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\noindent {\bf Problem statement} The numbers $R_1$, $R_2$, $R_3$, and
$R$ satisfy the following equation:

$$ {1 \over {R_1}} + {1 \over {R_2}} + {1 \over {R_3}} = {1 \over
R}\,.$$

\noindent (Physics and engineering students may recognize this as a
formula for the total resistance, $R$, of a circuit composed of three
resistances $R_1$, $R_2$, and $R_3$ connected in parallel.)

\medskip 

\noindent a) If $R_1 = 1$ and $R_2 = 2$ and $R_3 = 3$, compute $R$
exactly.  

\medskip 

\noindent b) If both $R_1$ and $R_3$ are held constant, and $R_2$ is
increased by $.05$, what is the approximate change in $R$?

\medskip 

\noindent c) If both $R_1$ and $R_2$ are held constant, and $R_3$ is
increased by $.05$, what is the approximate change in $R$?









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