Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate MathematicsHouston, Texas, November 1619, 1995Paper C011
An Interesting Problem From Calculus and Much More 
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In the latest, 3rd edition of Calculus by Stewart, early
transcendentals, we can encounter many new and challenging
problems whose solutions can be obtained, in an enjoyable way, by
using modern technologies. Further, these problems can lead to a
sophisticate mathematical thinking and discovering new Mathematics.
One of such problems is the problem mentioned in our title. Shortly,
this problem is about two circles: C, xy1; and C2, (x1)yr. And the
problem is to find a limit of x intercept of the line passing through
the point (O, r) and the intersection point of C1 and C2, as r
approaches 0. We will discuss not only solution to this problem, but
more interestingly, its many generalizations. For example, when the
circle C2 is replaced by any curve passing through the origin, which
will lead to surprising results. In the process of seeking solutions,
we will make frequent references to the Geometer's Sketchpad and
Mathematica which turn out to be indispensable tools for handling
complicate formulas. All the discussion is easily accessible to
Calculus students, and might be used for students' research projects.
Keyword(s): calculus, geometry, Mathematica, Geometer's Sketchpad