 Download Download Presentation The Idea of ‘Limits’

# The Idea of ‘Limits’

Download Presentation ## The Idea of ‘Limits’

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. 1.4 The Idea of ‘Limits’

2. Average velocities over time:

3. “Instantaneous” velocity at one moment in time:

4. Limit of the Average velocity = the Instantaneous velocity: The Secant approaches the Tangent (average velocity) (instantaneous velocity)

5. 1.5 The Limit of a Function

6. Definition and Notation

7. Finding Limits using Graphs:

8. Finding Limits using Tables:

9. One-Sided Limits:

10. Example Table

11. The limit exists if and only if “left” limit = “right” limit

12. Example where limit does not exist: “Jump” behavior As x → 2: Left limit? Right limit?

13. Infinite Limits (When x approaches a number, f(x) approaches infinity)

14. Example:

15. Example:

16. All 4 possibilities:

17. Vertical Asymptote:

18. Example:

19. or Limits at Infinity (x approaches infinity, f(x) approaches a finite limit L, or infinity)

20. Example:

21. Horizontal Asymptotes:

22. Example:

23. Example:

24. Examples:

25. Examples: