The following applet can be used to examine the limit of a sequence of functions f_n(x) as n approaches infinity. Simply enter the functions f_n(x) and F(x) (the proposed limit of f_n(x)) as well as the values a, b, and ε (epsilon).

The values a, b, and ε can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point along the appropriate axis. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.