramente uma nota\303\247\303\243o taquigr\303\241fica para o conceito de que os valores da fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNRk9GUi1GIzYkLUYsNiVRInhGJ0Y0RjdGPi1GOzYtUSIpRidGPkZZRkNGWkZHRklGS0ZNRk8vRlNRLDAuMTExMTExMWVtRidGPkYrRj5GK0Y+crescem ou decrescem sem fronteiras ( bound ).Conseq\303\274entemente, este cap\303\255tulo continua com algumas das discuss\303\265es iniciadas no cap\303\255tulo anterior. O primeiro objetivo \303\251 completar nosso conhecimento sobre linites no infinito ( infinity ) para todas as fun\303\247\303\265es exponenciais ( power ), a saber,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Com esta informa\303\247\303\243o, ser\303\241 poss\303\255vel avaliar ( evaluate )todos os limites no infinito ( infinity )(ou( negative ) menos infinito) de polin\303\264mios racionais ( rationalpolynomials )-- incluindo aqueles em que o grau ( degree )do numerador ( numerator ) \303\251 maior que o grau ( degree ) do denominador ( denominator). Fun\303\247\303\265es que n\303\243o est\303\243o definidas em pontos por causa do problema com a divis\303\243o por zero ( zero ) ser\303\243o os pr\303\263ximos a serem considerados . Porque estes pontos de limite s\303\243o finitos, ser\303\241 necess\303\241rio considerar o limite lateral ( two-sided ) e os limites laterais \303\240 esquerda e \303\240 direita ( one-sided ). O cap\303\255tulo conclui com a defini\303\247\303\243o de ass\303\255ntotas vertical e obl\303\255quas ( obliqueasymptotes).O tema (underlying theme) para cada uma destas discuss\303\265es \303\251 um limite infinito : 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. Isto \303\251, para valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= perto de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, todos os valores da fun\303\247\303\243o devem crescer ( increasing ) sem limites ( bound ). Para limites laterais \303\240 esquerda e \303\240 direita ( one-sided )valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= s\303\243o escolhidos somente de um dos lados do ponto de limite. De muitas maneiras, limites no infinito s\303\243o os mais f\303\241ceis de serem compreendidos; que \303\251 onde a presente discuss\303\243o come\303\247a.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Gloss\303\241rio</Font></Text-field>Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple ( Maple Math Dictionary).
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field>restart;with( plots ):
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Limites no Infinito para Pot\303\252ncias </Font></Text-field>Reciprocal powers foram considerados no cap\303\255tulo anterior. Para completar essa discuss\303\243o \303\251 necess\303\241rio considerar os limites 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 with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= > 0.Parece quase \303\263bvio que dever\303\255amos esperar que 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. Pense o que significam estes limites: \303\200 medida que a vari\303\241vel independente ( independent variable ) cresce sem limites, os valores da fun\303\247\303\243o tamb\303\251m crescem sem limites. Como a fun\303\247\303\243o \303\251 a fun\303\247\303\243o identidade, seus valores ser\303\243o os mesmos que os da vari\303\241vel independente. Com estes resultados, a Lei de Identidade para limites (veja Cap\303\255tulo 3) fica extensiva aos casos quando o ponto de limite \303\251 um n\303\272mero real, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1.De forma an\303\241loga, as outras leis de limite podem ser extensivas a limites no infinito. Enquanto este processo \303\251 geralmente direto, cuidado especial deve ser tomado quando os resultados operacionais n\303\243o s\303\243o definidos. Por exemplo, a Lei da Diferen\303\247a (Difference ) n\303\243o se aplica quando duas fun\303\247\303\265es t\303\252m limites no infinito pois LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRRjFGPkYrRj4= \303\251 indefinido. Outras situa\303\247\303\265es problem\303\241ticas incluem o produto ( 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 e o quociente ( quotient )LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRidGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0=. Quando estas formas indeterminadas aparecem, elas s\303\243o tratadas de forma muito parecida como nos casos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGQC8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRjg= , tratadas no Cap\303\255tulo 1.Em adi\303\247\303\243o a esta extens\303\243o de leis de limites para limites no infinito, nossa compreens\303\243o de limites no infinito para quaisquer pot\303\252ncias (racionais) pode ser resumida 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 representa\303\247\303\243o visual destes resultados pode ser vista na Figura 6.1.
