1. Chapter 1: Limits

2. Section 1.1:Limit of a Sequence An infinite sequence is the range of a function which has the set of natural numbers as its domain. n F(n)

4. Your turn….

5. Notes:

6. Convergent vs. Divergent sequences If the terms of an infinite sequence approach a unique finite value, that sequence is called a convergent sequence. A sequence which does not converge is called divergent.

7. Example 4

8. A ball is dropped from a height of 2m above flat ground. Each time it hits the ground, after falling a distance h, it rebounds 0.75h. The heights to which the ball rises form a sequence. What is the sequence and what is the limit.

9. Example 1: Find the limit

10. Example 2:

11. Notes

12. Example 3:

13. Your turn:

14. Section 1.2: Limit of a Series Recall from 30-1 that a series is the SUM of the terms of a sequence. An infinite series in the sum of the terms of an infinite sequence. In this section, we will be working with infinite geometric series. Infinite Geometric Sequence: (what does it look like) Infinite Geometric Series: Two different formulas Standard: (for n terms)If -1 < r <1 :

15. Example 1:

16. Your turn:

17. Converting recurring decimals into fractions: Question: Convert 0.12121212……. into fractions 0.12121212…..= A=r= S=

18. Section 1.3: The Limit of a Function

19. Example 1: X4.14.014.0014.0001 F(x) X3.93.993.999 F(x)

21. Left- and Right- Hand Limits

22. Example 1 A parking lot charges $2.00 for the first hour and $1.00 for every subsequent hour. Draw a graph of the charges C (in dollars) versus time t (in hours). Does the limit as t->2 h exist? Explain. This graph is an example of a step function. This is a function which is constant throughout the intervals. What happens when you approach 2 h from the left? Important:

23. Example 2

24. Example 3

25. Example 4: Piece-wise function

26. Continuity:

27. Continuity

28. Note:

29. Example 2:

30. Example 3:

31. Limit Theorems

32. Example 1:

33. Example 2:

34. Limits of Algebraic functions

36. Limits of Infinity (asymptotes)