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\noindent {\bf Question}

\noindent  Evaluate the limit
\[ \lim_{h\rightarrow 0} \frac{ \frac{1}{2+h} - \frac{1}{2}}{h}.\]

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\noindent {\bf Answer}

\noindent Either use l'Hopital's rule, since it has the
indeterminate form $\frac{0}{0}$, or notice that this is the
definition of the derivative of $f(x) =\frac{1}{x}$ at $x+0 =2$,
namely
\[ \lim_{h\rightarrow 0} \frac{ \frac{1}{2+h} - \frac{1}{2}}{h} =f'(2)
=-\frac{1}{4}. \]



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