% (find-LATEX "2023-1-C2-volumes.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2023-1-C2-volumes.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2023-1-C2-volumes.tex" "Success!!!"))
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% (defun e () (interactive) (find-LATEX "2023-1-C2-volumes.tex"))
% (defun o () (interactive) (find-LATEX "2023-1-C2-volumes.tex"))
% (defun u () (interactive) (find-latex-upload-links "2023-1-C2-volumes"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2023-1-C2-volumes.pdf"))
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%          (code-eec-LATEX "2023-1-C2-volumes")
% (find-pdf-page   "~/LATEX/2023-1-C2-volumes.pdf")
% (find-sh0 "cp -v  ~/LATEX/2023-1-C2-volumes.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2023-1-C2-volumes.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2023-1-C2-volumes.pdf")
%   file:///home/edrx/LATEX/2023-1-C2-volumes.pdf
%               file:///tmp/2023-1-C2-volumes.pdf
%           file:///tmp/pen/2023-1-C2-volumes.pdf
%  http://anggtwu.net/LATEX/2023-1-C2-volumes.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise1")
% (find-Deps1-cps   "Caepro5 Piecewise1")
% (find-Deps1-anggs "Caepro5 Piecewise1")
% (find-MM-aula-links "2023-1-C2-volumes" "C2" "c2m231volumes" "c2vo")

% «.defs»		(to "defs")
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% «.djvuize»		(to "djvuize")



% <videos>
% Video (not yet):
% (find-ssr-links     "c2m231volumes" "2023-1-C2-volumes")
% (code-eevvideo      "c2m231volumes" "2023-1-C2-volumes")
% (code-eevlinksvideo "c2m231volumes" "2023-1-C2-volumes")
% (find-c2m231volumesvideo "0:00")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
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\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
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%\usepackage{tikz}
%
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%\usepackage{proof}   % For derivation trees ("%:" lines)
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%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
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\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
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% «defs»  (to ".defs")
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% (find-LATEX "edrx21.sty")

\def\drafturl{http://anggtwu.net/LATEX/2023-1-C2.pdf}
\def\drafturl{http://anggtwu.net/2023.1-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2023-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2023-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

% «defs-T-and-B»  (to ".defs-T-and-B")
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\def\T(Total: #1 pts){{\bf(Total: #1)}}
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\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B       (#1 pts){\ColorOrange{\bf(#1 pts)}}

% «defs-caepro»  (to ".defs-caepro")
%L dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L V = nil                           -- (find-angg "LUA/Pict2e1.lua" "MiniV")
%L dofile "Piecewise1.lua"           -- (find-LATEX "Piecewise1.lua")
%L Pict2e.__index.suffix = "%"
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\pu



%  _____ _ _   _                               
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%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m231volumesp 1 "title")
% (c2m231volumesa   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 2 - 2023.1}

\bsk

Aula 27: volumes e comprimento de arco

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://anggtwu.net/2023.1-C2.html}

\end{center}

\newpage

% «links»  (to ".links")

{\bf Links}

\scalebox{0.9}{\def\colwidth{12cm}\firstcol{

\par \Ca{StewPtCap15p6} (p.874) 15.1 Integrais múltiplas sobre retângulos
\par \Ca{Miranda285} 9.3 Volume
\par \Ca{Miranda288} O volume da esfera de raio $r$ é $\frac43πr^3$
\par \Ca{Miranda285} 9.3.1 Secções transversais
\par \Ca{Miranda289} 9.3.2 Sólidos de revolução
\par \Ca{Miranda292} \standout{Façam os exercícios 2, 3, 4 e 5}

\msk

\par \Ca{3cT75} Pirâmide (3D)
\par \Ca{3cT76} Cruz (3D)
\par \Ca{3eT23} Low Poly (até o final do PDFzão)

% (find-books "__analysis/__analysis.el" "bressoud")

% (find-dmirandacalcpage 285 "9.3 Volume")
% (find-dmirandacalcpage 288   "volume da esfera")
% (find-dmirandacalctext 288   "volume da esfera")
% (find-dmirandacalcpage 285 "9.3.1 Secções Transversais")
% (find-dmirandacalcpage 289 "9.3.2 Sólidos de Revolução")

}\anothercol{
}}


\newpage

{\bf Introdução a volumes}

Preciso digitar essas contas daqui:

\par \Ca{2gQ58}


\newpage

{\bf Comprimento de arco}

\def\dx  {x_i-x_{i-i}}
\def\dy  {y_i-y_{i-i}}
\def\pdx{(\dx)}
\def\pdy{(\dy)}
\def\dydx{\frac{\dy}{\dx}}
\def\yx{f'(x_i)}

\scalebox{0.6}{\def\colwidth{9cm}\firstcol{

As contas começam assim, mas eu não terminei...

$$\begin{array}{l}
  \sqrt{dx^2 + dy^2} \\
  =\; \sqrt{dx^2 + (\frac{dy}{dx}dx)^2} \\
  =\; \sqrt{dx^2 + (y_xdx)^2} \\
  =\; \sqrt{dx^2 + {y_x}^2 dx^2} \\
  =\; \sqrt{(1+{y_x}^2)dx^2} \\
  =\; \sqrt{(1+{y_x}^2)}\;\sqrt{dx^2} \\
  =\; \sqrt{(1+{y_x}^2)}\;dx^2 \\
  \end{array}
$$

$$\begin{array}{l}
  \sqrt{\pdx^2 + \pdy^2} \\
  =\; \sqrt{\pdx^2 + (\dydx\pdx)^2} \\
  =\; \sqrt{\pdx^2 + (\yx\pdx)^2} \\
  =\; \sqrt{\pdx^2 + \yx^2 \pdx^2} \\
  =\; \sqrt{(1+\yx^2)\pdx^2} \\
  =\; \sqrt{(1+\yx^2)}\;\sqrt{\pdx^2} \\
  =\; \sqrt{(1+\yx^2}\;\pdx \\
  \end{array}
$$

}\anothercol{
}}




\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}

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