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\noindent {\bf Problem statement} Suppose $\displaystyle 
f(x) = {{\sqrt{2-\sqrt{4-x^2}}}\over x}$.

\medskip

\noindent a)~Find $\lim\limits_{x \to 0^{+}}{f(x)}$ and
$\lim\limits_{x \to 0^{-}}{f(x)}$.  

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\noindent {\it Suggestion:}\/ Rewrite $f(x)$ as $\displaystyle f(x) =
{{\sqrt{2-\sqrt{4-x^2}}}\over x}\cdot {{\sqrt{2+\sqrt{4-x^2}}}\over
{\sqrt{2+\sqrt{4-x^2}}}}\,$.

\medskip

\noindent b) Sketch the graph of $y = f(x)$ in the viewing window
$[-2,2]{\times}[-1,1]$.

\medskip

\noindent c) Use the graph to check your answer to a). Explain any
interesting behavior, particularly involving signs.

%contributed by Michael O'Nan

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