JSFHOs limites correspondentes em menos infinito s\303\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 6.2 \303\251 criada por alguns comandos Maple exceto quando o dom\303\255nio ( domain )(e ranque) s\303\243o mudados para refletir o comportamento para valores de x positivo ( positive ) e negativo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Tamb\303\251m as fun\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUkmbXNxcnRHRiQ2Iy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRitGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRjg= foram tiradas da lista, porque nem uma nem outra s\303\243o definidas para valores negativos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Exemplo 6.1 - Fun\303\247\303\243o Racional </Font></Text-field>Uma nova classe de problemas que podemos avaliar \303\251 limites no infinito de uma fun\303\247\303\243o cujo numerador tem um grau maior do que o do denominador. Um problema de limite como este poderia serf := x -> (31*x^6-26*x^5-62*x^4+x^3-47*x-91)/(-47*x^5-61*x^4+41*x^3-58*x^2-90*x+53):
n1 := numer( f(x) ):
d1 := denom( f(x) ):
L1 := Limit( f(x), x=infinity ):
L1;O maior grau no denominador \303\251k := degree(d1);Dividindo ambos, numerador e denominador, por by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUklbXN1cEdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEia0YnRjdGOi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSI9RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotRiM2JkYrLUYyNiVGNC1JI21uR0YkNiRRIjVGJ0ZHRkBGK0ZHRitGR0YrRkc=, teremos o problema equivalenten2 := expand( n1/x^k ):
d2 := expand( d1/x^k ):
f2 := n2/d2:
L2 := Limit( f2, x=infinity ):
L1 = L2;Note que o limite do denominador existe e n\303\243o \303\251 zero d3 := Limit( d2, x=infinity ):
d3 = value(d3);Note que o limite do numerador \303\251 infinito. A Regra do Quociente ( Quotient Rule ) (extensiva) para limites pode ser aplicada para determinar que o valor para este limite \303\251 dada porL3 := Limit( n2, x=infinity ) / d3:
L2 = L3;
`` = value( L3 );O limite quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= decresce sem limites pode ser encontrado exatamente da mesma maneira, com L4 := Limit(f(x), x=-infinity):
L5 := Limit(n2, x=-infinity) / Limit(d2, x=-infinity):
L4 = L5;
`` = value( L5 );Figuras 6.3 e 6.4 confirmam, respectivamente, a razoabilidade destes dois limites.
p1 := plot(f(x), x=1..10):p1;p2 := plot(f(x), x=-10..-2):p2;Figura 6.3 Gr\303\241fico para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUknbXVuZGVyR0YkNiUtSSNtb0dGJDYuUSRsaW1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dRJXRydWVGJy8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjE2NjY2NjdlbUYnLUYjNihGKy1GLDYlUSJ4RicvJSdpdGFsaWNHRksvRjxRJ2l0YWxpY0YnLUY1Ni5RLSZyaWdodGFycm93O0YnRjhGO0Y+RkEvRkRGS0ZFRkcvRkpGQEZML0ZPUSwwLjI3Nzc3NzhlbUYnL0ZSRl1vLUkjbW5HRiQ2JFEoJmluZmluO0YnRjtGK0Y7LyUsYWNjZW50dW5kZXJHRkAtRjU2LVEwJkFwcGx5RnVuY3Rpb247RidGO0Y+RkFGQ0ZFRkdGW29GTEZOL0ZSRlAtRiM2Ky1GLDYlUSJmRidGWUZlbkZlby1JKG1mZW5jZWRHRiQ2JC1GIzYkRlZGO0Y7LUY1Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y7Rj5GQUZDRkVGR0Zbb0ZMRk5GaG8tRjU2LVEiPUYnRjtGPkZBRkNGRUZHRltvRkxGTkZob0ZjcC1GNTYtUSgmbWludXM7RidGO0Y+RkFGQ0ZFRkdGW29GTEZORmhvRl9vRjtGK0Y7RitGOw==Figura 6.4 Gr\303\241fico para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSdtdW5kZXJHRiQ2JS1JI21vR0YkNi5RJGxpbUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR1EldHJ1ZUYnLyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictRiM2KUYrLUYsNiVRInhGJy8lJ2l0YWxpY0dGSS9GOlEnaXRhbGljRictRjM2LlEtJnJpZ2h0YXJyb3c7RidGNkY5RjxGPy9GQkZJRkNGRS9GSEY+RkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGW28tRjM2LVEoJm1pbnVzO0YnRjlGPEY/RkFGQ0ZFRmluRkpGTC9GUEZOLUkjbW5HRiQ2JFEoJmluZmluO0YnRjlGK0Y5LyUsYWNjZW50dW5kZXJHRj4tRjM2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY8Rj9GQUZDRkVGaW5GSkZMRmBvLUYjNiotRiw2JVEiZkYnRldGWUZnby1JKG1mZW5jZWRHRiQ2JC1GIzYkRlRGOUY5LUYzNi1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjxGP0ZBRkNGRUZpbkZKRkxGYG8tRjM2LVEiPUYnRjlGPEY/RkFGQ0ZFRmluRkpGTEZgb0ZkcEZhb0Y5RitGOQ==
Como antes, simplesmente olhar este gr\303\241fico \303\251 insuficiente. O conhecimento do comportamento da fun\303\247\303\243o para -10 < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIjJGJ0YvRi8= e 1 < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 10 n\303\243o prev\303\252 nada sobre seu comportamento para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIzEwRidGL0Yv ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= > 10. O gr\303\241fico \303\251, entretanto, uma ferramenta \303\272til quando usada em combina\303\247\303\243o com as an\303\241lises anteriores. As an\303\241lises desta fun\303\247\303\243o continuam nos Exemplos 2 e 4 mais adiante neste cap\303\255tulo.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Limites na Origem para Pot\303\252ncias</Font></Text-field>Um leitor observador vai perceber que existem dois gr\303\241ficos imediatamente anteriores ao Exemplo 1, porque alguma coisa diferente acontece pr\303\263ximo \303\240 origem, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Aqui, a situa\303\247\303\243o \303\251 o complemento da an\303\241lise rec\303\251m terminada para limites no infinito. A Lei de Pot\303\252ncia ( Power ) para limites nos diz que 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 sempre que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for um inteiro positivo ou um n\303\272mero racional com um denominador \303\255mpar ( odd ). (Se o denominador for par, ent\303\243o 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 ,mas o limite lateral n\303\243o existe.) Que acontece com pot\303\252ncias negativas de x pr\303\263ximas \303\240 origem?O exemplo mais simples a considerar \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GT0ZRRlQtRiM2JC1GLDYlUSJ4RidGNkY5RkAtRj02LVEiKUYnRkBGZW5GRUZmbkZJRktGTUZPRlEvRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZlby1JJW1zdXBHRiQ2JUZpbi1GIzYmRistRiM2JS1GPTYtUSgmbWludXM7RidGQEZCRkVGR0ZJRktGTUZPRlFGVC1JI21uR0YkNiRRIjFGJ0ZARkBGK0ZALyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRkBGK0ZA = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkovJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y4 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for um n\303\272mero pequeno positivo, ent\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkovJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y4 ser\303\241 um n\303\272mero grande positivo e o limite lateral \303\240 direita deve ser infinito, e escrever\303\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Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for um n\303\272mero pequeno negativo, ent\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkovJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y4 ser\303\241 um um n\303\272mero grande negativo. Isto sugere que o limite lateral \303\240 esquerda deve ser 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Por esta raz\303\243o, o limite lateral 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 n\303\243o existe.Considere agora 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Porque LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtbkdGJDYkUSIyRicvRjtRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRkFGK0ZB \303\251 positivo para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== \303\251 um n\303\272mero grande positivo quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for pequeno -- quer seja positivo ou negativo. Portanto,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 = 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assim o limite lateral correpondente existe. Neste caso, escrevemos 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 mesmo que este limite n\303\243o exista (como um n\303\272mero real).Em geral, estes limites podem ser resumidos com os dois seguintes enunciados:
N\303\243o h\303\241 raz\303\243o para criar um resumo para os limites laterais correspondentes. O limite lateral existe somente quando os limites \303\240 direita e \303\240 esquerda existam e forem iguais.Figura 6.5 cont\303\251ms os gr\303\241ficos de fun\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJrRidGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrL0Y5USdub3JtYWxGJw== para v\303\241rios valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e para valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= pr\303\263ximos a zero.
