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philosolog committed Jan 12, 2024
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\documentclass[12pt]{beamer}
\usetheme{Warsaw}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[font=Times,timeinterval=1,timeduration=2.0,timedeath=0,fillcolorwarningsecond=white!60!yellow,timewarningfirst=50,timewarningsecond=80,resetatpages=2]{tdclock}
\usepackage{tabularx}
\usepackage{array}
\usepackage{multicol}
\usepackage{longtable}
\usepackage{xcolor}
\usepackage{textcomp, gensymb}
\usepackage{pgfplots}
\usepackage[makeroom]{cancel}

\graphicspath{ {./references/} }
\pgfplotsset{
soldot/.style={color=black,only marks,mark=*},
holdot/.style={color=black,fill=white,only marks,mark=*},
compat=1.12
}
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\makeatletter
\def\@listii{\leftmargin\leftmarginii
\topsep 2ex
\parsep 0\p@ \@plus\p@
\itemsep \parsep}
\makeatother
\newcommand\at[2]{\left.#1\right|_{#2}}

\begin{document}
\begin{frame}
\frametitle{Bellwork 1/12}
\initclock

\vfill
\vfill
\vfill
\Large
Find the general indefinite integral:
\vfill
\[\int (2+\tan^2\theta)d\theta\]
\vfill
\vfill
\vfill
\vfill
\vfill

\small
\crono
\resetcrono{\beamerbutton{reset}}
\end{frame}
\begin{frame}
\frametitle{Bellwork 1/12 - Solution}

\large
\begin{align*}
\int_{0}^{4}(4-t)\sqrt{t}dt &= 4\int_{0}^{4}\sqrt{t}dt-\int_{0}^{4}t^\frac{3}{2}dt \\
&= \frac{8}{3}\left[t^\frac{3}{2}\right]_0^4 - \frac{2}{5}\left[t^\frac{5}{2}\right]_0^4 \\
&= \frac{8}{3}\left(4^\frac{3}{2}\right) - \frac{2}{5}\left(4^\frac{5}{2}\right) \\
&= \boxed{\frac{128}{15}}
\end{align*}
\end{frame}
\begin{frame}
\frametitle{Exercise 1}


\end{frame}
\begin{frame}
\frametitle{Exercise 1 - Solution}


\end{frame}
\begin{frame}
\frametitle{Exercise 2}


\end{frame}
\begin{frame}
\frametitle{Exercise 2 - Solution}


\end{frame}
\end{document}

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