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Unformatted text preview: 1.2 The Concept of a Limit Definition (not rigorous): Consider a function f and a number c that has a neigh borhood where f is defined (though f need not be defined at c itself). c c e c e 1. The limit of f ( x ) as x goes to c from below (or from the left) , lim x c f ( x ), is that number that the outputs of f get closer and closer to as the inputs increase and get closer and closer to c . If the outputs of f arent getting close to any number then we say that this limit does not exist or is undefined . If the outputs of f are positive and get huger and huger then formally the limit is undefined but to describe why it is undefined we say that the limit is equal to + . If the outputs of f are negative and get huger and huger (in absolute value) then again the limit is formally undefined but we say that it is equal to in order to describe why it is undefined. 2. The limit of f ( x ) as x goes to c from above (or from the right) , lim x c + f ( x ), is defined in exactly the same way as the limit of...
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This note was uploaded on 05/06/2008 for the course MATH 118x taught by Professor Vorel during the Spring '07 term at USC.
 Spring '07
 Vorel
 Calculus, Limits

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