# Precise definitions of a limit

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 Author: Jamie_Bee ID: 291059 Filename: Precise definitions of a limit Updated: 2014-12-08 18:28:46 Tags: InterCalcI Folders: Description: Different cases of the precise definition of a limit Show Answers:

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1. Definition of a Left-Hand Limit
if for every number ε>0 there is a number δ>0 such that if a-δ<x<a then |f(x)-L|<ε
2. Definition of a Right-Hand Limit
if for every number ε>0 there is a number δ>0 such that if a<x<a+δ then |f(x)-L|<ε
3. Positive Infinite Limit
means that for ever positive number M there is a positive number δ such that if 0<|x-a|<δ then f(x)>M
4. Negative Infinite Limit
means that for every negative number N there is a positive number δ such that if 0<|x-a|<δ then f(x)<N
5. Positive Limit at Infinity
Let f be defined on (a,∞). Then means that for ever ε>0 there is a corresponding number N such that if x>N then |f(x)-L|<ε
6. Negative Limit at Infinity
Let f be defined on (-∞,a). Then means that for every ε>0 there is a corresponding number N such that if x<N then |f(x)-L|<ε

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