Continuity
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Continuity
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Transcript of Continuity
![Page 1: Continuity](https://reader036.fdocuments.net/reader036/viewer/2022082810/558670eed8b42a043b8b45b8/html5/thumbnails/1.jpg)
Continuity
![Page 2: Continuity](https://reader036.fdocuments.net/reader036/viewer/2022082810/558670eed8b42a043b8b45b8/html5/thumbnails/2.jpg)
Do Now: An volt battery to a 12 volt battery 7 seconds after being turned on. Graph the battery
voltage against electrical circuit switches instantaneously from a 6 time. Write the function
represented by the graph. What can you say about the continuity of this function?
![Page 3: Continuity](https://reader036.fdocuments.net/reader036/viewer/2022082810/558670eed8b42a043b8b45b8/html5/thumbnails/3.jpg)
When is a function continuous at a point?
A function f(x) is continuous at c if:
a. f(c) exists
b.
c.
limx c
exists
lim ( )x c
f c
![Page 4: Continuity](https://reader036.fdocuments.net/reader036/viewer/2022082810/558670eed8b42a043b8b45b8/html5/thumbnails/4.jpg)
Types of discontinuity:
1. Jump
2. Removable (hole)
3. Infinite (vertical asymptote)
4. Oscillating
![Page 5: Continuity](https://reader036.fdocuments.net/reader036/viewer/2022082810/558670eed8b42a043b8b45b8/html5/thumbnails/5.jpg)
How can we make a function continuous?
4
2)(
2
x
xxf
Redefine the function as piecewise(Fill in the hole)
2,2
2,2)(
xkx
xxxf
Set branches =, sub in x, and solve for coefficient or constant