1. The Limit of a Function

2. Definition: Limit
The limit of f(x) as x approaches a, equals L if we can make the values of f arbitrarily close to L (as close to L as we like) by taking x to be sufficiently close to a (on either side of a) but not equal to a. The limit of f(x) as x approaches a, equals L is denoted

3. Possible Limit Situationsf a f L1 L2
DNE = Does Not Exist

4. Definition: One Sided Limits
Left-Hand Limit: The limit of f as x approaches a from the left equals L is denoted
Right-Hand Limit: The limit of f as x approaches a from the right equals L is denoted

5. Definition: Limit
if and only if
and

6. Possible Limit Situationsf a f
DNE = Does Not Exist

7. Example
Use your calculator to determine the following:
(a)
(b)