this is called an indeterninateformof-oior.fi?afleleitns derivatives can now differentiable and give 0 on on open interval containing I agree to.

Size: px

Start display at page:

Download "this is called an indeterninateformof-oior.fi?afleleitns derivatives can now differentiable and give 0 on on open interval containing I agree to."

Charles Fields
5 years ago
Views:

1 hl sidd r L Hospitl s Rul 11/7/18 Pronouncd Loh mtims splld Non p t mtims w wnt vlut limit ii m itn ) but irst indtrnintmori?lltns indtrmint t inn gl in which cs th clld n i 9kt ti not ncssrily snsign ; m o typ HA ) W hv sn mpls o th b but now drivtivs cn Gon tims) hlp m (Lillo spitl s Rul ) Suppos Lcpt possibly t l Suppos g r dirntibl giv 0 on on opn intrvl contining igro o ki ro o R suppos iv gr Thn ii E tt s long s limit on right ts ) Th l holds on limits limits s s tmpl Lts ind h lution lt n tho w cn pply Mospitd! ET Y Tki Y ( both sids r now nonzro t l ) Y L

2 sin sin ti W tmpl Lts ind lim HA t lution Th on Ahs sitution w pply thos itd # iii E Th still on Ahs sitution but w cn pply Hospitl WN! tin E D Nonmpt Lts ind Wro#iodoi Apply ii in 1 Mo spitl right wy 9 without chcking whr it s n lt bcus cos 91 sin but sin 0 indtrmint m o Th not crct nswr though! Rightt First chk king inn ros gt n inn hiy cos m 2 nsi o no! Ml t Mo spitl s rol not lwys pplicbl quotints indtrmintly! mtims w wnt NUN ns but high ro hig ro ric vrs ) Th limit n indrminttpo# But w try inositw En Ttro E o could try rwriting limit s

3 Mo spitl twic gol Writ tmpl Lts ind li? h lution li limo h hi # A w try H Mo spitl tino hitmn it ll nti HT Thn Don t try using Mo spit gin hr just yt ; simpliy irst nti ot X no nd us ndtrmintion mtims w wnt inl ro ndtrmint o typ A! Try writ s dirncs vn though l in rt s quotints inl Ws tmpl Lts ind him El Combin rctions t E rl nsmint o tr Not t inosil W stir i Kttrmint o tr N gin ) i rl u inosil B gin) rhinl o i

4 ndtrmintion typ no E mtims indtrmint b now o rt which writ w w g wnt w d n n prl vlut inl whr z groin ro Etmnpl lution Th no it 5 cot tin typ hro nno o typ indtrmint t Singl ht # ind i indtrmint o ind Lts #n lit sin irst comput W 40 root HHM no 9019 ndtrmint tnk it sin N [ Not sin ld com 4 Bl o typ 010 ) Monit ) cos Sco Thn w 74 hv him Hts ig t sing CurvSthiny A?on Th ind ntrcpts ind book ight stps givs not sinnd t strtch grph o unction domin ro ) ) y intrcpt Csynntrym/odd/priodirDAsynpots Hizontl i ins ro L h r i intrcpts possibl ruit n EL L ) sympt ) on Encrslbcrgi Vrticl W i will not intrvls numbrs slnt dcuss nd Flocdmslniyi tid r him n n t n sympt ) sympts ) whr irst incrsing drivtiv tst i dcrsing convnint using scond sign drivtiv o tst

5 Gconcvityntinlrtbnpointsvsmg Not Msk#h A Domin Y intrcpt lu Non Asympts D only ro Hizontl i hizontl sympt FN ncrs ldcrsi k rom k mkins ngtiv hr positiv N CNN point 2 H2 intrcpt Hospitl ) > lwys 0 tho N zro tko N on tht by #v whr t nlys in i * by Us Concvity! hr) vrticl sympts no Kk Kollk t t G intrcpt y only li H on Locl trring sympt incrsing F concvity ccding grph vrywhr dind # iii 0 no htro lt ind W shin chngs sign ndtrmint o Vrticl kid 0 mt on in ill out whr intrcpts G C Symmtry A in hrd B w l Strtch Etnpl got you points ny o sign tru t Nt grph concv gos Us r 037 locl t min Th only vlu chngs Knick 2 Th ttl! rs KN rom down kno CNN t 2 consrv tht up r W hv n s 2 inlction

6 MAH roommt prliminry plot o points! # rom d) Concv down Concv up Now ill in! Empir my Concv down Concv up Sction 45 in book hs mny m mpls

Limits Indeterminate Forms and L Hospital s Rule

Limits Indeterminate Forms and L Hospital s Rule Limits Indtrmint Forms nd L Hospitl s Rul I Indtrmint Form o th Tp W hv prviousl studid its with th indtrmint orm s shown in th ollowin mpls: Empl : Empl : tn [Not: W us th ivn it ] Empl : 8 h 8 [Not: