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User:JaviPrieto/Limits

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if and only if for all there exists S > 0 such that whenever x > S.

if and only if for all there exists S < 0 such that whenever x < S.

if and only if for all there exists such that whenever .

The complex plane with metric is also a metric space. There are two different types of limits when the complex-valued functions are considered.

if and only if for all e > 0 there exists a d > 0 such that for all real numbers x with , then .

, and ,

is not true. However, this "chain rule" does hold if, in addition, either f(d) = e (i. e. f is continuous at d) or g does not take the value d near c (i. e. there exists a such that if then ).

A short way to write the limit is . A short way to write the limit is . A short way to write the limit is .