Question

What is the basic diffrence between limit of a function of a real variable and that of a complex variable

Answer 1

According to the definition of Continuity : The function f is continuous at some point c of its domain if the limit of f(x) as x approaches c through the domain of f exists and is equal to f(c). In mathematical notation, this is written as

Lim x-c f(x)=f(c)

continuity

Hence , for a function to be continuous at any point c, the limit of the function should exists and equals to the f(C).

So , from the point of view of continuity , continuity of f(x) at x=c exist only if limit of a function f(x) as x-->c exists and equals to f(c).
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