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\begin{center}
{\Large Warm-Up Problems and Lecture Problems

February 19, 2003}
\end{center}

\begin{enumerate}


\item  Find the area trapped between the curves:
	\begin{enumerate}
	\item  $y=x^2$ and $y=2-x^2$
		\\\sol
		\[
		\int_{-1}^1 (2-x^2)-(x^2) \; dx = \frac{8}{3}
		\]
	\item  $x=y^2-1$ and $x=1-y^2$
		\\\sol
		\[
		\int_{-1}^1 (1-y^2) - (y^2-1) \; dy = \frac{8}{3}
		\]
	\end{enumerate}

\newpage
\lecture

\item  Verify the solutions to the following differential equations.
	Determine the order of each differential equation.
	\begin{enumerate}
	\item  $y'=3x^2$; $y=x^3+7$
	\item  $y''+4y=0$; $y=\cos 2x$
	\item  $y'=y+2e^{-x}$; $y=e^x-e^{-x}$
	\item  $y'+2xy^2=0$; $y=\frac{1}{1+x^2}$.
	\end{enumerate}

\newpage

\item  For the slopefield below, sketch several possible solution curves.

\newpage

\item  For the slopefield below, sketch solutions satisfying (one curve for each subpart):
	\begin{enumerate}
	\item  $y(0)=0$
	\item  $y(1)=1$
	\item  Can you find some curves that exhibit ``different behavior?''
	\end{enumerate}
	


\newpage

\item  For the slopefield below, sketch solutions satisfying (one curve for each subpart):
	\begin{enumerate}
	\item  $y(0)=0$
	\item  $y(1)=1$
	\item  Can you find some curves that exhibit ``different behavior?''
	\end{enumerate}
	
\newpage

\item  For the slopefield below, sketch solutions satisfying (one curve for each subpart):
	\begin{enumerate}
	\item  $y(0)=0$
	\item  $y(1)=1$
	\item  Can you find some curves that exhibit ``different behavior?''
	\end{enumerate}
	



\end{enumerate}



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