1. AP Calculus BC Tuesday, 08 September 2015 OBJECTIVE TSW (1) study and use a formal definition of a limit. WS Practice with Limits is due Friday, 09/11/15. T-shirt money due today!!! Test on Chapter 2 is Friday.

2. Formal Limits and Limits at Infinity A Formal Definition of Limit  -  Definition Let f be a function defined on an open interval containing c (except possibly at c) and let L be a . The statement means that for each  > 0,  a  > 0  if A real number Epsilon “There exists” Delta “Such That”

3. A Formal Definition of Limit  -  Definition Formal Limits and Limits at Infinity

4. A Formal Definition of Limit Ex: Given that Find  such that whenever

5. Formal Limits and Limits at Infinity A Formal Definition of Limit Ex: Given that Find  such that whenever

6. Formal Limits and Limits at Infinity

8. Limits at infinity have many of the same properties of limits at specific values.

9. Formal Limits and Limits at Infinity

10. Ex:Find each limit: Divide numerator and denominator by the highest power of the variable. Apply “Limits at Infinity” theorem.

11. Formal Limits and Limits at Infinity Ex:Find each limit:

12. Formal Limits and Limits at Infinity

13. How to find horizontal asymptotes: 1)Degree of Num. < Degree of Denom. HA: y = 0 2)Degree of Num. = Degree of Denom. HA: 3)Degree of Num. > Degree of Denom. HA: none

14. Formal Limits and Limits at Infinity Ex:Find each limit:

15. Formal Limits and Limits at Infinity Ex:Find each limit: