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Prove the statement using the e, 6 definition of a limit. lim (3 + ) - 4 Given e> 0, we need 6 -Select- v ] such that if o < Ix - 4| < 6, then |(3 +) - 4|-Select-v). But |(3 +) - 4

Prove the statement using the e, 6 definition of a limit. lim (3 + ) - 4 Given e> 0, we need 6 -Select- v ] such that if o < Ix - 4| < 6, then |(3 +) - 4|-Select-v). But |(3 +) - 4

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Prove the statement using the ɛ, ô definition of a limit. lim (3 +) = |(3 ++) - 4| <c- -1|<c-||x - 41 < e= Ix - 4| < Select- V Given a > 0, we need ô --Select--- v such that if 0 < |x - 4| < ô, then ---Select--- V But So if we choose ô = -Select- v then 0 < |x - 4| < ô = <a. Thus, lim = 4 by the definition of a limit. Illustrate with a diagram. y y 4 +€ 4 +€ 4 -€ 4 - € 4 -6 4+6 4 -6 4+6 y 4 +8 4 +6 4 4 4- 6 4 - 6 4 -€ 4+€ 4 -€ 4+€
Transcribed Image Text:Prove the statement using the ɛ, ô definition of a limit. lim (3 +) = |(3 ++) - 4| <c- -1|<c-||x - 41 < e= Ix - 4| < Select- V Given a > 0, we need ô --Select--- v such that if 0 < |x - 4| < ô, then ---Select--- V But So if we choose ô = -Select- v then 0 < |x - 4| < ô = <a. Thus, lim = 4 by the definition of a limit. Illustrate with a diagram. y y 4 +€ 4 +€ 4 -€ 4 - € 4 -6 4+6 4 -6 4+6 y 4 +8 4 +6 4 4 4- 6 4 - 6 4 -€ 4+€ 4 -€ 4+€
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