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MAT137Y1 Lecture 9: Proofs with Limits

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indigoyak978
2 Feb 2020
School
UTSG
Department
Mathematics
Course
MAT137Y1
Professor
Thaddeus Janisse

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MAT137Y1 Lecture 8: Definition of a Limit

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MAT137Y1 Lecture 9: Proofs with Limits

10

MAT137Y1 Lecture Notes - Lecture 10: Product Rule

Document Summary

The limit lim f(x) = l means that for all > 0, there exists > 0 such that if 0 < |x c| < , then. The two definitions of limit in definition 1. 5 and. 2. x (c , c) (c, c + ) if and only if. 0 < |x c| < ; f(x) (l , l + ) if and only if. |(2x + 1) 9| = |2x 8| = |2(x 4)| = 2|x. 4|, so |(2x+1) 9| < when 2|x 4| < . choose = /2. lim x 1=0 x 1. Given > 0, choose = . Then 1 < x < 1 + , which means that 0 < x 1 < . | x 1 0|=| x 1|= x 1< = 2 = . conclude that whenever x (1,1+ ),we also have| x 1 0|< lim 1/x = 0 x -> . Given > 0, choose n = .

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