In this lecture we are going to talk about algebraic evaluation of limits. In previous lesson, we were talking about limit investigations and now we will do just a quick review of it. Sometimes, the limit is in a type 0/0 . In these cases, an algebraic rearrangement will help us to evaluate a limit. Our first example will be to compute the limit: lim (x→9)((√x-3)/(x-9)) . This is a 0/0 limit, so called indeterminate type. To solve this, we need to write this limit in some other form using algebraic tricks. Further steps are shown in video. Additional examples are also included.
Remember that we
are looking at what happens as
(not what happens at
For limits as
we are looking at what happens as x increases or decreases without
algebraic rearrangement will help you to evaluate a limit.
For limits of
rational functions as
starting by dividing the numerator and denominator by the highest
power of x appearing in the denominator.
Algebraic Evaluation of Limits
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.