HW1_m3a3.pdf - LAST NAME First Name Homework 1 ID Math 3A03...

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LAST NAME, First NameHomework # 1ID # :Math 3A03DUE:by 11:00pm on Saturday January 25, using Crowdmark.1.LetSRbe a nonempty set which is bounded above, andu= supS.(a)Show that for eachn2Nthere existsxn2Ssuch that:u-1n< xnu,8n2N.(b)Prove that the sequence (xn)n2Nconverges tou.
LAST NAME, First NameHomework # 1ID # :Math 3A03DUE:by 11:00pm on Saturday January 25, using Crowdmark.1.LetSRbe a nonempty set which is bounded above, andu= supS.(a)Show that for eachn2Nthere existsxn2Ssuch that:u-1n< xnu,8n2N.23.4(b)Prove that the sequence (xn)n2Nconverges tou.Lemma23.4
Homework # 1 / Math 3A3-2-NAME:ID #:2.Let (an)n2Nbe the sequence withan=pn2+ 4-n,n2N.(a)Prove that limn!1
(b)Letbn=n an. FindL= limn!1bn, and prove the limit exists, by using the definition.

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