Chapter 2 section 8

# Chapter 2 section 8 - Chapter 2 section 8 Precise...

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Chapter 2 section 8 Precise definition of limit

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Objectives 1. Find  δ  in terms of  ε , given a limit. 2. Construct a formal proof of a limit of a  linear function.
Definition of limit Let f be a function defined on some open interval  that contains the number “a,” except, possibly at  “a” itself. Then, we say that the limit of f(x) as  x  approaches “a” is L and we write  lim x a f(x) = L  if for every number  ε  > 0,  there is a corresponding number  δ  > 0, such that  |f(x) – L| <  ε  whenever 0 <|x - a|< δ   or  if 0 < |x - a| <  δ , then |f(x) – L| <  ε .

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That is, lim x a f(x) = L means the distance between f(x)  and L (which is  ε ) can be made arbitrarily  small by taking the distance from x to “a”  (which is  δ ) sufficiently small (but   0).
Example Given f(x) = 1/x, find  δ  such that |1/x – 0.5| < 0.2  whenever |x - 2| <  δ .

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## This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 2 section 8 - Chapter 2 section 8 Precise...

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