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Res the limit is not equal fo FCc). € ft ot ee s UINTOMTIVE DEFINITION OF A LIMIT Solve through graph: : hin ¢ OX) =L _— Xoo 1 i on acunction fla, we can determine * ie 4 the value of ¢(c) ig CIS in the do- a i 4 main! OF F(x)i Otherwise, Mhe Value E i a Spof KO msenot-degined ln mosteaces ? 1 i | en FX) 2 £(e), However, there arc times € A ¢ shee es : aR” 4 i q _ Based on the araphy lira (2x4!) = 4 © there are ways doilivchrate he i OP ona (2 ‘mit ofa fonchon bhere Tig Now, LEP DS determin’ zy : 1 1. lable-wpvolues FOY= Rett a 2. Gea) MeeOrOhip ss | Example 4° + lim (2x rl) | ‘=e il ny eS ‘Wolvethrough table oF valuec + Aine ne 1 en) = 4 aed (la) 4,4 i xed]: S | 3.4 | 9.44 | 9.4aq ows het lina (24H) = #0. e0[ @ [69 [eas] e278 x1 fas fad [aot vee dD - Example 25. =a : FO) i [42 [aor Boe let E(x) = - axe. = Can we cvaunte Based on the table of. Values, we - lim ()v ovkan (ay CON abserve that as x approaches Rae s ‘ : Ie Cither from the lect or right, oy Delermine the vale pe ein | we Stace loser to the given: simit. Eee = NS i la ia — = \In lim ¢ @), the value onc is -2 xg Step 2° Sole for C2) 2 12. £6) 5 Nea We = (-2)?-(-2)-6 LL . Tae es 442-6 fo) =o dD " LIMITS WHERE Im ¢(x) ¢ ¢(c) a x6 Wecewise Funchone Let e(y- XA, 1 XF 4 (OCS Exe 4, determine fi ; me, pees using terble of valves, x 2.5| 34 [ 3.44 3.424 let us ¢(x)|-0.5]-01 | -0.01 |-0-601 Solve fer Ment) The regulting Valve ic o whichis x [ 4.5 i 4.1 [ 4.01 ‘| 4.001 Indeterminate. Thos, WE Cannot vce £(x) | OS | 0.| | 0.0\ | -00\ £ (-2)46 evaluate tim FO). Kayn2 Example 3: ' t. Determine the Verlve, of t . ‘| J B a ©. Ys Vs 2, 2 . x21 pa x-1, > Lek 0x) = passionate Trg) =F) Nim | X221 - ARIAT Solve FOr lim KAA XA KHL Based on the table. o¢ values the ya- ue of ¢(x) as x approaches 4 Gtr Frm lech or right Is 0. TWheregore, . ES Wn glad PEA EAT ie otis, that €(4)= 6, Since tim 4020 | Gnd f(4)rs, we.can see that . i Tye #44). lim ¢(). Soe for ¢(-1). pa i: $007 Site Solbtion: 3 had Solve er Vien $() 3 als GEn22(-1)-3 X22 Beg tls 1+) livm (x) = Item (x-3) in iy if im(x-3 Xez Yar = _ Veaes : 2 > SG = 41-3 2 = o S41) a 2 Solve for lim §{x). i Arg Cy, the fonction becomes xeor z determinate. Theccpore, sim sax Liss » 4) al (2x 7) : eam eS ] ig * In e(x) RS ~ om ih * cethe demain 6p E(x) This showe 5 > ee for valves of x that art not part Since dien n§0del and lien VFO s = CF Ine domain, we canShil) Colve = porte limit: 6p the funckon: it sath! thet Ara flO al im ng lx). ae We sla Na i Vv si == Tws, Hing) does nok pet i 2 we alve oa Yim z= TAKENOTE: Ex. 2. Determine tev Urns = WWndepied= The denominator is 0. | . ey ™ tndekermingtt— Both numécator andl € e (Sie 2 denommator are 0; 2. Selotion: Sve Fer hon oe a Chae — see ves fe3.5 [3.1 [sot f-3.001 2 eS. (xel(xecy [Ole [- “110 [0100 Ft co1000 ; XS Xe ASL al Mid. 1) UITAR GS S 2 sim (ert) 6 pen for lim, Taye ial olf 5 a fines ares a Example 1 eh . . : 7 ; 4 a] oy ale 4900 494 000 ah: ei wpxaa Oe Gr aa oil ret ie ee Jerr aps © ond ANE 2 3c y73t (Bye! 
