## LHopital Applet

LHopital is used to explain conceptually why L'Hopital's rule works. It shows the graph of the function, f(x)/g(x), whose limit we want to find. It also shows a separate graph plotting f and g. The user can zoom in on the graph of f and g to see how local linearity allows you to replace the functions with linear approximations. In this applet, "a" is the x value where the limit is desired to be taken.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.LHopital" codebase="../../assets"

archive="webcompmath.jar,calculus.jar" height="400" width="800">

<param name="Example1" value="1. An Example;e^(2x)-1;x;0;-5,5,-5,5;-5,5,-5,5" />

<param name="Example2" value="2. Another Example;sin(x);x;0;-5,5,-5,5;-5,5,-5,5" />

<param name="Example3" value="3. Not Applicable;1/x+sin(1/x);1/x;0;-5,5,-5,5;-5,5,-5,5" />

</applet>

</p>

This applet takes the following parameters:

Param NameTypeDefaultDescriptionExample1, ...String N/A Each example is a list of strings separated by semicolons. The strings, in order, are:

1. The name of the example, displayed in the example menu.

2. The expression for f(x), the numerator function.

3. The expression for g(x), the denominator function.

4. The value for a.

5. The xmin, xmax, ymin, and ymax to use for the left graph, as a list of comma-separated numbers.

6. The xmin, xmax, ymin, and ymax to use for the right graph, as a list of comma-separated numbers.