1 / 21

Warm – Up: NO CALCULATOR!

Warm – Up: NO CALCULATOR!. Homework: pg. 65 (23 – 35 odd). 31. 1 33. ½ 35. -1. 23. a. 4 b. 64 c. 64 25. a. 3 b. 2 c. 2 27. 1 29. -.5. Homework: Packet pg. 4. 1.0 2.  2 3. 5/3 4. 8/9 5. 2 6. -2/7 7. -3/2 8. 2a 9. 27 10. -1 11. 2 12. -1/a 2 -1/9 3a 2

kelly-english
Download Presentation

Warm – Up: NO CALCULATOR!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm – Up: NO CALCULATOR!

  2. Homework: pg. 65 (23 – 35 odd) 31. 1 33. ½ 35. -1 23. a. 4 b. 64 c. 64 25. a. 3 b. 2 c. 2 27. 1 29. -.5

  3. Homework: Packet pg. 4 1.0 2. 2 3. 5/3 4. 8/9 5. 2 6. -2/7 7. -3/2 8. 2a 9. 27 10. -1 11. 2 12. -1/a2 • -1/9 • 3a2 • 1/27 • 2 • -1 • -1 • 1 • 10 • 3 • -1 • 1 • DNE • 14 • 18 • DNE • 0 • 1

  4. Quiz • Good Luck • Show lots of work • You may use an extra sheet of paper!

  5. Video: Segment 1 www.calculus-help.com/continuity/

  6. Summary : Types Discontinuities 3 main types: 1) Point discontinuity Type(s) of Function: _______________ 2) Infinite discontinuity Type(s) of Function: _______________ 3) Jump Discontinuity Type(s) of Function: _______________ . Discontinuity can either be REMOVALBE or NONREMOVABLE. Points are Removable. Infinite and Jump are Not

  7. Discuss the discontinuity (if any) of the functions below: Continuity at a Point

  8. Video: Segment 2

  9. Continuity at a Point Function f is continuous at x = c if and only if 1. f(c) exists 2. 3.

  10. Continuity at a Point If a function f is not continuous at a point c , we say that f is discontinuous at c and c is a point of discontinuity of f. Note that c need not be in the domain of f.

  11. Example Continuity at a Point [-5,5] by [-5,10]

  12. Where are these discontinuous?And what type?

  13. Video: Intermediate Value Theorem • http://www.calculus-help.com/the-intermediate-value-theorem/

  14. Intermediate Value Thm. A continuous functions on [a,b] A continuous function takes on all y values between f(a) and f(b). In other words… If k is between f(a) & f(b), then k = f(c) for some c in [a,b]

  15. Graphically: f(b) Any k value in here will be “hit” at least once f(a) a b

  16. Example 1: Make the function continuous • Steps: • Determine if discontinuity is removable • Find values that are causing discontinuity • Find the limit at the found value(s) • Write a piecewise function that includes found value

  17. Example 2: Make the following continuous

  18. Example 3: Make the following continuous

  19. Example 4: Make the following continuous

  20. Example 5: Determine the value of k that makes the following continuous

  21. Packet pg. 5

More Related