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G Ha , Ba Pa Ma a , I c K H , Lab H a a Sa F N A caG(x) = 1 M−f(x) Clearly, g is well defined on a,b since f(x) < M for all x ∈a,b Moreover, g is continuous on a,b by Theorem 67 of M1P1 as a quotient of two continuous functions with nonvanishing denominator Now, by the definition of the supremum,M is the smallest upper bound for f This means that for any >0 the number M− is notT C g g b v> R r A C> y I X X i zColumbia( R r A) f B X g C _ 5 ^23 D0cm 327 iGator j O ̃y W Let F X B A Function For All X In R And F 0 1 Then G X F ƒgƒC ƒXƒg[ƒŠ[ ƒAƒ"ƒfƒB ‚Ì •"‰® ŠG

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BigO Notation Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers We say f(x) is O(g(x)) if there are constants C and k such that jf(x)j Cjg(x)j whenever x > k In other words, BigO is the upper bound for the growth of a function62 = H > B R G B D g Z F b g g h _ h e h ` d b y m g b \ _ j k b l _ l " K \ B \ Z g J b e k d b", L h f 53, K \I 1 1, F _ o Z g b a Z p b y, _ e _ d l j b nU 07 N f V ^ O v ・ I @ X V N C X 00C SRT8 ・A ・・・f J ・・・o ・I @ X V SAMURAI BLUE FAIR J ・・l f ・ I @ X V Consider The Following Reaction A G B Clutch Prep A b c d e f g h i k l m n o p q r s t v x y z