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\begin{document}


\noindent
{\bf  MAT 331 Fall 2017, Practice Quiz  1  \\
Quiz on   Tuesday Sept 12, 2017 (30 minutes)}


\vskip .1in 
\noindent
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xxxxx}$}}
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\vskip.1in
\noindent
{\bf For answers that are real numbers, include all non-zero
 digits to the left of the decimal place, include the decimal place 
in a box, and as many digits to the right  of the decimal place 
as will fit in the remaining boxes. Truncate, do not round, e.g., 
given five boxes for $\sqrt{7}=2.64575131106\dots$, write ``2.645''.
If a number has no digits to the left of the decimal point, start
with the decimal point, e.g., given ten boxes, write $1/\sqrt{2}$ as 
``$.707106781$''.
}
{\bf 
Right justify integer answers, and place blanks (or zeros) in any 
remaining boxes on the left. For example, given 10 boxes to write 
$2^{20}$ either write ``0001048576'' or ``1048576'' preceded by 
three blank boxes.
}


\vskip.2in

\begin{enumerate}


\item \dbten 

\vskip.1in \noindent  
 Find $\sqrt{2}$. 
% 1.414213562373095
\vskip .5in 

\item \dbten
\vskip.1in \noindent 

 Sum $1/n$ from $n=1$ to $n=10,000$.
% 9.787606036044348
\vskip.5in

\item \dbten 

\vskip.1in  \noindent 
 Use  the command \verb+solve+
 to   solve $x+\sin(x) = e^{-x}$. 
%to nine digits following
%the decimal place (truncate, do not round,your answer)
\vskip .5in
%0.35446310437502532437461

\item \dbten 

\vskip.1in  \noindent 
Use the command \verb+root+ to find the largest real root of 
%$p(x) = x^8 - 10*x^7 -2* x^3 + 3*x^2 + 4$.
$p(x) = x^8 - 10 x^7 -2 x^3 + 3 x^2 + 4$.


%10.00016958902440876627

\vskip.5in 
\item \dbten  

\vskip.1in  \noindent 
What is the maximum value of 
$ \exp(\cos(10x)) + x - x^2$ over all real $x$? 
%2.37928681749274421715951
\vskip.5in 

\item \dbten

\vskip.1in  \noindent 
  Find the first place in the decimal
expansion of $\pi$ that the sequence ``2017'' occurs. 
What are the ten digits that follow these?
Use the command \verb+y=char(vpa(pi,n))+
 to create a string 
on the first $n$ digits (including the $3$ and the ``.'').
Then use \verb+strfind+.
%2017 92896 47669 75832
% for sqrt(2) the answer is 2017 82685794

    

\end{enumerate}


\end{document}