plot( F_list, x=-2..2, y=-10..10, color=C_list);L_list := [seq(sprintf("k = %a",k), k=K)]:
legend_plot := plot([0$9], x=-1..1, y=1..2, legend=L_list, color=C_list):
L_title := textplot([0,1.6,"Legend"]):
display([legend_plot,L_title], axes=none);Figura 6.5 Gr\303\241ficos de 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 para valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= pr\303\263ximos a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMEYnRjlGOQ==
Para concluir esta discuss\303\243o, observe que existe uma forte conex\303\243o entre os limites \303\240 esquerda e \303\240 direita para pot\303\252ncias em zero e limites para pot\303\252ncias no infinito e em menos infinito.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Ass\303\255ntotas Verticais</Font></Text-field>Na se\303\247\303\243o anterior deste cap\303\255tulo, consideramos somente pot\303\252ncias simples e limites na origem ( origin ).Lembre que a Regra do Quociete para Limites pode ser aplicada somente quando o limite do denominador exista e n\303\243o seja zero. Se os limites do numerador e denominador forem ambos zero, existe uma chance de que manipula\303\247\303\243o adicional da fun\303\247\303\243o possa produzir uma formula\303\247\303\243o equivalente do problema que evite divis\303\243o por zero. Se o limite do numerador n\303\243o for zero, ent\303\243o precisamos considerar os limites \303\240 esquerda e \303\240 direita e ficarmos em alerta para a possibilidade de que um ou mais destes limites possam ser infinito.
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Defini\303\247\303\243o - Ass\303\255ntota Vertical </Font></Text-field>Uma Ass\303\255ntota vertical para o gr\303\241fico de 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 \303\251 uma reta (vertical) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRImFGJ0Y0RjdGPkYrRj4= onde pelo menos um dos limites dos dois lados de 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRImFGJ0Y0RjdGPkYrRj4= \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1.Por exemplo, o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnLUYsNiVRImtGJ0ZSRlUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGNUYrRjU= para qualquer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 0 tem uma ass\303\255ntota vertical em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=.Note que uma fin\303\247\303\243o pode ter mais de uma ass\303\255ntota ( asymptote) vertical. Em cada ass\303\255ntota vertical, o gr\303\241fico de uma fun\303\247\303\243o vai saltar ( jump). (A fun\303\247\303\243o poderia saltar em outros pontos tamb\303\251m; Isto ser\303\241 discutido com mais detalhes no cap\303\255tulo Continuidade ( Continuity ).)
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Exemplo 6.2 - Fun\303\247\303\243o Racional</Font>(cont.)</Text-field>A fun\303\247\303\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primeiramente vista no Exemplo 6.1. quando foi determinado que 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 e 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. Este resultados anal\303\255ticos tiveram o apoio das Figuras 6.4 (6.3?)e 6.4 contendo os gr\303\241ficos da fun\303\247\303\243o para 1 < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 10, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIzEwRidGL0Yv < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIjJGJ0YvLUYsNi1RIixGJ0YvRjJGNUY3RjlGO0Y9Rj9GQS9GRUZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZORi8=respectivamente.O objetivo do Exemplo 6.2 \303\251 determinar toda e quaisquer ass\303\255ntotas verticais para esta fun\303\247\303\243o. Baseado no gr\303\241fico produzido no Exemplo 6.1, todas as ass\303\255ntotas verticais devem ocorrer no intervalo ( interval )LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIjJGJ0YvRi8= < x < 1. Interpretando a Figura 6.6, que cont\303\251m um gr\303\241fico desta fun\303\247\303\243o, apresenta alguns desafios interessantes.
