1. 13.1 Finding Limits Using Tables and Graphs

2. As x gets closer to c, but remains unequal to c, the corresponding values of f(x) get closer to N.

4. Example
(Left)
(Right)

6. y 8
(2, 7) 6 4 2 x 2 4 6

7. Use graphing utility to find

11. Does the limit exist at x = 1 if so what is it?

12. One-Sided Limits

13. RECAP Definitions
This means that as x gets closer to a, but remains less than a, the corresponding values of f(x) get closer to L.
This means that as x gets closer to a, but remains greater than a, the corresponding values of f(x) get closer to L.

14. Equal and Unequal One-Sided Limits
One-sided limits can be used to show that a function has a limit as x approaches a:
One-sided limits can be used to show that a function does not have a limit as x approaches a:

15. 3 1 -1 -3 -2 -1 -3
No limit.