Discussion:  All in Calculus 
Topic:  Definition of Limit Tool  Simple, Yet Effective 
Related Item:  http://mathforum.org/mathtools/tool/1134/ 
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Subject:  Definition of Limit Tool  Simple, Yet Effective 
Author:  Eric Goolish 
Date:  Feb 10 2004 
http://mathforum.org/mathtools/tool.html?id=1134
While this tool does not provide much in terms of a visual understanding of
limit, it does well in providing an entry level understanding of limit. The
initial tutorial provides an understandable working definition of limit. The
tool then easily allows the user to see what the function does near a value, c,
by plugging in numbers near c. This technique is effective in fostering the
early understanding of limits.
This applet could possibly be improved by providing graphs to go along with
plugging numbers into the functions. Visually seeing the function being
evaluated at points near c can be very beneficial, especially if the function is
discontinuous at c.
Moreover, when evaluating the function at values near c, it may be helpful to
choose numbers larger than and small than c. This could help demonstrate the
limit by 'seeing the squeeze from both sides.' Moreover, this could lead to
evaluating limits from the left or right.
Just some thoughts, but a pretty good tool.
http://www.mste.uiuc.edu
Eric
 
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