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How to find the limit of a function using its graph.

Finding a limit graphically is used almost every day, especially whenever trends and patterns are analyzed to find an expected value.

What is the expected population a few years from now? Limits on a graph of a certain population give insight into population trends over time, something of interest to governments at all levels.
What is the anticipated effect of deep space travel on the human body? Finding limits on a graph relating the force of gravity to blood pressure helps scientists know what effect being in space will have on the human heart.
What value of an investment is expected at some future date? Interpreting a graph using limits allows financial analysts to predict future values for, say, the purpose of saving up for a purchase or retirement.

GRAPHICAL IDEA OF A LIMIT
fx=-0.5x-2x≤-12-x2-1<x<12x=12-x21<x≤20.1x-23-2x≥2
fx=x2x2-1
fx=sin⁡1x
=
=
1 2 3
1. The limit of f (x) as may be different than f (c). For what values of c does the limit of f (x) as exist but not equal f (c)? Check all that apply.
2. When the limit of f (x) as does equal f (c) , the function is said to be continuous at c. At which of the following values of c is f (x) continuous? Check all that apply.
3. The limit of f (x) as does not exist for which of the following values of c? Check all that apply.
1 2 3
1. Slowly move x toward 1 from the left. As , we say that there is no expected value of f (x), so the limit of f (x) as does not exist. Why?
2. Slowly move x toward 1 from the right. As , we say that there is no expected value of f (x), so the limit of f (x) as does not exist. Why?
3. Move x toward the far right. What happens to the value of f (x) as x gets bigger and bigger? That is, does the limit of f (x) as exist, and if so, what is it?
1 2 3
1. Move x toward 0 slowly from the left. What is the behavior of f (x)?
2. Move x toward 0 slowly from the right. What is the behavior of f (x)?
3. Which of the following statements is true?
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