Complex Analysis - Maths KU

2.6 Limits and Continuity 115
Before stating Theorem 2.1, we recall some of the important concepts
regarding limits of real-valued functions of two real variables F (x, y). The
following definition of lim F (x, y) =L is analogous to both (1) and
(x,y)→(x0,y0)
Definition 2.8.
Limit of the Real Function F (x, y)
The limit of F as (x, y) tends to (x0, y0) exists and is equal to
the real number L if for every ε>0 there exists a δ>0 such that (7)
|F (x, y) − L|