p3 := plot(f(x), x=-2..1, y=-10..20, color=blue, discont=true):
display([p1,p2,p3]);
Figura 6.6 Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkYrRj5GK0Y+ mostrando ass\303\255ntotas verticais
Figura 6.6 parece sugerir que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg==tem duas ass\303\255ntotas verticais, mas na verdade tem tr\303\252s. Para localizar estas linhas verticais com precis\303\243o, come\303\247\303\243omos por localizar os zeros (reais)(ra\303\255zes reais) do denominador. Como o denominador \303\251 um polin\303\264mio de quinto grau ( quintic ) com coeficientes reais, ele deve ter cinco zeros (raizes) - incluindo possivelmente um ou dois pares de complexos conjugados ( complex conjugates). N\303\243o \303\251 poss\303\255vel encontrar uma representa\303\247\303\243o expl\303\255cita ( explicit ) para estas ra\303\255zes. Aproxima\303\247\303\265es das ra\303\255zes reais do polin\303\264mios ,encontradas com o uso do comando ( fsolve ), s\303\243oZf_r := fsolve( denom(f(x))=0, x );
Os limites \303\240 esquerda e \303\240 direita de cada umas destas ra\303\255zes aproximadas obtidos no seguinte loop :for a in Zf_r do
LL := Limit( f(x), x=a, left ):
LR := Limit( f(x), x=a, right ):
print( LL = value( LL ));
print( LR = value( LR ));
end do:
Embora nenhum destes limites seja infinito, todos os valores s\303\243o extremamente grandes. A raz\303\243o para isto \303\251 que as ra\303\255zes s\303\243o somente aproximadas. Os valores grandes s\303\243o fortes indica\303\247\303\265es de que cada um destes valores \303\251 uma aproxima\303\247\303\243o para a ass\303\255ntota vertical da fun\303\247\303\243o. O suporte adicional para que estes valores sejam ass\303\255ntotas verticais \303\251 dado pela vertical Figura 6.7 onde uma pequena diferen\303\247a de escala mostra um terceiro ramo da fun\303\247\303\243o situado entre as duas ass\303\255ntotas cujo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI8RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMEYnRjlGOQ==.
p4 := implicitplot( {seq(x=a,a=Zf_r)},
x=-2..1, y=-10..20, color=cyan ):
display([p1,p2,p3,p4], view=[-8..8, -5..10]);Figura 6.7 Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkYrRj5GK0Y+ e suas ass\303\255ntotas verticais
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Exemplo 6.3 - Fun\303\247\303\243o Trigonom\303\251trica</Font></Text-field>Ass\303\255ntotas verticais podem ser encontradas em fun\303\247\303\265es trigonom\303\251tricas ( trigonometric ) quando um zero \303\251 encontrado no denominador. A fun\303\247\303\243o tangente ( tangent )g := tan(x):
y = g;
\303\251 o exemplo mais simples deste tipo. A fun\303\247\303\243o tangente \303\251 definida para todos valores de x para os quais 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. em geral, 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 quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um \303\255mpar m\303\272ltiplo ( multiple )de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y6LUYjNiQtSSNtbkdGJDYkUSIyRidGOkY6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZILyUpYmV2ZWxsZWRHRjlGK0Y6. Alguns destes valores est\303\243o contidos na listaiZ := [ seq( (2*k+1)*Pi/2, k=($-3..3) ) ];
Um gr\303\241fico da fun\303\247\303\243o tangente mostrando algumas de suas ass\303\255ntotas verticais aparece na Figura 6.8.
t1 := plot( g, x=-3*Pi..4*Pi, y=-20..20, discont=true ):
t2 := implicitplot({seq(x=a,a=Z)}, x=-8..12, y=-20..20, color=cyan):
display( [t1,t2]);Figura 6.8 Gr\303\241fico 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 e algumas de suas ass\303\255ntotas verticais
Quest\303\243o 6.1Calcule o seguinte limite:
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Se o limite for infinito, digite sua resposta como infinito ou at\303\251 -infinito. Se o limite \303\251 indefinido, digite sua resposta como dne.Quest\303\243o 6.2Calcule o seguinte limite:
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 o limite for infinito, digite sua resposta como infinito ou at\303\251 -infinito. Se o limite \303\251 indefinido, digite sua resposta como dne.Quest\303\243o 6.3Encontrar todas as ass\303\255ntotas verticais de:
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Identificar cada ass\303\255ntota como uma equa\303\247\303\243o x = c para um valor apropriado de c, digite sua resposta na forma {x = c} ou {x = c1, x = c2}.(Nota: Voc\303\252 deve digitar uma resposta antes de clicar em "Grade".)
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Ass\303\255ntotas Obl\303\255quas</Font></Text-field>Quando o gr\303\241fico da fun\303\247\303\243o, 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, se aproxima de uma linha horizontal , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRIkxGJ0Y0RjdGPkYrRj4=, quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= cresce ou decresce sem limite, a linha LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRIkxGJ0Y0RjdGPkYrRj4= \303\251 uma ass\303\255ntota horizontal de 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. Uma fun\303\247\303\243o racional tem uma ass\303\255ntota horizontal quando o numerador e denominador t\303\252m o mesmo grau. Uma ass\303\255ntota obl\303\255qua \303\251 similar; a diferen\303\247a \303\251 que a linha da qual o gr\303\241fico de 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 se aproxima tem uma inclin\303\247\303\243o( slope ) n\303\243o nula.
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Defini\303\247\303\243o - Ass\303\255ntota Obl\303\255qua</Font></Text-field>Uma ass\303\255ntota obl\303\255qua para o gr\303\241fico de 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 \303\251 uma reta 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 para a qual pelo menos um dos 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\303\251 mantido.Uma fun\303\247\303\243o racional tem uma ass\303\255ntota obl\303\255qua somente quando o grau (degree) do numerador \303\251 um a mais que o grau do denominador. Longa divis\303\243o (ou sint\303\251tica) pode ser usada para encontrar a equa\303\247\303\243o da ass\303\255ntota obl\303\255qua. (Voc\303\252 pode parar assim que obter um resto ( remainder ) cujo grau for menor que o grau do denominador.)
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Exemplo 6.4 - Fun\303\247\303\243o Racional</Font>(cont.)</Text-field>Para concluir a investiga\303\247\303\243o da fun\303\247\303\243o considerada nos Exemplos 6.1 e 6.2, encontre suas ass\303\255ntotas obl\303\255quas. Neste caso, a longa divis\303\243o (long division) fornece o quocienteQUO := quo(numer(f(x)),denom(f(x)),x,'r');e o resto r;tal que a longa divis\303\243o resulta em f1 = QUO + r/denom(f1);A ass\303\255ntota obl\303\255qua \303\251 ent\303\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Figura 6.9 adiciona o gr\303\241fico da ass\303\255ntota obl\303\255qua \303\240 Figura 6.8, completando, desse modo, nossas an\303\241lises de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkYrRj5GK0Y+.
p5 := plot(QUO, x=-10..10, discont=true, color=green ):
display([p1,p2,p3,p4,p5], view=[-8..8,-5..10]);Figura 6.9 Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkYrRj5GK0Y+ e suas ass\303\255ntotas verticais e obl\303\255quas
(N\303\243o tem import\303\242ncia que o gr\303\241fico de 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 corte uma ass\303\255ntota obl\303\255qua na parte finita ( finite ) do plano. A propriedade de ser um ass\303\255ntota obl\303\255qua reside ou em valores grandes ou em pequenos valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, isto \303\251, para valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= que se aproximam de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NzM0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ou deLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKCZtaW51cztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRjVGK0Y1. A mesma observa\303\247\303\243o se aplica para ass\303\255ntotas horizontais. Entretanto, o gr\303\241fico da fun\303\247\303\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 nunca interceptar\303\241 uma ass\303\255ntota vertical porque ass\303\255ntotas verticais ocorrem para valores finitos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.)
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7"><Font encoding="UTF-8">Exemplo 6.5 - Uma Fun\303\247\303\243o com Todos os Tr\303\252s Tipos de Ass\303\255ntotas</Font></Text-field>Para concluir nossa discuss\303\243o de limites no infinito, considere a fun\303\247\303\243of := x -> (x^3 + abs(x)^3 - 6*x^2 + 12) / (x+2)^2:
'f'(x) = f(x);Nosso objetivo para determinar todas as ass\303\255ntotas (vertical, horizontal, e obliqua) para esta fun\303\247\303\243o \303\251 preparar um gr\303\241fico da fun\303\247\303\243o e de todas as suas ass\303\255ntotas.Um gr\303\241fico da fun\303\247\303\243o n\303\243o \303\251 dif\303\255cil de se obter e aparece na Figura 6.10.
Uma observa\303\247\303\243o importante \303\251 que para x > 0 e para x < 0 a fun\303\247\303\243o simplifica em diferentes fun\303\247\303\265es racionais.f_pos := simplify( f(x) ) assuming x::positive:
f_neg := simplify( f(x) ) assuming x::negative:
f = piecewise( x>0, f_pos, x<0, f_neg );Isto significa que se deve esperar que a fun\303\247\303\243o tenha comportamentos assint\303\263ticos diferentes no infinito e em menos infinito . Para x > 0, a fun\303\247\303\243o racional tem uma ass\303\255ntota obl\303\255qua q2 := quo(numer(f_pos),denom(f_pos),x):
OA_f := y = q2:
OA_f;Para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, a fun\303\247\303\243o racional tem uma ass\303\255ntota horizontalHA_f := y = limit( f(x), x=-infinity ):
HA_f;Para encontrar ass\303\255ntotas verticais, os zeros do denominador s\303\243o encontrados facilmenteVA_f := seq( x=a, a={solve( denom(f(x))=0, x )} ):
VA_f;A vers\303\243o final do gr\303\241fico da fun\303\247\303\243o e suas ass\303\255ntotas est\303\241 contida na Figura 6.11.
