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\noindent {\bf Problem statement}
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\noindent Suppose $f(x)=\sqrt{2+3x}$, and suppose that the sequence $\{a_n\}$
has the following recursive definition:

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\qquad $a_1=1$; $a_{n+1}=f(a_n)$ for $n>1$.

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\noindent a) Compute decimal approximations for the first 5 terms, $a_1$, $a_2$,
$a_3$, $a_4$, and $a_5$, of the sequence.

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\noindent b) The graph to the right shows parts of the line $y=x$ and the curve
$y=\sqrt{2+3x}$. Locate on this graph or on a copy to be handed in the
following points: $(a_1,a_2)$, $(a_2,a_2)$, $(a_2,a_3)$, $(a_3,a_3)$,
$(a_3,a_4)$, $(a_4,a_4)$, $(a_4,a_5)$, and $(a_5,a_5)$. Also show
$a_1$, $a_2$, $a_3$, $a_4$, and $a_5$ on the $x$-axis. (You must draw
{\bf 13 points}.)


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\noindent c) Write a statement of a result in section 10.1} \noindent
which shows that this sequence converges. You must find a
specific {\ssb THEOREM} in the section which will guarantee
convergence.

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\noindent d) Compute the limit of $\{a_n\}$.

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