On this page, students are able to define a rectangular box on a larger graph, and are shown an enlarged version of the box in a separate graph window.  They are introduced to the the following concept: the graph of a function fits within the box if it runs from the left side to the right side without going off the top or the bottom.  The dimensions of the box are determined by student input.  The height is twice epsilon, the width is twice delta.  Working with these parameters, students are asked to play a game.  The first player enters a value of epsilon, the second enters a value of delta.  If the graph stays in the box the second player wins, otherwise the first player wins.  These outcomes can be equivalently described as follows.  If  f (x)  stays  within  epsilon  of f (x) for all x which are within delta of a,  then player 2 wins.  Thus, playing the game and  determining who wins gives the students direct experience with the inequalities that define the limit concept.

The second screen connects the epsilon-delta game to the limit concept. See the screen image below.

Here, it is explained how the epsilon-delta game determines whether or not a limit is given by a certain value.  Students are asked to practice there understanding of this idea by playing the game in connection with several proposed limits.

On the third screen, an alternate means is used to visualize the playing of the epsilon delta game. See the screen image below.  

For this activity, students input a function f, values of a and L, and an initial epsilon and delta. That produces a graph centered at (a,L), and extending 3 delta left and right, and 3 epsilon up and down.  A series of lines are drawn vertically from the interval of width delta centered at a, to the graph of f, and then horizontally to the y axis.  The point is to see whether all of these lines strike the y axis within the interval of width epsilon centered at L.   The value of delta can be revised by clicking on the x axis, causing a new set of lines to be drawn.  The lines are drawn dynamically, so that the process of staring with x values and generating y values is highlighted by the animation.