% (find-LATEX "2022-1-C2-MT2.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2022-1-C2-MT2.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2022-1-C2-MT2.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2022-1-C2-MT2.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2022-1-C2-MT2.pdf"))
% (defun e () (interactive) (find-LATEX "2022-1-C2-MT2.tex"))
% (defun o () (interactive) (find-LATEX "2022-1-C2-MT2.tex"))
% (defun u () (interactive) (find-latex-upload-links "2022-1-C2-MT2"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2022-1-C2-MT2.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2022-1-C2-MT2")
% (find-pdf-page   "~/LATEX/2022-1-C2-MT2.pdf")
% (find-sh0 "cp -v  ~/LATEX/2022-1-C2-MT2.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2022-1-C2-MT2.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2022-1-C2-MT2.pdf")
%   file:///home/edrx/LATEX/2022-1-C2-MT2.pdf
%               file:///tmp/2022-1-C2-MT2.pdf
%           file:///tmp/pen/2022-1-C2-MT2.pdf
% http://angg.twu.net/LATEX/2022-1-C2-MT2.pdf
% (find-LATEX "2019.mk")
% (find-sh0 "cd ~/LUA/; cp -v Pict2e1.lua Pict2e1-1.lua Piecewise1.lua ~/LATEX/")
% (find-sh0 "cd ~/LUA/; cp -v Pict2e1.lua Pict2e1-1.lua Pict3D1.lua ~/LATEX/")
% (find-sh0 "cd ~/LUA/; cp -v C2Subst1.lua C2Formulas1.lua ~/LATEX/")
% (find-sh0 "cd ~/LUA/; cp -v Lazy2.lua Lazy3.lua Lazy4.lua Verbatim1.lua ~/LATEX/")
% (find-CN-aula-links "2022-1-C2-MT2" "2" "c2m221mt2" "c2mt2")

% «.defs»		(to "defs")
% «.title»		(to "title")
% «.questao-E1»		(to "questao-E1")
% «.questao-C1»		(to "questao-C1")
% «.gabarito»		(to "gabarito")
%
% «.djvuize»		(to "djvuize")



% <videos>
% Video (not yet):
% (find-ssr-links     "c2m221mt2" "2022-1-C2-MT2")
% (code-eevvideo      "c2m221mt2" "2022-1-C2-MT2")
% (code-eevlinksvideo "c2m221mt2" "2022-1-C2-MT2")
% (find-c2m221mt2video "0:00")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%\usepackage{emaxima}              % (find-LATEX "emaxima.sty")
%
%\usepackage[backend=biber,
%   style=alphabetic]{biblatex}            % (find-es "tex" "biber")
%\addbibresource{catsem-slides.bib}        % (find-LATEX "catsem-slides.bib")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")
%L dofile "Piecewise1.lua"           -- (find-LATEX "Piecewise1.lua")
%L dofile "QVis1.lua"                -- (find-LATEX "QVis1.lua")
%L dofile "Pict3D1.lua"              -- (find-LATEX "Pict3D1.lua")
%L dofile "C2Formulas1.lua"          -- (find-LATEX "C2Formulas1.lua")
%L dofile "Lazy4.lua"                -- (find-LATEX "Lazy4.lua")
%L Pict2e.__index.suffix = "%"
\pu
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\celllower=2.5pt

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\u#1{\par{\footnotesize \url{#1}}}

\def\drafturl{http://angg.twu.net/LATEX/2022-1-C2.pdf}
\def\drafturl{http://angg.twu.net/2022.1-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% «formulas-defs»  (to ".formulas-defs")
% (c2m221ftp 1 "title")
% (c2m221fta   "title")
% (c2m221fda   "title")
\input 2022-1-C2-formulas-defs.tex


%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
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%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m221mt2p 1 "title")
% (c2m221mt2a   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 2 - 2022.1}

\bsk

Mini-teste 2

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://angg.twu.net/2022.1-C2.html}

\end{center}

\newpage

% «questao-E1»  (to ".questao-E1")
% (c2m221mt2p 2 "questao-E1")
% (c2m221mt2a   "questao-E1")

\scalebox{0.5}{\def\colwidth{10.5cm}\firstcol{

{\bf Mini-teste 2}

(Veja o rodapé pra detalhes).

\msk

Isto aqui é um exemplo do livro do Miranda:

\msk

% (find-dmirandacalcpage 189 "6.2 Integração por Substituição")
% (find-dmirandacalcpage 190 "6.2 Integração por Substituição")

{\color{blue} Problema.} Calcule a antiderivada de $(\sen 4x)^5 \cos 4x$.

