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Precise definitions of a limit
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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
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
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
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
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
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
Author:
Jamie_Bee
ID:
291059
Card Set:
Precise definitions of a limit
Updated:
2014-12-08 23:28:46
Tags:
InterCalcI
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Description:
Different cases of the precise definition of a limit
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