One+sided+Limits+1

Created by: Kara Sanna, Robert McCloud and Klajdi Myslimaj‍‍‍‍‍‍‍ Online Graphing Calculator **Vocabulary** **‍‍‍‍‍‍Limit** - This is the single value that a function //f// (//x//) approaches as the variable //x// approaches a constant //c//. Ordinarily, the term "limit" used by itself refers to a two-sided limit. **One-Sided Limit** - This is the sort of limit that is obtained when the variable //x// is allowed to approach the constant //c// from only one side, i.e. from values greater than //c// or values less than //c//, but not both. One-sided limits can be either a left-hand limit or right-hand limit. **Left-Hand Limit** - This is the one-sided limit obtained by allowing the variable //x// to approach the constant //c// from "the left side" only, i.e. from values of //x// less than //c//.

**Right-Hand Limit** - This is the one-sided limit obtained by allowing the variable //x// to approach the constant //c// from "the right side" only, i.e. from values of //x// greater than //c//. **Continuous** - Intuitively, a function is continuous if you can draw it without lifting your pen from the paper. Formally, a function //f// (//x//) is continuous at a point //x// = //c// if the following is true at that point: //f// (//x//) = //f// (//c//) A continuous function is one that is continuous for all points in its domain.

*The above information and examples are fromSparkNotes  * One of the only big differences between normal limits and one-sided limits is the range of x's that are looked at when determining the value of the limit.



Example: When the Limit does not exist
Estimate the value of the following Limits.When we graph the function we see that the function does not settle down to a single number on either side of t=0. Because of this, neither the left-handed or right-handed limit exist in this case. Just like normal limits are not guarenteed to exist, neither are one-sided limits.

Example:
Estimate the value of the following Limits.

*The above information and examples are from
Pauls Online Notes : Calculus

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 * Play video from 6:25-8:27 to see a problem worked out about One-sided limits.**

=** One Sided Limits Assessment **= = =