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1.2-limits_intuitive

# 1.2-limits_intuitive - 1.2 The Concept of a Limit...

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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 c 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 aren’t 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 f ( x ) as x

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1.2-limits_intuitive - 1.2 The Concept of a Limit...

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