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\noindent {\bf Problem statement} Consider the function
$f(x)=\sin\!\left({1\over x}\right)$ with domain $(0,\infty)$ (that
is, $x$'s which are {\it positive}). $f$ is a strange function. A
graph of $f$ on the interval $[.5,2]$ is shown to the right (no
strangeness there).

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\noindent a) Find all $x$ in the domain for which $f(x)=0$ (there are
many!). }

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\noindent b) Find a positive number $A$ so that the interval $[A,.5]$
contains exactly 5 roots of $f(x)=0$. Explain why this is so, and
provide a graph of $f$ on this interval.









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