This site contains an interactive applet that provides an illustration to the rigorous "epsilon-delta" definition of the limit of a function.
Type of Material:
Simulation
Recommended Uses:
This applet could be used for an in-demonstration, group exploration, or individual study.
Technical Requirements:
Any browser.
Identify Major Learning Goals:
To develop a better understanding of the "epsilon-delta" definition of a limit.
Target Student Population:
College Lower Division, Calculus I students
Prerequisite Knowledge or Skills:
Calculus I
Content Quality
Rating:
Strengths:
The definition of a limit of a function is, without a doubt, one of the most fundamental and important concepts in Calculus. This site allows the user to visually explore the rigorous “epsilon-delta” definition of function limit that is typically introduced in the very beginning of the first semester of Calculus. Given a function, the user has control (via a slider) over delta parameter to choose a value of delta that is small enough to accommodate a generated value of epsilon. Also, there are two fields where the user can enter the actual limit value and the numeric value of delta based on the observation. These answers can be checked by pressing a button. Several exploration questions are also offered.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This hands-on tool provides a clear picture of the relationship between epsilon and delta. The use of colors is very helpful in visualizing the intervals. Typically, Calculus I student experience difficulties understanding the “epsilon-delta” definition of limit. Therefore, the site can be used as a part of in-class demonstration, homework assignment, or perhaps a self-guided activity. A set of exploration questions is a helpful way to check the understanding of the material.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The tool is very intuitive, everybody can start using it right away.
Readability settings include sliders to allow users to adjust the font and margin sizes. This is especially useful for viewing the applet on a smartphone or other device.
Concerns:
None.
Creative Commons:
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