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The original is across this link,
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% (find-angg "LATEX/2015-1-C2-lista-edrx-1.tex")
% (find-angg "LATEX/2015-1-C2-lista-edrx-1.lua")
% (defun c () (interactive) (find-LATEXsh "lualatex 2015-1-C2-lista-edrx-1.tex"))
% (defun c () (interactive) (find-LATEXsh "lualatex --output-format=dvi 2015-1-C2-lista-edrx-1.tex"))
% (defun d () (interactive) (find-xpdfpage "~/LATEX/2015-1-C2-lista-edrx-1.pdf"))
% (defun d () (interactive) (find-xdvipage "~/LATEX/2015-1-C2-lista-edrx-1.dvi"))
% (defun e () (interactive) (find-LATEX "2015-1-C2-lista-edrx-1.tex"))
% (defun l () (interactive) (find-LATEX "2015-1-C2-lista-edrx-1.lua"))
% (defun eg () (interactive) (find-LATEX "2015-1-GA-lista-edrx-1.tex"))
% (find-xpdfpage "~/LATEX/2015-1-C2-lista-edrx-1.pdf")
% (find-xdvipage "~/LATEX/2015-1-C2-lista-edrx-1.dvi")
\documentclass[oneside]{book}
\usepackage[latin1]{inputenc}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
\usepackage{edrx15}               % (find-angg "LATEX/edrx15.sty")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{luacode}
\begin{document}

% \directlua{dofile "\jobname.lua"}
\def\th{\theta}
\def\sen{\operatorname{sen}}
\def\arcsen{\operatorname{arcsen}}
\def\Intsab{\int_{s=a}^{s=b}}
\def\Barsab{\left.\right|_{s=a}^{s=b}}
\def\nip{\par\noindent}

{\setlength{\parindent}{0em}
\footnotesize
\par CÃˇlculo 2
\par PURO-UFF - 2015.1
\par Lista de exercícios 1 - Eduardo Ochs
\par VersÃŁo: 15/abril/2015 12:40
\par Links importantes:
\par \url{http://angg.twu.net/2015.1-C2.html} (pÃˇgina do curso)
\par \url{http://angg.twu.net/2015.1-C2/2015.1-C2.pdf} (quadros)
\par \url{http://angg.twu.net/2015.1-C2/????.pdf} (livro)
\par \url{http://angg.twu.net/2015.1-C2/2015-1-C2-lista-edrx-1.pdf}
     (lista, atualizada)
\par {\tt eduardoochs@gmail.com} (meu e-mail)
}

\bsk
\bsk

\nip Lembre que estamos usando os seguintes materiais no curso:
\par [RI1], [RI2], ..., [RI6]: vídeos do Reginaldo Demarque sobre integraÃ§ÃŁo
\par [H]: Cristiane R.\ R.\ A.-F.\ HernÃˇndez - Apostila de CÃˇlculo IIA (para EAD) 
\par [T]: Thomas/Weir/Hass/Giordano: CÃˇlculo, vol.1, 11ª ed
\nip Tem links pra eles (exceto o [T]) na pÃˇgina do curso.

\bsk

Digamos que $u = f(x)$ e $v = g(x)$. EntÃŁo, por exemplo,

$$\begin{array}{ll}
  \frac{d(u^4)}{dx} = 4 u^3 u_x \\
  d(u^4) = 4 u^3 u_x \, dx = 4 u^3 \, du \\
  \frac{d(u^{-1})}{dx} = (-1) u^{-2} u_x \\
  d(u^{-1}) = - \frac{1}{u^2} u_x \, dx = - \frac{1}{u^2} \, du \\
  \frac{d(uv)}{dx} = u_x v + u v_x = \frac{du}{dx} v + u \frac{dv}{dx} \\
  d(uv) = v\,du + u\,dv \\
  \end{array}
$$


\bsk

Sejam:

$$\begin{array}{ll}
  c: = \cos \th,                               & \th = \arccos c, \\
  s: = \sen \th,                               & \th = \arcsen s, \\
  t: = \tan \th = \frac{\sen \th}{\cos \th},   & \th = \arctan s, \\
  \end{array}
$$

EntÃŁo $ds/d\th = c$,
      $ds = c \, d\th = \sqrt{1-s^2} d\th$,
      $\frac{1}{\sqrt{1-s^2}} ds = d\th$,
      $\Int \frac{1}{\sqrt{1-s^2}} ds = \Int d\th = \Int 1\,d\th = \th$,
      $\Intsab \frac{1}{\sqrt{1-s^2}} ds = \th \Barsab = \arcsen s \Barsab$,
      

% \nip O objetivo desta lista é {\sl complementar} os materiais acima em 




\end{document}