1 / 12

Continuity

Continuity. 2.3. Continuity at a point. A function is continuous at any point given three things 1. The function exists 2. The limit as x approaches that point exists 3. The function = the limit at that point. Continuous from the right/left.

muncel
Download Presentation

Continuity

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. Continuity 2.3

  2. Continuity at a point • A function is continuous at any point given three things • 1. The function exists • 2. The limit as x approaches that point exists • 3. The function = the limit at that point

  3. Continuous from the right/left • All of the same rules apply, but we only check the one sided limit in question

  4. Example • Is the given function continuous at x=1? • X=4? • X=5? • Why not?

  5. Continuity on an interval • To be continuous on an interval means that the function is continuous at every point on that interval.

  6. Continuity on an interval • The following types of functions are continuous everywhere on their domain: • Polynomials, rational functions, root functions, trig functions, exponential functions, and logarithmic functions

  7. Continuity rules • If f and g are continuous functions • f + g is continuous • f - g is continuous • f x g is continuous • f / g is continuous where g ≠ 0 • f(g) is continuous

  8. Example • Where are each of the following functions discontinuous

  9. Example • Show that the following function is continuous on the interval[-1, 1]

  10. Types of discontinuity • A point of discontinuity is called REMOVABLE if the limit exists • A point of discontinuity is called NONREMOVABLE if the limit does not exist

  11. Example • Find any points of discontinuity and tell whether they are removable or nonremovable

  12. Homework • Pg 84 #1-14, 19-24

More Related