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 Discussion: All Topics Topic: limit (e^x-1)/x Related Item: http://mathforum.org/mathtools/tool/1038/

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 Subject: RE: limit (e^x-1)/x Author: Chuck Date: Apr 6 2004
Hi, Jeanette
This limit is equivalent to the rule that the derivative of e^x is e^x.  In
calculus class it is an excellent way show that e was invented so we could have
a function f(x) = e^x that is its own derivative, thus providing a solution to
the important differential equation f'(x) = f(x).  This offers a real insight
into the nature of mathematics, that functions are invented to provide tools to
solve problems.

I had never thought of using it with 6th graders, but why not!  If they have
graphing calculators, it can lead to interesting investigations.

Charles Oelsnet
Syracuse, NY

On Apr 06, 2004, Jeanette E. Horng wrote:

http://mathforum.org/mathtools/tool.html?id=1038

I was on the search for a math tool having to do with the coordinate plane,
since I am planning on introducing it to 6th graders next week.  However, the
only tools I found were ones that were graphers, assuming you already knew how
to graph and how to interpret them.  Are there any you can find?

As I looked at this applet, however, I found it to be a good visual aid in
showing the limit of that function.  I enjoy how there is a proof shown,
explaining the reasoning behind your solution.  It may be a good tool to show to
a class.

--Jeanette