{\color{blue} Solução.} Observamos que a derivada de $\sen 4x$ é
$4 \cos x$, que é um múltiplo do fator $\cos 4x$ que aparece no
integrando. Isso motiva a substituição
%
$$u = \sen 4x,
  \qquad
  du = 4 \cos 4x \, dx
  \qquad
  \frac{du}{4} = \cos 4x \, dx
$$

e assim:
%
$$\begin{array}{rcl}
  \D \intx{(\sen 4x)^5 \cos 4x}
  &=& \D \frac14 \intu{u^5} \\
  &=& \D \frac14 · \frac16 u^6 + C \\[5pt]
  &=& \D \frac1{24} (\sen 4x)^6 + C. \\
  \end{array}
$$

Justifique o passo $\intx{(\sen 4x)^5 \cos 4x} = \frac14 \intu{u^5}$.
Mais precisamente: imagine que você tentou justificar ele dizendo que
ele é verdadeiro ``por mudança de variáveis'', e o jogador $O$
respondeu: ``me mostra um caso particular do \ga{[MV1]} que justifica
esse passo'' --- e o jogador $O$ te dá essa dica daqui: ``o \ga{[MV1]}
é sobre integrais definidas, então suponha que a primeira integral vai
de $x=a$ até $x=b$''.

}\anothercol{
}}


\newpage

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% | |  _ / _` | '_ \ / _` | '__| | __/ _ \ 
% | |_| | (_| | |_) | (_| | |  | | || (_) |
%  \____|\__,_|_.__/ \__,_|_|  |_|\__\___/ 
%                                          
% «gabarito»  (to ".gabarito")
% (c2m221mt2p 4 "gabarito")
% (c2m221mt2a   "gabarito")
% (c2m221dp1p 2 "C2Formulas1")
% (c2m221dp1a   "C2Formulas1")

{\bf Gabarito}

% (find-angg "LUA/Lazy4.lua" "MT2-tests")

%L ang = Ang.from([[
%L   <out>
%L   $\scalebox{1.0}{$\begin{array}{c}
%L      <MT2_> = <Paren(MT2)>  \\
%L      <MV2_> = <Paren(MV2)>  \\
%L      <MV2_><SMV2a.bsm> = <Paren(SMV2a(MV2))> \\
%L      <MV2_><SMV2b.bsm> = <Paren(SMV2b(MV2))> \\
%L      <MV2_><SMV2c.bsm> = <Paren(SMV2c(MV2))> \\
%L    \end{array}
%L    $}
%L   $
%L ]])
%L ang:sa("gab"):output()
\pu

\scalebox{0.7}{\def\colwidth{20cm}\firstcol{

{\footnotesize

Veja estes PDFs pra mais detalhes:

\ssk

% (c2m221dp1p 2 "introducao")
% (c2m221dp1a   "introducao")
%    http://angg.twu.net/LATEX/2022-1-C2-dicas-pra-P1.pdf
\url{http://angg.twu.net/LATEX/2022-1-C2-dicas-pra-P1.pdf}

% (c2m221p1p 4 "fracoes-parciais-gab")
% (c2m221p1a   "fracoes-parciais-gab")
%    http://angg.twu.net/LATEX/2022-1-C2-P1.pdf#page=4
\url{http://angg.twu.net/LATEX/2022-1-C2-P1.pdf\#page=4}

}

\msk

As contas são:

\bsk

\ga{gab}



}\anothercol{
}}


\ssk




% (c2m221dp1p 2 "C2Formulas1")
% (c2m221dp1a   "C2Formulas1")
% (find-angg "LUA/C2Formulas1.lua")
% (c2m221prp 4 "C2Formulas1-test")
% (c2m221pra   "C2Formulas1-test")
% (find-LATEX "edrxgac2.tex" "C2" "Definite integrals")
% \input 2022-1-C2-formulas-defs.tex


% (find-angg "LUA/C2Formulas1.lua" "TFC2")






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

\end{document}

%  ____  _             _         
% |  _ \(_)_   ___   _(_)_______ 
% | | | | \ \ / / | | | |_  / _ \
% | |_| | |\ V /| |_| | |/ /  __/
% |____// | \_/  \__,_|_/___\___|
%     |__/                       
%
% «djvuize»  (to ".djvuize")
% (find-LATEXgrep "grep --color -nH --null -e djvuize 2020-1*.tex")

%  __  __       _        
% |  \/  | __ _| | _____ 
% | |\/| |/ _` | |/ / _ \
% | |  | | (_| |   <  __/
% |_|  |_|\__,_|_|\_\___|
%                        
% <make>

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2022-1-C2-MT2 veryclean
make -f 2019.mk STEM=2022-1-C2-MT2 pdf

% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2mt2"
% ee-tla: "c2m221mt2"
% End:
