Summary: 14.2 Limits and Continuity
1
0 0( , ) ( , )
lim ( , )
x y x y
fFormal Definition of x y

Assume the function f is defined at all points within a disk centered at ,
except possibly at . We will write
0 0( ,x y )
)0 0( ,x y
0 0( , ) ( , )
lim ( , ) = L
x y x y
f x y

if for any given number 0 > , we can find number 0 > such that ( , )f x y satisfies
| ( , ) |f x y L - <
whenever the distance between ( , and ( , satisfies)x y 0 0)x y
2 2

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

Collections: Mathematics