L'Hospital's Rule states that if f(x)/g(x) is an indeterminate quotient, then

The following applet can be used to verify this rule by graphing the relevant functions. Simply enter the functions f(x) and g(x) and the value a. The applet will automatically display two charts. The top chart shows the graphs of f(x) and g(x) while the bottom chart shows the graphs of f'(x) and g'(x).

The value of a can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change this value by using the up/down arrow keys or by dragging the corresponding point left or right. 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.