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--- calculus:resources:calculus_flipped_resources:applications:3.4_horizontal_asymptotes_tex [2014/09/06 17:13]
jbrennan
+++ calculus:resources:calculus_flipped_resources:applications:3.4_horizontal_asymptotes_tex [2015/08/28 22:19] (current)
nye Page moved from people:jbrennan:calculus_flipped_resources:applications:3.4_horizontal_asymptotes_tex to calculus:resources:calculus_flipped_resources:applications:3.4_horizontal_asymptotes_tex
@@ Line 1: / Line 1: @@
+TeX code compiled with \documentclass{beamer} using the Amsterdam theme.\\
+<nowiki>
+\begin{document}
+\begin{frame}
+    Find the following limits, if they exist.
+    \vskip 5pt
+        \begin{itemize}
+            \item[\bf a)] $\dlim_{x\to\infty}\dfrac{7x^2 - x + 1}{3x^2 + 5x - 5} $
+            and $ \dlim_{x\to-\infty}\dfrac{7x^2 - x + 1}{3x^2 + 5x - 5}$.
+            \vskip 30pt
+            \item[\bf b)] $\dlim_{x\to\infty}\dfrac{8x - 9}{2x + 4}$ and
+            $\dlim_{x\to-\infty}\dfrac{8x - 9}{2x + 4}$.
+                \vskip 30pt
+            \item[\bf c)] $\dlim_{x\to\infty}\dfrac{x - 8}{x^2 + 7}$ and
+            $\dlim_{x\to-\infty}\dfrac{x - 8}{x^2 + 7}$.
+        \end{itemize}
+\end{frame}
+\begin{frame}
+    Find the following limits, if they exist.
+    \vskip 5pt
+        \begin{itemize}
+            \item[\bf d)] $\dlim_{x\to\infty}\dfrac{\sqrt{4x^6-x}}{x^3+3}$ and
+            $\dlim_{x\to-\infty}\dfrac{\sqrt{4x^6-x}}{x^3+3}$.
+                \vskip 20pt
+            \item[\bf e)] $\dlim_{x\to\infty}(\sqrt{25x^2+x}-5x)$ and
+            $\dlim_{x\to-\infty}(\sqrt{25x^2+x}-5x)$.
+                \vskip 20pt
+        \pause
+            \item[\bf f)] $\dlim_{x\to-\infty}(x+\sqrt{x^2+2x})$
+            \vskip 10pt
+            \item[\bf g)] $\dlim_{x\to\infty} 6\cos(x)$
+            \vskip 10pt
+            \item[\bf h)] $\dlim_{x\to\infty}\frac{x^4 - 3x^2 + x}{x^3 - x + 3}$
+        \end{itemize}
+\end{frame}
+\begin{frame}
+    Find the horizontal and vertical asymptotes of each curve.
+\begin{enumerate}[a)]
+\item $$y=\frac{8x + 3}{x - 4}$$
+\item $$y=\frac{x^2 + 1}{9x^2 - 80x - 9}$$
+\item $$y=\frac{x^2 - x}{x^2 - 8x + 7}$$
+\end{enumerate}
+\end{frame}
+\begin{frame}
+    Let $P$ and $Q$ be polynomials with positive coefficients.
+\begin{enumerate}[a)]
+\item If the degree of $P$ is less than the degree of $Q$, what is
+$$\lim_{x\to\infty}\frac{P(x)}{Q(x)}?$$
+\item If the degree of $P$ is greater than the degree of $Q$, what is
+$$\lim_{x\to\infty}\frac{P(x)}{Q(x)}?$$
+\item If the degree of $P$ equals the degree of $Q$, what is
+$$\lim_{x\to\infty}\frac{P(x)}{Q(x)}?$$
+\end{enumerate}
+\end{frame}
+\begin{frame}
+     A tank contains 120 L of pure water. Brine that contains 25 g of salt per liter
+     of water is pumped into the tank at a rate of 25 L/min.
+     \vskip 15pt
+\begin{enumerate}[a)]
+\item Find the concentration of salt after $t$ minutes (in grams per liter).
+\vskip 15pt
+\item As $t$ approaches infinity, what does the concentration approach?
+\end{enumerate}
+\end{frame}
+\begin{frame}
+Find $$\lim_{x\to\infty}(\sqrt{x^2+cx}-\sqrt{x^2+dx}).$$
+(Here $c$ and $d$ represent arbitrary real numbers.)
+\vskip 25pt
+Find $$\lim_{x\to -\infty}(x^2+x^3).$$
+\end{frame}
+\end{document}
+</nowiki>

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