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\begin{document}
	
	\mbox{}
	\title{Quiz 3 (Math 1B)}
	
	\maketitle
	
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	
	%---------------------------------PROBLEM 1
	
	\begin{problem}
		Find the Maclaurin series of $f(x) = \frac{1}{\sqrt{5-x}}$.
	\end{problem}
	
	%---------------------------------PROBLEM 2
	
	\begin{problem}
		Evaluate $\int_0^1 e^{-x^2} \, dx$ correct to within an error of $0.001$. [Hint: Use Taylor expansion, then use the Alternating Estimation Theorem.]
	\end{problem}
	
	%---------------------------------PROBLEM 3
	
	\begin{problem}
		Solve the differential equation $\frac{dy}{dx} = \frac{x^5 + 1}{x^3y^2 + y^4x^3}$.
	\end{problem}
	
	%---------------------------------PROBLEM 4
	
	\begin{problem}
		Suppose that a population develop according to the logistic equation $dP/dt = 0.06P - 0.0006P^2$, where $t$ is measured in weeks. (a) What is the carrying capacity? (b) What is the value of $k$? (c) What are the equilibrium solutions. (d) If the initial population is $50$, what is the population after $10$ weeks?
	\end{problem}
	
	%---------------------------------PROBLEM 5
	
	\begin{problem}
		Solve the first-order linear differential equations:
		\begin{enumerate}
			\item $y' - y = e^x$
			\item $y' + 2xy = 1$.
		\end{enumerate}
	\end{problem}
	
%	\begin{thebibliography}{20}
		
	%	\bibitem{jS15} J.~Stewart: \emph{Single Variable Calculus} 8th Edition, Cengage Learning, Boston 2015.
		
%	\end{thebibliography}
	
\end{document}