1 / 6

2-3 continuity

2-3 continuity. Def: A function is continuous at: (1) an interior point if (2) a left endpoint if (3) a right endpoint if. a c b. How can a function be discontinuous?. Continuous Removable discontinuity. (limit exists). *to “remove” the discontinuity we

mercury
Télécharger la présentation

2-3 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. 2-3 continuity

  2. Def: A function is continuous at: (1) an interior point if (2) a left endpoint if (3) a right endpoint if a c b How can a function be discontinuous? Continuous Removable discontinuity (limit exists) *to “remove” the discontinuity we can assign a value f (0) = limit

  3. JumpInfiniteOscillating DiscontinuityDiscontinuity Discontinuity limit DNE from the from the right left Strategies for removing a discontinuity: (1) Factor top & bottom (2) Something cancels (3) Use what’s left to assign value

  4. Def: A function is continuous on an intervaliff the function is continuous at every point on the interval Def: A function is a continuous functioniff the function is continuous at every point in its domain Note: This function has an infinite discontinuity at x = 0. However, we still consider the function to be a continuous function because x = 0 is not in its domain. Ex: Properties of Continuous Functions If f and g are continuous at x = c, then the following are also continuous at x = c: f + g (2) f – g (3) f g (4) k  f (5) f / g, g (c)  0 Also note that, composites of continuous functions are continuous

  5. Intermediate Value Theorem for Continuous Functions If a function is continuous on closed interval [a, b], then for some c in [a, b], y0 = f (c) where y0 is between f (a) & f (b). f (b) y0 f (a) a c b Ex 5) Is any real number exactly 1 less than it’s cube? Compute any such value accurate to three decimal places. x3 – 1 = x x3 – x – 1 = 0 Graph it  (1.325, 0)

  6. homework Pg. 76 #6, 18, 24, 30, 36, 42, 48, 54 Pg. 84 #2 – 44 (mult of 2+3n)

More Related