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
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InterCalcI
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Description:
Different cases of the precise definition of a limit
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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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