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Graphically Exploring Limits

Author:L. Marizza A. Bailey, Chris Odden

What is the limit of f as x approaches 5 from the left?

You can drag the gray dot, x-value, on the x-axis. 1. Drag the x-value so that it is approaching 5 from the left, or from the negative side. 2. Watch the values of f(x) = y as you slide the x-value towards 5 from the left. (DON'T LET THE GRAY DOT TOUCH x = 5, but get as close as you can) 3. This is the limit of f(x) as x approaches 5 from the left:

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What is the limit of f as x approaches 5 from the right?

1. Drag the x-value so that it is approaching 5 from the right, or from the positive side. 2. Watch the values of f(x) = y as you slide the x-value towards 5 from the right. (DON'T LET THE GRAY DOT TOUCH x = 5, but get as close as you can) 3. This is the limit of f(x) as x approaches 5 from the left:

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What is f(5)?

Enter 5 into the box labeled "x = ", you will see the value of f(x) at x = 5.

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Check for Understanding

Question 1

What is ?

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Question 2

What is ?

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Question 3

What is ?

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Question 4

What is ?

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