In this video, the outline for using the epsilon-delta definition to prove that the limit of a function has a particular value y = L at x = a has two main parts. First, we determine what range of y values the function takes when x is restricted to intervals on either side of the value x = a of interest. Then, we ask whether we can narrow these intervals sufficiently to ensure that the range of y values taken by the function is contained within a range of y values of interest centered at y = L. When we conclude that this can be done for any finite range of such y values, we conclude that the limit of interest exists.
