Question

Define limit & Continuity of the function of complex variables.​

Answer 1

Answer:

The limit of w = f(z) as z → z0 is a number l such that |f(z) − l| can be made as small as we wish by making |z − z0| sufficiently small. In some cases the limit is simply f(z0), as is the case for w = z2 − z. For example, the limit of this function as z → i is f(i) = i2 − i = −1 − i.

Answer 2

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

Then is said to be Continuous at if $\displaystyle{\lim_{z \to z_0} f(z) = f(z_0)}$. ... If is continuous for every point then is said to be Continuous on . If is not continuous at then is said to be Discontinuous at .