Opener
This presentation is the property of its rightful owner.
Sponsored Links
1 / 10

a) Identify the following discontinuities. b) Find a function that could describe the graph. PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on
  • Presentation posted in: General

Opener :. a) Identify the following discontinuities. b) Find a function that could describe the graph. c) Name an interval on which all of these functions are continuous. M439—Calculus A. Section 2.3: Continuity Continued. Intermediate Value Theorem. f(b). f(a). b. a.

Download Presentation

a) Identify the following discontinuities. b) Find a function that could describe the graph.

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


A identify the following discontinuities b find a function that could describe the graph

Opener:

a) Identify the following discontinuities.

b) Find a function that could describe the graph.

c) Name an interval on which all of these functions are continuous


M439 calculus a

M439—Calculus A

Section 2.3: Continuity Continued


A identify the following discontinuities b find a function that could describe the graph

Intermediate Value Theorem

f(b)

f(a)

b

a

If y = f(x) is continuous on a closed interval [a,b], then it takes on every value between f(a) and f(b) (and sometimes a couple extras)


A identify the following discontinuities b find a function that could describe the graph

Connectivity:

f(b)

f(a)

b

a

The intermediate value theorem implies that a continuous function will have no breaks (no jumps, holes, or limits whose values approach infinity).


Car application

Car Application

If your car is traveling at some speed, it must have gone every speed between 0 mph and your current speed during your drive.


Also works with superhero flight

Also Works With Superhero Flight


Properties of continuous functions

Properties of Continuous Functions:

  • If two functions , f and g, are continuous at x = c, then most combinations of f and g are continuous at x = c:

    1) Sums: f + g

    2) Differences: f – g

    3) Products: f • g

    4) Scalar Multiples: k • f (for any real number k)

    5) Quotients: f/g (as long as g(c) is nonzero)

    6) Compositions: f о g


Example 1

Example 1:

Show that is everywhere continuous.


Example 2

Example 2:

Where is continuous? Where is it not?


Removing a discontinuity

Removing a Discontinuity

We notice that g(x) has a “removable” discontinuity.

What does this mean? Which other discontinuities are NOT removable?

How do we remove it?

How do we extend the function to a new function, h(x)?


  • Login