% TEMPLATE FOR STANDARD QUIZ
% by laura
\documentclass[14pt,epsfig]{article}

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\usepackage{amsmath}
\usepackage{hyperref}
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%testpoints.tex
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\newcounter{problemnum}
\renewcommand{\theproblemnum}{\arabic{problemnum}}
\newcounter{partnum}[problemnum]
\renewcommand{\thepartnum}{\alph{partnum}}
\newcounter{totalpoints}
\newcounter{curprobpts}	
\newcounter{totalparts}
\newcounter{pagepoints}
\newenvironment{problem}[1]{
\refstepcounter{problemnum}
\vspace{0.15in} \par
\setcounter{curprobpts}{#1} \setcounter{totalparts}{0}
{\Large \bf \theproblemnum. \normalsize ({\it \arabic{curprobpts} point\null\ifnum \value{curprobpts} = 1\else s\fi}\/)}
}{\ifnum \value{totalparts} = 0
	\addtocounter{totalpoints}{\value{curprobpts}}	% Add pts to total.
	\addtocounter{pagepoints}{\value{curprobpts}}
	\else \ifnum \value{totalparts} = \value{curprobpts}
	\else \typeout{}
	\typeout{!!!!!!!   POINT ACCOUNTING ERROR   !!!!!!!!}
	\typeout{PROBLEM [\theproblemnum] WAS ALLOCATED \arabic{curprobpts} POINTS,}
	\typeout{BUT CONTAINS PARTS TOTALLING \arabic{totalparts} POINTS!}
	\typeout{}
	\fi
\fi
}
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{
\refstepcounter{partnum}
\hspace{0.25in}	
\ifnum #1 > 0
	\makebox[0.5in][l]{{\bf \thepartnum.} {\bf ({\it #1 pt\ifnum #1 = 1\else s\fi\/}) \,\,}}
\else
	\makebox[0.25in][l]{({\bf \thepartnum})}
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\hspace{0.1in}	
\addtocounter{totalparts}{#1}
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\addtocounter{totalpoints}{#1}
}
\newcommand{\skipproblem}[1]{\addtocounter{problemnum}{#1}}

\newcommand{\showpoints}
{
\typeout{}  
\typeout{====> A TOTAL OF \arabic{totalpoints} POINTS WERE READ.}
\typeout{}
}
%%%%%end testpoints.tex
%\input{testpoints}

\begin{document}


%%%(change to appropriate class and semester)
MATH 2222HJ Spring 2016

%%%(change to appropriate quiz type and date)
Quiz 2 \hspace{1.9in} {Name:} {\underline {\hspace{2.5in}}}
\vspace{2pc}

%%%(modify rules, time, points as appropriate)
Show all work clearly and in order, and circle your final answers.  

Justify your answers algebraically whenever possible. Unjustified work may not receive full credit.
\vspace{2pc}

\begin{problem}{2}
Find a parametrization of the tangent line of the helix $\vec{r}(t)=\left<\cos(t),\sin(t),t \right>$ at the point $\left(0,1,\dfrac{\pi}{2} \right)$.
\vfill
\end{problem}
\begin{problem}{3}
Find the arc length of the curve $\left\{ \begin{array}{ll} \vec{r}(t)=\left< t, -\log \left( \cos(t) \right) \right> \\
-\dfrac{\pi}{4} \leq t \leq \dfrac{\pi}{4}.
\end{array} \right.$ \\
Note: you may find the trigonometric identity $\tan^2(t)+1=\sec^2(t)$ and the following integral \href{http://www.wolframalpha.com/input/?i=antiderivative+of+sec%28t%29}{formula} useful:
$$\displaystyle\int \sec(t) \mathrm{d}t = \log(\tan(t)+\sec(t))+C$$
\vfill
\end{problem}


\showpoints
\end{document}