Limit definition

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Suppose that f(x) is defined in a neighborhood of the point 'c' (a finite number) except possibly at the point c itself. Then (see attached)

Formal Definition of a Limit:

Suppose that f(x) is defined in a neighborhood of the point 'c' (a finite number) except possibly at the point c itself. Then

if for every there is a >0, such that

We must exclude |x-c|=0 (i.e., we don't want ...