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% (find-LATEX "2021-2-C3-MT2.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2021-2-C3-MT2.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2021-2-C3-MT2.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2021-2-C3-MT2.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2021-2-C3-MT2.pdf"))
% (defun e () (interactive) (find-LATEX "2021-2-C3-MT2.tex"))
% (defun o () (interactive) (find-LATEX "2021-2-C3-MT2.tex"))
% (defun u () (interactive) (find-latex-upload-links "2021-2-C3-MT2"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2021-2-C3-MT2.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (code-eec-LATEX "2021-2-C3-MT2")
% (find-pdf-page "~/LATEX/2021-2-C3-MT2.pdf")
% (find-sh0 "cp -v ~/LATEX/2021-2-C3-MT2.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2021-2-C3-MT2.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2021-2-C3-MT2.pdf")
% file:///home/edrx/LATEX/2021-2-C3-MT2.pdf
% file:///tmp/2021-2-C3-MT2.pdf
% file:///tmp/pen/2021-2-C3-MT2.pdf
% http://angg.twu.net/LATEX/2021-2-C3-MT2.pdf
% (find-LATEX "2019.mk")
% (find-CN-aula-links "2021-2-C3-MT2" "3" "c3m212mt2" "c3mt2")
% «.videos» (to "videos")
% «.video-a» (to "video-a")
% «.video-b» (to "video-b")
% «.video-c» (to "video-c")
% «.defs» (to "defs")
% «.title» (to "title")
% «.itens» (to "itens")
% «.gabarito» (to "gabarito")
% «.gabarito-maxima» (to "gabarito-maxima")
% «.gabarito-5x5» (to "gabarito-5x5")
% «.figura-homogeneas» (to "figura-homogeneas")
%
% «.djvuize» (to "djvuize")
% «videos» (to ".videos")
% «video-a» (to ".video-a")
% (c3m212mt2a "video-a")
% (find-ssr-links "c3m212mt2a" "2021-2-C3-MT2" "Rz01pLaL9Z0")
% (code-eevvideo "c3m212mt2a" "2021-2-C3-MT2" "Rz01pLaL9Z0")
% (code-eevlinksvideo "c3m212mt2a" "2021-2-C3-MT2" "Rz01pLaL9Z0")
% (find-c3m212mt2avideo "0:00")
% (find-c3m212mt2avideo "0:40" "Diagramas de sinais")
% (find-c3m212mt2avideo "2:25" "zeros na diagonal")
% «video-b» (to ".video-b")
% (c3m212mt2a "video-b")
% (find-ssr-links "c3m212mt2b" "2021-2-C3-MT2-2" "lDvAMU5aNvc")
% (code-eevvideo "c3m212mt2b" "2021-2-C3-MT2-2" "lDvAMU5aNvc")
% (code-eevlinksvideo "c3m212mt2b" "2021-2-C3-MT2-2" "lDvAMU5aNvc")
% (find-c3m212mt2bvideo "0:00")
% (find-c3m212mt2bvideo "2:25" "rodar a figura")
% (find-c3m212mt2bvideo "3:10" "acrescentei um plano horizontal")
% (find-c3m212mt2bvideo "4:40" "olhar pra segunda derivada")
% (find-c3m212mt2bvideo "5:50" "f(x,y) = xy")
% (find-c3m212mt2bvideo "7:50" "raízes reais")
% «video-c» (to ".video-c")
% (c3m212mt2a "video-c")
% (find-ssr-links "c3m212mt2c" "2021-2-C3-MT2-3" "cL3G-t3mILs")
% (code-eevvideo "c3m212mt2c" "2021-2-C3-MT2-3" "cL3G-t3mILs")
% (code-eevlinksvideo "c3m212mt2c" "2021-2-C3-MT2-3" "cL3G-t3mILs")
% (find-yttranscript-links "c3m212mt2c" "cL3G-t3mILs")
% (find-c3m212mt2cvideo "0:00")
% (find-c3m212mt2cvideo "1:45" "x0 e y0")
% (find-c3m212mt2cvideo "2:38" "uma outra linha de zeros aqui")
% (find-c3m212mt2cvideo "4:06" "f(2,1) = f(-2,-1)")
% (find-c3m212mt2cvideo "7:25" "e se α=2?")
% (find-c3m212mt2cvideo "10:35" "(x,y) = (0.5,1)")
% (find-c3m212mt2cvideo "10:42" "e eu multiplico esse ponto por 4? z=20...")
