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~
\vspace{2cm}

\noindent
\textbf{Directions:}  
\begin{enumerate}
	\item Write your name with one character in each box below.
	\item Show all work.  No credit for answers without work.
\end{enumerate}

\newpage
\headers{Math156 Sec 005}{Quiz 1}{Aug 21, 2026}

~
\vspace{1.5cm}

\begin{enumerate}

\newcommand{\myspc}{\vspace{2.25cm}\\~}
\item\ppoints{4}{1} Compute the derivatives of the following functions.
\begin{multicols}{2}
\begin{enumerate}
	\item $f(x)=\cos(1)$
	\myspc
	\item $g(t)=\frac{2t+2}{t+2}$
	\myspc
	
	\columnbreak
	\item $u(z) = \tan^3(z^2)$
	\myspc
	\item $h(y) = \ln(\sqrt{y})$
	\myspc
\end{enumerate}
\end{multicols}

\item\ppoints{4}{1} Compute the following indefinite integrals.
\begin{multicols}{2}
\begin{enumerate}
	\item $\displaystyle \int \frac{1}{2z} \:dz$
	\myspc
	\item $\displaystyle \int \sec^2 x \:dx$
	\myspc
	
	\columnbreak
	\item $\displaystyle \int \csc x\cot x \:dx$
	\myspc
	\item $\displaystyle \int (y+2)(y^2-1) \:dy$
	\myspc
\end{enumerate}
\end{multicols}

\item\points{2} Find the number $b$ so that the area under the curve $y=x^2$ from $x=1$ to $x=b$ is exactly $1$.
\vfill

\end{enumerate}
\end{document}