Note: As x gets closer to c, the closer y gets to L
Example:
- One way to solve this is by putting 2 in for x.
- Another way is to make a table
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The closer x gets to 2 (from both sides) the closer f(x) gets to 5
Describing the limit
Limits that Do Not Exist (DNR):
- when the left and right behaviors are different
the limit from the left would be -2, but the limit from the right would be 2.
The limit from the left side is described as =L "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
The - sign above the 2 shows it is from the left side
The limit from the right side is 2 (c) with a + sign =L "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
2. If a function increases without a bound, f(x) can be as large as you want
The asymptote of x=0 causes you to be able to choose a number as close to 0 and it keeps decreasing 3. When it Oscillates between two different numbers
the limit just switches between 1 and -1.
Continuity:
If a function is continuous at c then =\lim_{x\rightarrow c^{+}}f(x)=f(c) "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
- A trick for knowing if a graph is continuous is if you can draw it out without lifting up your pencil.
- Discontinuous graphs include: BREAKS, HOLES AND ASYMPTOTES
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