\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Choose an appropriate starting guess
and then use three iterations of Newton's method to find the smallest
positive solution to

$$ {1 \over {1+x^2}} = \tan x\, .$$

\noindent How many positive solutions to this equation are there? Why?
What would you guess is true about the spacing and location of
positive solutions to this equation as $x\to \infty$?  (Pictures will
help answer this question; explain your conclusions in sentences,
referring to these pictures as needed.)









\vfil\eject\end