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Exploration: Exponential Functions and Derivatives
This module uses a small sample of the applets in the
Mathlets package together to explore
exponential functions and their derivatives in depth.
Journal of Online Mathematics and its Applications
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Generating Tables to Demonstrate Limits
From the Mathlets: JavaTM Applets for Math Explorations site -- see the links at the left to the site and to the author's module published in the same issue of JOMA. This applet demonstrates limits visually by showing values for f(x) as x approaches a given constant c. A zoom option is provided, and a very wide array of expressions are accepted for f(x). Instructions and examples are included on the page.
Editor's Note: We acknowledge that this author used the term "mathlet" before we did, although his Mathlets site was not the source of our inspiration. Rather, we patterned the term after "physlet", a registered trademark of Wolfgang Christian at Davidson College. Fortunately for us, Prof. Leathrum did not register "mathlet" as a trademark.
Tom Leathrum is Associate Professor of Mathematics at Jacksonville State University. He is also an Associate Editor of this Journal.
INTENDED USES:
The mathlet is appropriate for both classroom demonstrations and independent student use.
AUTHOR'S STATEMENT:
This applet demonstrates the limit of a function f(x) at x = c by generating tables of values of f(x) for values of x near c. The applet takes the user's input, in the form of a simple text expression for the function f(x) (as well as values for c and the starting distance from c), and uses it to generate the tables. The user can then "zoom" to values closer to c, and the tables will automatically adjust. The applet is part of a larger package refered to by the name "Mathlets," which provides many small, focused explorations of particular concepts in calculus.
Open Generating Tables to Demonstrate Limits in a new window.
SOFTWARE SPECIFICATIONS:
Any Web browser with Java1.1 or higher runtime (may also use Java2 plug-in) -- author has tested on Netscape 4.06 and higher and on Internet Explorer 4.01 and higher -- he STRONGLY recommends that Netscape users update to at least version 4.75, since earlier versions have a security problem in the built-in Java runtime.
Operating systems used in testing: Windows 98, MacOS 9.0.3
Browsers: Internet Explorer 5, Netscape 4.7
Editor's note, 01/05: The author reports that he has upgraded the applet to Java2, so he now recommends at least Java plug-in 1.3 or later (1.4.2 or later preferable). Also, he has started using some HTML4 character entities for greek letters, so he now recommends browsers IE6.x, Netscape 7.x, Mozilla/Firefox 1.x (or later).
SOFTWARE AVAILABILITY:
Source code for most of the mathlets is available on the Web site.