% (find-c3m212mt2cvideo "13:02" "esse z e' 4 vezes esse z")
\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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%
% (find-dn6 "preamble6.lua" "preamble0")
%\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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%\usepackage{emaxima} % (find-LATEX "emaxima.sty")
%
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% style=alphabetic]{biblatex} % (find-es "tex" "biber")
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%
% (find-es "tex" "geometry")
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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 "2021pict2e.lua" -- (find-LATEX "2021pict2e.lua")
%L Pict2e.__index.suffix = "%"
\pu
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
% %L dofile "edrxtikz.lua" -- (find-LATEX "edrxtikz.lua")
% %L dofile "edrxpict.lua" -- (find-LATEX "edrxpict.lua")
% \pu
% «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/2021-2-C3.pdf}
\def\drafturl{http://angg.twu.net/2021.2-C3.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
% | | | | |_| | __/ | |_) | (_| | (_| | __/
% |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
% |_| |___/
%
% «title» (to ".title")
% (c3m212mt2p 1 "title")
% (c3m212mt2a "title")
\thispagestyle{empty}
\begin{center}
\vspace*{1.2cm}
{\bf \Large Cálculo 3 - 2021.2}
\bsk
Mini-teste 2
\bsk
Eduardo Ochs - RCN/PURO/UFF
\url{http://angg.twu.net/2021.2-C3.html}
\end{center}
\newpage
{\bf Avisos}
As regras vão ser as mesmas do mini-teste 1.
\msk
As questões deste mini-teste vão ser baseadas
nos exercícios 4 e 6 deste PDF:
\ssk
{\footnotesize
\url{http://angg.twu.net/LATEX/2021-2-C3-diag-nums.pdf}
}
% (c3m212dnp 11 "exercicio-4")
% (c3m212dna "exercicio-4")
% (c3m212dnp 13 "exercicio-6")
% (c3m212dna "exercicio-6")
\msk
As questões vão ser disponibilizadas às 20:40 da sexta
7/janeiro/2021 e vocês vão ter 24 horas pra entregar
as respostas.
\newpage
% «itens» (to ".itens")
% (c3m212mt2p 3 "itens")
% (c3m212mt2a "itens")
\scalebox{0.9}{\def\colwidth{12cm}\firstcol{
Para cada uma das superfícies abaixo faça o diagrama de
numerozinhos e o diagrama de sinais dela. As definições
vão ser iguais às do PDF sobre diagramas de numerozinhos,
mas aqui vamos usar $x_0=\ColorRed{4}$ e $y_0=\ColorRed{3}$.
\msk
a) $Δx$
b) $Δy$
c) $Δy-Δx$
d) $(Δy-Δx)^2$
e) $Δy(Δy-Δx)$
\bsk
\bsk
Você pode fazer os diagrama de numerozinhos usando só
os 9 pontos com $Δx,Δy∈\{-1,0,1\}$, mas se você não
conseguir descobrir qual é o diagrama de sinais do
último item usando só esses 9 pontos você pode fazer
um diagrama de numerozinhos maior, com os 25 pontos
com $Δx,Δy∈\{-2,-1,0,1,-2\}$.
%}\anothercol{
}}
\newpage
% «gabarito» (to ".gabarito")
% (c3m212mt2p 4 "gabarito")
% (c3m212mt2a "gabarito")
\vspace*{-0.7cm}
{\bf Gabarito}
%L Pict2e.new()
%L :setbounds(v(0,0), v(5,4))
%L -- :grid()
%L :add("#1")
%L :axesandticks()
%L :add("#2")
%L :bepc()
%L :def("funcaof#1#2")
%L :output()
\pu
%L nineputs = function (str)
%L local xl,xc,xr = 3,4,5
%L local ya,yc,yb = 4,3,2
%L local ns = split(str)
%L local out = ""
%L local put = function (x, y, idx)
%L -- out = out..format("\\put(%s,%s){\\cell{%s}}\n", x, y, ns[idx] or "?")
%L out = out..format("\\put(%s,%s){\\cell{\\text{%s}}}\n", x, y, ns[idx] or "?")
