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51graph.png

$$\begin{document} \begin{frame} For each of the two regions described below, sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area. \vskip 10pt $$y = 2x + 3\qquad y = 13 - x^2\qquad x = -1\qquad x = 2$$ \vskip 35pt $$x = 45 - 5y^2\qquad x = 5y^2 - 45$$ \end{frame} \begin{frame} Sketch the region enclosed by the given curves. Then find the area. \begin{enumerate}[a)] \item $$x = 6y^2\qquad x = 4 + 5y^2$$ \item $$y = 6 \cos(\pi x)\qquad y = 12x^2 - 3$$ \pause \item $$y = 4 \cos(6x)\qquad y = 4 \sin(12x)\qquad x = 0\qquad x = \pi/12$$ \item $$y = \sqrt{x} \qquad y = \frac{1}{2}x\qquad x = 25$$ \pause \item $$y = |3x|\qquad y = x^2 - 4$$ \end{enumerate} \end{frame} \begin{frame} Two cars, A and B, start side by side and accelerate from rest. The graphs of their velocity functions are given below. \begin{figure}[h]\centering{ \includegraphics[height=1.7in]{51graph.png}} \end{figure} \begin{enumerate}[a)] \item Which car is ahead at time $a$? Explain. \item Interpret the area of the shaded region in physical terms. \item Which car is ahead after $1.5a$ minutes? Explain. \end{enumerate} \end{frame} \begin{frame} Find the number $b$ such that the line $y = b$ divides the region bounded by the curves $y = 4x^2$ and $y = 16$ into two regions with equal area. \end{frame} \end{document}$$