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\begin{document}
	
	\mbox{}
	\title{Mock Quiz 3}
	\maketitle

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%\section{Introduction} \label{sec:intro}
%	\noindent {\footnotesize Note: Most of the problems were taken from the textbook} \cite{jS15}.
		
	\begin{problem}
		Compute
		\[
			\lim_{x \to 0} \frac{ \frac 12 + \frac x{16} - \frac{1}{\sqrt{4-x}}}{x^2}
		\]
		by expanding $\frac{1}{\sqrt{4-x}}$ as a Maclaurin series.
	\end{problem}
	
	\vspace{8.5cm}
	
	\begin{problem}
		Evaluate $\int_0^1 \sin(x^2) \, dx$ correct to within an error of $0.001$. [Hint: Use Taylor expansion, then use the Alternating Estimation Theorem.]
	\end{problem}
	
	\newpage
	
	\vspace{-20pt}
	\begin{problem}
		Solve the differential equation $\frac{dy}{dx} = \frac{xy^2\sqrt{1 + x^2}}{\ln y}$.
	\end{problem}
	

	\vspace{6cm}
	
	\begin{problem}
		Exercise 2, Section 9.4.
	\end{problem}
	
	\vspace{7cm}
	
	\begin{problem}
		Solve the first-order linear differential equation $xy' + y = \sqrt{x}$.
	\end{problem}
	
%	\newpage

%	{\bf A Few Standard Integrals}
%	
%	\begin{enumerate}[topsep=8pt, itemsep=15pt, partopsep=1ex, parsep=1ex]
%		
%		\item $\bigintsss a^x\, dx = \frac{a^x}{\ln a} + C$;
%		
%		\item $\bigintsss \sec^2 x \, dx = \tan x + C$;
%		
%		\item $\bigintsss \csc^2 x \, dx = - \cot x + C$;
%		
%		\item $\bigintsss \tan x \, dx = \ln|\sec x| + C$;
%		
%		\item $\bigintsss \cot x \, dx = \ln|\sin x| + C$;
%		
%		\item $\bigintsss \sec x \, dx = \ln |\sec x + \tan x| + C$;
%		
%		\item $\bigintsss \csc x \, dx = - \ln |\csc x + \cot x| + C$;
%		
%		\item $\bigintsss \frac{1}{x^2 + a^2} \, dx = \frac 1a \tan^{-1}(\frac xa) + C;$
%		
%		\item $\bigintsss \frac 1{\sqrt{a^2 -x^2}} \, dx = \sin^{-1}(\frac xa) + C$, \ \ $a>0$.
%	\end{enumerate}
%	
%	\vspace{15pt}
%	
%	{\bf Formula for the Area of a Surface of Revolution}
%	
%	\vspace{10pt}
%	
%	\begin{center}
%		$A_f([a,b]) = \bigintss_a^b 2\pi f(x) \sqrt{1 + [f(x)']^2} \, dx$
%	\end{center}
	
%	\begin{thebibliography}{20}
%		
%		\bibitem{jS15} J.~Stewart: \emph{Single Variable Calculus} 8th Edition, Cengage Learning, Boston 2015.
%		
%	\end{thebibliography}
	
\end{document}