One+Sided+Limits

=﻿One-sided Limits =

=Define Word= A limit that is not continuous, but exist from one direction.

For some functions, it is appropriate to look at their behavior from one side only. If //x// approaches //c// from the right only, you write

or if //x// approaches //c// from the left only, you write

It follows, then, that if and only if Because //x// is approaching 0 from the right, it is always positive;  is getting closer and closer to zero, so. Although substituting 0 for //x// would yield the same answer, the next example illustrates why this technique is not always appropriate. Because //x// is approaching 0 from the left, it is always negative, and does not exist. In this situation, DNE. Also, note that DNE because.
 * Example 1:** Evaluate [[image:http://media.wiley.com/Lux/59/39159.ngr014.gif align="absmiddle"]]
 * Example 2:** Evaluate [[image:http://media.wiley.com/Lux/62/39162.ngr017.gif align="absmiddle"]].
 * Example 3:** Evaluate
 * [[image:http://media.wiley.com/Lux/98/39098.nce005.gif align="absmiddle"]] ||
 * [[image:http://media.wiley.com/Lux/98/39098.nce005.gif align="absmiddle"]] ||

> || || > ||   || || > ||  || > ||   || ||
 * 1) As //x// approaches 2 from the left, //x// − 2 is negative, and | //x// − 2|=− ( //x// − 2); hence,
 * 1) As //x// approaches 2 from the right, //x// − 2 is positive, and | //x// − 2|= //x// − 2; hence;
 * 1) Because [[image:http://media.wiley.com/Lux/67/39167.ngr022.gif align="absmiddle"]]

=Three Links=

http://www.sagemath.org/calctut/onesided.html http://www.cliffsnotes.com/study_guide/Onesided-Limits.topicArticleId-39909,articleId-39872.html http://planetmath.org/encyclopedia/OneSidedLimit.html

=Three Different Searches=

One-sided Limits Tutorial One-sided Limits Examples One-sided Limits Practice

 =Evaluation with Rubric=

