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### 7 Cards in this Set

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 Limit Let f:D  R be a function with D in R, xo in R is an accupoint of D. Moreover, let L be in R. We say f(s) has a limit L at xo iff the following holds: -For every positive real number E, there exists a positive real d, such that whenever x is in D\{xo}, with |x-xo|=an+1 for all positive integers n. Monotone a sequence is either increasing or decreasing Summary of proofs with lim arithmetic Take arbitrary sequence that converges to x0 Use thm 16lim(fxn)=A Use some other rule for lim seq Use thm 16 in other direction Summary of proofs with convergent arithmetic Set up convergent definition of an and bn with N1 and N2 (For multiplication add |an|<=M bounded) (For division |bn|>c by lemma) Define E 1. For addition-E=E/2 2. For multiple-E’=E/(/(|B|+M)>0 3. For division-E=|B|E*c N=max(N1,N2) and then put everything together Will use triangle inequality