Function Limits VII: Putting It All Together With Useful Examples
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Lesson Summary:
We provide some useful examples and a graph that summarizes what we have learned about function limits.
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SAMPLE LESSON
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Lesson:
| Example Description | Limit Existence | Examples |
|---|---|---|
| The function is defined at a point and continuous. | Limit Exists | Straight Lines, Polynomials, Quotient of Polynomials, and <Sign in to see all the formulas>See more examples on our list of continuous functions. |
| The function is defined but not continuous at a point. The left-side and right-side function limits exist and are equal. | Limit Exists | <Sign in to see all the formulas>and<Sign in to see all the formulas> |
| The function is not defined at a point but is defined around it. The left-side and right-side function limits exist and are equal. | Limit Exists | <Sign in to see all the formulas>and<Sign in to see all the formulas>and<Sign in to see all the formulas> |
| The limit from the left is different from the limit from the right | Limit does not exist | <Sign in to see all the formulas> |
| The function becomes infinitely large at some point | Limit does not exist | <Sign in to see all the formulas>and<Sign in to see all the formulas> |
Here is a visual example to help you remember when function limits exists and don't exist.
