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\noindent {\bf Question}

\noindent Explain {\it exactly} what is meant by the statement
\[ \lim_{x\rightarrow 4} (x^2 -e^x) =16 - e^4.\]

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\noindent {\bf Answer}

\noindent For every $\varepsilon &gt;0$, there exists $\delta &gt;0$ so
that if $0 &lt;|x-4| &lt;\delta$, then $| (x^2 -e^x) - (16 - e^4)|
&lt;\varepsilon$.


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