%L end
%L put(xl,ya,1); put(xc,ya,2); put(xr,ya,3);
%L put(xl,yc,4); put(xc,yc,5); put(xr,yc,6);
%L put(xl,yb,7); put(xc,yb,8); put(xr,yb,9);
%L return out
%L end
\pu
\def\nineputs#1{\funcaof{\expr{nineputs("#1")}}{}}
% (find-LATEX "edrx21.sty" "picture-cells")
\unitlength=8pt
\celllower=2.5pt
\def\cellfont{\footnotesize}
\def\cellfont{\scriptsize}
\msk
$\begin{array}{ccl}
Δx &=& \nineputs{-1 0 1 -1 0 1 -1 0 1} \\[15pt]
Δy &=& \nineputs{1 1 1 0 0 0 -1 -1 -1} \\[15pt]
Δy-Δx &=& \nineputs{2 1 0 1 0 -1 0 -1 -2} \\[15pt]
(Δy-Δx)^2 &=& \nineputs{4 1 0 1 0 1 0 1 4} \\[15pt]
Δy(Δy-Δx) &=& \nineputs{2 1 0 0 0 0 0 1 2} \\
\end{array}
$
% «gabarito-maxima» (to ".gabarito-maxima")
% (setq eepitch-preprocess-regexp "^")
% (setq eepitch-preprocess-regexp "^%T ")
%
%T * (eepitch-maxima)
%T * (eepitch-kill)
%T * (eepitch-maxima)
%T x0 : 4;
%T y0 : 3;
%T Dx(x) := x - x0;
%T Dy(y) := y - y0;
%T z(x,y) := Dy(y) * (Dy(y) - Dx(x));
%T z(0,0);
%T plot3d (z(x,y), [x, x0-1, x0+1], [y, y0-1, y0+1]);
%T plot3d (z(x,y), [x, x0-2, x0+2], [y, y0-2, y0+2]);
%T plot3d (z(x,y), [x, x0-4, x0+4], [y, y0-4, y0+4]);
%T cap(z) := max(min(z, 0.1), -0.1);
%T plot3d ( cap(z(x,y)), [x, x0-1, x0+1], [y, y0-1, y0+1] );
%T plot3d ([cap(z(x,y)), 0, [x, x0-1, x0+1], [y, y0-1, y0+1]]);
%T plot3d ([ z(x,y) , 0, [x, x0-1, x0+1], [y, y0-1, y0+1]]);
%T **
%T plot2d ([contour, z(x,y)], [x, x0-4, x0+4], [y, y0-4, y0+4]);
\newpage
% «gabarito-5x5» (to ".gabarito-5x5")
% (c3m212mt2p 5 "gabarito-5x5")
% (c3m212mt2a "gabarito-5x5")
%L Pict2e.new()
%L :setbounds(v(0,0), v(6,5))
%L -- :grid()
%L -- :add("#1")
%L :axesandticks()
%L :run(function (p)
%L for y=3+2,3-2,-1 do
%L for x=4-2,4+2 do
%L local Dx,Dy = x-4,y-3
%L p:puttext(v(x,y), Dy * (Dy - Dx))
%L end
%L end
%L end)
%L :bepc()
%L :def("GabBig")
%L :output()
\pu
\vspace*{5.5cm}
$Δy(Δy-Δx) \;\;=\;\; \GabBig$
\newpage
Nós vamos usar algumas idéias deste mini-teste
pra entender máximos e mínimos de superfícies.
Assista os vídeos:
\bsk
12/jan/2022, primeira metade:
{\footnotesize
\url{http://angg.twu.net/eev-videos/2021-2-C3-MT2.mp4}
\url{https://www.youtube.com/watch?v=Rz01pLaL9Z0}
}
\msk
12/jan/2022, segunda metade:
{\footnotesize
\url{http://angg.twu.net/eev-videos/2021-2-C3-MT2-2.mp4}
\url{https://www.youtube.com/watch?v=lDvAMU5aNvc}
}
\bsk
14/jan/2022 (sobre funções homogêneas):
{\footnotesize
\url{http://angg.twu.net/eev-videos/2021-2-C3-MT2-3.mp4}
\url{https://www.youtube.com/watch?v=cL3G-t3mILs}
}
\newpage
% «figura-homogeneas» (to ".figura-homogeneas")
% (c3m212mt2p 7 "figura-homogeneas")
% (c3m212mt2a "figura-homogeneas")
\unitlength=15pt
%L Pict2e.new()
%L :setbounds(v(-5,-5), v(5,5))
%L :axesandticks()
%L :run(function (p)
%L for y=-4,4 do
%L for x=-4,4 do
%L p:puttext(v(x,y), (x-y) * (x+2*y))
%L end
%L end
%L end)
%L :bepc()
%L :def("Foo")
%L :output()
\pu
$$(x-y) (x+2y)
\;\;=\;\;
\Foo
$$
%\printbibliography
\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")
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-fline "~/2021.2-C3/")
# (find-fline "~/LATEX/2021-2-C3/")
# (find-fline "~/bin/djvuize")
cd /tmp/
for i in *.jpg; do echo f $(basename $i .jpg); done
f () { rm -v $1.pdf; textcleaner -f 50 -o 5 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf; textcleaner -f 50 -o 10 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf; textcleaner -f 50 -o 20 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 15" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 30" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 45" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.5" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.25" $1.pdf; xpdf $1.pdf }
f () { cp -fv $1.png $1.pdf ~/2021.2-C3/
cp -fv $1.pdf ~/LATEX/2021-2-C3/
cat <<%%%
% (find-latexscan-links "C3" "$1")
%%%
}
f 20201213_area_em_funcao_de_theta
f 20201213_area_em_funcao_de_x
f 20201213_area_fatias_pizza
% __ __ _
% | \/ | __ _| | _____
% | |\/| |/ _` | |/ / _ \
% | | | | (_| | < __/
% |_| |_|\__,_|_|\_\___|
%
% <make>
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2021-2-C3-MT2 veryclean
make -f 2019.mk STEM=2021-2-C3-MT2 pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c3mt2"
% ee-tla: "c3m212mt2"
% End: