Limit of a function
For the function , we can get as close to  in the -values as we want, so long as we do not make  equal to . For instance, we could make x=.00000001 or -.00000001, but never 0. Therefore, we can get  as close as we want to , but without reaching it. The left limit is any value that approaches the limit from numbers less than the number, and the right limit is any value that approaches the limit from number greater than the limit number. For instance, in the function , since the limit for  is 0, if , it approaches the limit from the right. If we instead choose -1, we say it approaches the limit from the left.