\input epsf
\nopagenumbers
\magnification=\magstep1

\vtop{\hsize=2.93in \noindent {\bf Problem statement} A point is
moving along the curve displayed in the direction indicated. Its
motion is parameterized by arc length, $s$, so it is moving at unit
speed. Arc length is measured from the point $P$ (both backward and
forward). The curve is intended to continue indefinitely both forward
and backward in $s$, with its forward motion curling more and more
tightly around the indicated circle, $B$, and, backward, curling more
and more tightly around the other}

\noindent circle, $A$. Near $P$ the curve is parallel to the line
segment shown near $P$. Sketch a graph of the curvature, $\kappa$, as
a function of the arc length, $s$. What are ${\lim\limits_{s\to
+\infty} \kappa(s)}$ and ${\lim\limits_{s\to -\infty} \kappa(s)}$? Use
complete English sentences to explain your graph and the numbers
given.


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