MATH 6A Lecture 6: Lecture 6
Document Summary
Recall: a single variable real valued function has limit l as x approaches , written. , if and only if for any , there exists such that , where. Approaching from both above and below must give the same answer in order for the limit to exist. The open ball with center and radius is the set of all points in with. All points in the disc of radius , centered on. Thinking of intervals as open balls , we can generalize the. The limit of as approaches is the real number , written if and only if for any , there exists some so that whenever and. The limit of as approaches may not exist. If approaching along two different paths gives different answers, the limit does. Therefore, the limit of at is not defined because diferent approaches towards tend toward different values. Showing that a limit doesn"t exist at is easy.
