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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2021-2-C3-P2.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2021-2-C3-P2.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2021-2-C3-P2.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2021-2-C3-P2.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2021-2-C3-P2.pdf"))
% (defun e () (interactive) (find-LATEX "2021-2-C3-P2.tex"))
% (defun o () (interactive) (find-LATEX "2021-2-C3-P2.tex"))
% (defun u () (interactive) (find-latex-upload-links "2021-2-C3-P2"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2021-2-C3-P2.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (code-eec-LATEX "2021-2-C3-P2")
% (find-pdf-page "~/LATEX/2021-2-C3-P2.pdf")
% (find-sh0 "cp -v ~/LATEX/2021-2-C3-P2.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2021-2-C3-P2.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2021-2-C3-P2.pdf")
% file:///home/edrx/LATEX/2021-2-C3-P2.pdf
% file:///tmp/2021-2-C3-P2.pdf
% file:///tmp/pen/2021-2-C3-P2.pdf
% http://angg.twu.net/LATEX/2021-2-C3-P2.pdf
% (find-LATEX "2019.mk")
% (find-CN-aula-links "2021-2-C3-P2" "3" "c3m212p2" "c3p2")
% «.defs» (to "defs")
% «.defs-T-and-B» (to "defs-T-and-B")
% «.title» (to "title")
% «.regras-e-dicas» (to "regras-e-dicas")
% «.questao-1» (to "questao-1")
% «.questao-2» (to "questao-2")
% «.ideias» (to "ideias")
%
% «.djvuize» (to "djvuize")
% <videos>
% Video (not yet):
% (find-ssr-links "c3m212p2" "2021-2-C3-P2")
% (code-eevvideo "c3m212p2" "2021-2-C3-P2")
% (code-eevlinksvideo "c3m212p2" "2021-2-C3-P2")
% (find-c3m212p2video "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 "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}}
% «defs-T-and-B» (to ".defs-T-and-B")
% (c3m202p1p 6 "questao-2")
% (c3m202p1a "questao-2")
\long\def\ColorOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B (#1 pts){\ColorOrange{\bf(#1 pts)}}
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
% | | | | |_| | __/ | |_) | (_| | (_| | __/
% |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
% |_| |___/
%
% «title» (to ".title")
% (c3m212p2p 1 "title")
% (c3m212p2a "title")
\thispagestyle{empty}
\begin{center}
\vspace*{1.2cm}
{\bf \Large Cálculo 3 - 2021.2}
\bsk
Segunda prova (P2)
\bsk
Eduardo Ochs - RCN/PURO/UFF
\url{http://angg.twu.net/2021.2-C3.html}
\end{center}
\newpage
% «regras-e-dicas» (to ".regras-e-dicas")
% (c3m212p2p 2 "regras-e-dicas")
% (c3m212p2a "regras-e-dicas")
As regras e dicas são as mesmas dos mini-testes,
exceto que a prova será disponibilizada às 21:00
da quarta, 2/fev/2022, e você deverá entregá-la
até as 21:00 da quinta, 3/fev/2022.
\msk
Várias das questões desta prova são baseadas nos
exercícios sobre funções homogêneas que nós discutimos
na última aula antes da prova. Leia o log aqui:
\msk
{\footnotesize
% http://angg.twu.net/tmp/C3-M1-RCN-PURO-2021.2-4.pdf#page=6
\url{http://angg.twu.net/tmp/C3-M1-RCN-PURO-2021.2-4.pdf\#page=6}
}
\msk
Obs: esse log vai ser deletado logo depois da prova.
\newpage
% «questao-1» (to ".questao-1")
% (c3m212p2p 3 "questao-1")
% (c3m212p2a "questao-1")
{\bf Questão 1.}
\T(Total: 2.5 pts)
Digamos que $(x_0,y_0)=(4,3)$ e que $f(x,y)$ é uma
função que obedece isto aqui:
%
$$f(x_0+kΔx, y_0+kΔy) \;\;=\;\; k^3 f(x_0+Δx, y_0+Δy).$$
Complete o diagrama de numerozinhos da
página seguinte. Os números dele indicam valores
que você sabe, como por exemplo $f(0,1)=3$, e
os pontos de interrogação dele indicam valores que
você tem que descobrir... por exemplo ``$g(0,2)=\ColorRed{?}$''.
\newpage
% (find-LATEX "edrx21.sty" "picture-cells")
\unitlength=8pt
\celllower=2.5pt
\def\cellfont{\scriptsize}
\def\cellfont{\footnotesize}
\unitlength=20pt
%L Pict2e.__index.axes_ = "\\linethickness{0.1pt}"
%L Pict2e.__index.axes_ = "\\color{gray}"
%L
%L Pict2e.new()
%L :setbounds(v(0,0), v(6,5))
%L :axesandticks()
%L :run(function (p)
%L local f = function(x, y, z)
%L p:puttext(v(x+4,y+3), z or "\\ColorRed{?}")
%L end
%L f(1,1,2); f(2,2); f(0,0); f(-1,-1); f(-2,-2)
%L f(1,0,5); f(2,0); f(-1,0); f(-2,0)
%L f(-1,1); f(-2,2,8); f(1,-1); f(2,-2);
%L f(-1,2,4); f(1,-2)
%L end)
%L :bepc()
%L :def("Foo")
%L :output()
\pu
$$\Foo
$$
\newpage
% «questao-2» (to ".questao-2")
% (c3m212p2p 5 "questao-2")
% (c3m212p2a "questao-2")
{\bf Questão 2.}
\T(Total: 7.5 pts)
\scalebox{0.8}{\def\colwidth{8cm}\firstcol{
Digamos que $f(x,y)$ é uma função
que obedece isto aqui:
%
$$\begin{array}{c}
∀x,y,k. \; f(kx,ky) = k^3 f(x,y), \\[2.5pt]
∀y. \; f(1,y) = (y+1)·(y-0.5), \\[2.5pt]
∀y. \; f(0,y) = 0. \\
\end{array}
$$
a) \B(2.0 pts) Faça o diagrama de sinais
da função $f(x,y)$ na reta $x=1$.
\ssk
b) \B(1.0 pts) Faça o diagrama de sinais
da função $f(x,y)$ na reta $x=2$.
\ssk
c) \B(1.0 pts) Faça o diagrama de sinais
da função $f(x,y)$ na reta $x=-1$.
\ssk
d) \B(3.5 pts) Faça o diagrama de sinais
da função $f(x,y)$ em todo o plano $\R^2$.
%}\anothercol{
}}
\newpage
% «ideias» (to ".ideias")
% (c3m212p2p 2 "ideias")
% (c3m212p2a "ideias")
% Função quadrática centrada num ponto estranho
% Função homogênea
%\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-P2 veryclean
make -f 2019.mk STEM=2021-2-C3-P2 pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c3p2"
% ee-tla: "c3m212p2"
% End: