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‘is ig falling, (negative inginity), while if NoWce that as x appreaches positive. _ of negative inginity, YU becomes, | ~>0, the right- -tnd of the oe is ' Foca) to the x.- axis , but wil Tere? | “rising (positive infinity) . . . . inkeesect this fine. - at n is odd, the right and_ if ind The x-axis 1s the horizontal a Of the raph are in opposite directions, asymptote oF Fle) = 5. Thos, we / al ‘len is even, the rignt and left end olay ae aa i te araph are im the sa caezieN : ee, oo + en ma. i tin > Based on Yrese.end behaviors, we zp : J generalize ne value of the limits at , Pa bade el i lene : anne ac fay renal a nik of Polynomial Fonctions of Functions. a a eon n and t leading. east ee Lo hh | 00, i¢ ro mel Nigeven ad ; ony 1 295 if APO and nis event bale Cn) S07 Wh = (0). : Lnieodd lim x = lin ( a Xe Bes 8 xa too “Cs A MOOK | Consider the aragh O% £(X) = Gy the base ‘ic between O and 1. a im (SN q X-00- we ay 2 tt she (AY MN Seu (2) =o Sz) See) i. ) ee “ly The graphe of. ¢(x)= (+) “and (2) =2" ‘Ore reflections 6F each othee with “respect to the y - axis. They digger | rise and poull. Ih the cace of thd: (LY, “AS x Approaches posite inifirivh) , y moves closer ty zer0, Uuhilé as towards Positive “nginity, Me se: Sse) coe n(n) = “+ Properties of limits at inginihy of exponential unctions. . me eeor poet | ToS ae eee tin ee (22° re” 7 U0. j ‘+ For natural exponential Functions, we |: Mave:. . ess Figs lire €* = and Vie Ors! oO PMCS Pa AROS MED Seay Me DOTY | Propeches.o¢ Operations Involving - I" Ineinity PE, SORE 4 ooh geared —_—_ We Oe bad Ly dorms. oF the dicection phere shy “approaches ntqakve -inginity.yrnoves . Exist ~~ However, the Iimit aS x approaches let k be any teat homber | t) 2 oO+\e = hoo a) hook = 4, ig kro $)EOk= Fo,ip Keo 4.) £02 -D is indeterminate _ 8)’ =O h r yt ' Consider the araph of F(x) loge x. =I f) << iy -b car hea Does nob 29] i AOA A nna As x apercaches postive meinity, e Y moves towards. positive méini Fe ae n “negative inginity does not exTet since the ararh ig asymptote fo. Ss _ the Uraxic, which means thatit. _ does het. aperoach. negative inginity. SS “linn leq 2X = c0 andl limlog,x doce BS es ~*~ X98 eo. ok exist “Consider the graph of F(t)=log ix “the base ts between 0 gnett.. * | s & & & ~The graphs of #(x)= logax and ¢(x) Thus, lim 5e *=-00. los loga* ove replectionc oF cach [other with vecpect Yo the X-axis.” Ex... Evaluate. lim (-Zloq5 4x +10). FI the cast of 6(X)= log x, th could a be Obsexvid that ac x ‘ogproaches Step (le Apply the Nimit laws. Positive: IMFinitys Y moves toworde — lim (-2 lags 4x+10)= ( Yin -2) (tira, logy 4) © Regotive imginity. While, the limit “YF a 5. OSX. approaches neqate infinihy ae . dots not exist, similar t? ¢(x)= logs. fe xX, cas they. are both ASYmpolic to . ae (Ling logs Ax) + so a pe eal Step 2: Note, that the logarithmic Function if jim logs 1S iahos) and \im log 4% (x)= logs Ax 18 oF the form ¢(x) =loq4,%, Merete 9 © Where b> 4. Use the property of limits p , ra ’ = ~ - at infinity o¢ legartthmic Functions: [ Properticg of limits ab inginity. cr ic 4 sine E Legaritimic Functions 2H") +10°-2 [ings] +10 ; 2 -2(@)+ 10 : . “= -OH0 by . glimlegy X does not exich m . eC, Xe co PE is ff 2, 1 yee Oe a ons a peso. ee. : Thos, lim, (= 2 logs 4x #10) = -22.. sors mane r For natwral logarithmic funchonc’ EX. 3. What is the value of, itn (2) +a a a . ee ge spear no Cre aes \n.x = eo and lim ln » does not - = 4 (§) sR ta reer ne =-4(2) a 
