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INTRODUCTION TO GEOGEBRA
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In order to play with these interactive GeoGebra modules you will need to make sure that you have the Java Plugin installed. If you do have the plugin installed you will not see the interactive module below. If you don't see the interactive module below download the Java Plugin here. Once the Java plugin is installed restart your browser and come back to this page and will see the GeoGebra module below.

PLEASE  READ THE FOLLOWING:
To see some of the features that you can control in a GeoGebra module see my video here. Even though the video deals with the toolkit functions there is plenty to learn about how to interact with any GeoGebra module.

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THE CONCEPT OF A LIMIT OF A FUNCTION
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The concept of a limit of a function is more easily undertstood if you work with an interactive example. In this GeoGebra interactive example below you will see the graph of the function f(x) = x ².

There are two points, one blue and the other black, along the x axis. These points can be moved towards the red point at x = 5. As you move these points along the x-axis

As the blue or black point is moved there is a projected point on the function f(x) = x ². As the blue or black point gets closer to x = 5 notice what the y value of the projected point is getting closer to 25.

Given f(x) = x ², the limit of lim _{x→ 5}  f(x) = 25. Play with the module below and see why!

To reset the module to its original state, click the reset icon, , in the upper right hand corner of the module.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)