### Electronic Proceedings of the Eleventh Annual Conference on
Technology in Collegiate Mathematics

*CONTRIBUTED PAPER: 11-C38*
### A graphical tool for analysis courses

Jeffry L. Hirst

Department of Mathematical Sciences

Appalachian State University

Boone, NC 28608

Phone: (828) 262-2861

E-mail: jlh@math.appstate.edu

#### ABSTRACT

Due to the reform movement, many universities use technology in their calculus courses. By using
computer algebra systems in higher level courses, we can capitalize on skills students are learning
in their introductory courses. This paper describes a Maple procedure that illustrates the mechanics
of delta-epsilon proofs.
The Maple procedure works as follows. Students enter a function, a point in the domain of the
function, an expected limit, and the maximum value of epsilon to be considered. The procedure
then generates an animation where each frame corresponds to a value of epsilon. Each frame
displays the graph of the function, highlighting the region of the range corresponding to epsilon
and the region of the domain corresponding to delta. Additionally, a graph of the delta values
associated with each value of epsilon is provided. Students can apply modeling skills to find a
formula for delta in terms of epsilon.

Besides providing the Maple code for the procedure and some sample frames from the output, this
paper includes some tips on using the display command in Maple and on distributing Maple code in
the classroom.