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58_20111118fri_calc2_94159_f11

# 58_20111118fri_calc2_94159_f11 - FALL 20 u CALCIC 8 Fri u...

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Unformatted text preview: FALL. 20 u CALCIC 8 Fri. u m \lW MAC‘ZBLQ 94(59 (aw/224.9% (I.>S SH” §l(.[ :Seguemcec. E4335), [A] TM Sandwich Theorem fer Qeguemceslm TW“ 2 (E 735) E a; {an} {bu} and {Cu} are, s'ecLuences a? real 3:? numbers 932" if there ex‘csx‘s 0m index N suck {:ka’v g is!” (53 :For all n>N if??? an .4 5VI .6 Ch J £5 and I hm a : L, and HM Cm: ' m j n-Mo “ VP)!» 9 % (then Ifwx bh :2 ham Th“? 3 : The With/WmW5 vad'mnTheorem ﬂ rSeguewwsJ P 3% {an} \9 0L convergtiwk se Queue «:3; read numbers Gav—“P Lb améc {E is a q'fwchoh confq‘nuous «3v (suck that {an CdOVMS—L 21m ﬂan) —> 30—) E] WA ___._> 1 WM? Becaused ILL”: (+71; 1 V1 Qua I - (‘F We |€+ £CX)‘:\/-i‘) the” £15 COM-t @ i amol f(“+——i) I‘S deffnecﬂ for n=l,2)3)..1 @By’ﬁxma ’h+l‘___,>\/:,.i m D ”Mi/Wad, WM? mag—+0 Le+§(x)=2‘ [j 39 [S COM; @0 5‘1? 30(‘1' 7;)13c\e§Med fur V): IHZﬁ). Xoﬁﬂbaﬂm 21:221 54 A” . M [Ej iL’f-(tgpi'faUs 12:118. ([7. 73;): 3 EV : ‘ l V1 .. anm (e._ J1me 13W "' O ”'3760 n ‘/ by L,“ 00 Mm LL”, : (M I” = M” J. :o "'5’” M h->oo 1 PM " (E "Hwy; caMmou UMITS, (p.133); E! w L—w M"?°° Er] “V" 1":0 .§ !x(<1 -1<>c<1 M—‘MA ‘ n “3 =57 "‘> 0 3L) n E! Mm (I + Tax— : 81 7C 6 G? M900 [Q My: W7C” = o 7:633. h~>m n! W M M M W.M [a RCCULVSWQ geﬂue“cesg’(7~¥37>(éxaMplc : Ft'bcnaccé Seiuenoc> In 1)!)2') a) 5) 8) ‘3) 2‘) 34):” .an:an—I+ant—z Q11") (12 = I) Qua-1:51” +491“ an“ 3 dﬁanﬂ A“ WM m ,‘ DeF'3 Non—1766mm»: Se : JAG Qhéann yaw a“ n=l,2,3,.., then {aﬂg is a. non-decreasing gciuemce. (RE?) w—g ...
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58_20111118fri_calc2_94159_f11 - FALL 20 u CALCIC 8 Fri u...

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