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\vskip -1.936in \vtop{\hsize=3.45in \noindent {\bf Problem statement}~Fred {\it loves}\/ polynomials
with rational coefficients and only such polynomials. Suppose $f(x)=\sqrt{x}$. Find a polynomial $P(x)$ that Fred will adore so
that,
for any $x$ is in the interval $[3,5]$, the
difference
between $P(x)$ and $f(x)$ is less than $.01$.

\smallskip

\noindent {\bf Hint} The interval is $[3,5]$. What number is the {\it
center}\/ of that interval? And what is the function? To the right is
a graph of $\sqrt{x}$ and a polynomial on $[3,5]$ (yes, two functions,
even if you don't believe it). There are many polynomials which answer
this question correctly. Please find one and explain why it is such a
polynomial.

}











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