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Mathematics 21 Online
OpenStudy (anonymous):

what is the epsilon delta limit definiton?

OpenStudy (amistre64):

f(c) - L < epsilon 0 < |x-c| < delta

OpenStudy (amistre64):

something like that

OpenStudy (anonymous):

well depends what kind of limit

OpenStudy (amistre64):

limit is THE limit; unless stated otherwise

OpenStudy (amistre64):

If for every value of delta in the interval { 0 < |x-c|< d, you stay within {f(c)-L} epsilon of f(c) .... yada yada

OpenStudy (anonymous):

He's asking what the formal/rigorous definition is for the limit. My calc book says: Let f be a function defined on an open interval containing c (except possibly at c and let L be a real number. The statement \[\lim_{x \rightarrow c}f(x) = L\] means that for each \[\epsilon > 0\] there exists a \[\delta > 0 \] such that \[0 < \left| x - c \right| < \delta\], then \[\left| f(x) - L \right| < \epsilon\]

OpenStudy (anonymous):

limit of a function is not the same as a limit of a sequence, or at least I learnt it that way.

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