pa := implicitplot( {OA_f,HA_f,VA_f}, x=-10..20, y=-100..30, color=cyan ):
display( [pf,pa], thickness=2 );Figura 6.11 Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkYrRj5GK0Y+ e todas as suas ass\303\255ntotas
Quest\303\243o 6.4Encontrar todas as ass\303\255ntotas de:
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Digite sua resposta na forma y = a * x + b.(Nota: Voc\303\252 deve digitar uma resposta antes de clicar em "Grade".)
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Resumo</Font></Text-field>Os limites de pot\303\252ncias simples, na origem e em ambos os infinitos, s\303\243o resumidos em quatro resultados contidos na Tabela 6.1.
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 6.1 Limites de pot\303\252ncias simples na origem, e em ambos os infinitos
Note como o limite no infinito est\303\241 relacionado ao limite na origem pala direita e como o limite em menos infinito est\303\241 relacionado ao limite na origem pela esquerda.Existem tr\303\252s tipos de ass\303\255ntotas: Ass\303\255ntotas horizontais s\303\243o retas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRIkxGJ0Y0RjdGPkYrRj4= onde 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 ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNipGKy1JJ211bmRlckdGJDYlLUkjbW9HRiQ2LVEkbGltRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dRJXRydWVGJy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjE2NjY2NjdlbUYnLUYjNictRiw2JVEieEYnLyUnaXRhbGljR0ZKL0Y7USdpdGFsaWNGJy1GNzYtUScmcmFycjtGJ0Y6Rj1GQEZCRkRGRi9GSUY/RktGTS9GUUZPLUYjNiUtRjc2LVEoJm1pbnVzO0YnRjpGPUZARkJGREZGRmluRktGTUZqbi1GLDYlUSgmIzg3MzQ7RidGWEZaRjpGK0Y6LyUsYWNjZW50dW5kZXJHRj9GKy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC40ZW1GJy8lJmRlcHRoR0Zqby8lKmxpbmVicmVha0dRJWF1dG9GJ0YrLUYjNictRiw2JVEiZkYnRlhGWi1GNzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y6Rj1GQEZCRkRGRkZpbkZLRk1Gam4tRiM2Ji1GNzYtUSIoRidGOi9GPkZKRkAvRkNGSkZERkZGaW5GS0ZNRmpuLUYjNiRGVUY6LUY3Ni1RIilGJ0Y6RmBxRkBGYXFGREZGRmluRktGTS9GUVEsMC4xMTExMTExZW1GJ0Y6RitGOkYrRjotRjc2LVEiPUYnRjpGPUZARkJGREZGRmluRksvRk5RLDAuMjc3Nzc3OGVtRicvRlFGXXItRiw2JVEiTEYnRlhGWkY6RitGOg==.Ass\303\255ntotas obl\303\255quas s\303\243o retas 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 onde 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 ou 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.
(Tecnicamente, um limite horizontal \303\251 um ass\303\255ntota com inclina\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=.)
Ass\303\255ntotas verticais s\303\243o retas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRImFGJ0Y0RjdGPkYrRj4= onde 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 ou 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 s\303\243o infinitos (tanto infinito quanto menos infinito).
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field>O pr\303\263ximo cap\303\255tulo sobre continuidade ( continuity )aplicar\303\241 quase todos os conceitos introduzidos nos outros cap\303\255tulos na Unit 1. As id\303\251ias neste cap\303\255tulo s\303\243o simples. O resultado te\303\263rico que segue da defini\303\247\303\243o de continuidade s\303\243o cr\303\255ticos para o sucesso das unidades seguintes neste curso. A primeira aplica\303\247\303\243o te\303\263rica de continuidade \303\251 o Teorema do Valor M\303\251dio (Intermediate Value Theorem).Chapter Navigation<< Prev12345 6 78910111213141516171819202122232425262728293031Next >>
Table of Contents\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com