Limit (Function)

Definition

For one variable
f(x) goes closer to one and only one finite real number L for all values of x as x draws close to a from both sides, but not equal to a.
Then L is defined as limit of f(x) as x approaches a:

Consider the following examples:

1. f(a) is defined
2. f(a) is not defined (empty point at a)
3. f(a) is defined far away from the curve of f(x)
4. when left hand side limit () does not equal with right hand side limit ().

For two variables

for any > 0 and >0, if (x,y) belongs to D:

Note

Example