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Warning: this is an htmlized version!
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% (find-LATEX "2023-2-C2-VS.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2023-2-C2-VS.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2023-2-C2-VS.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2023-2-C2-VS.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2023-2-C2-VS.pdf"))
% (defun e () (interactive) (find-LATEX "2023-2-C2-VS.tex"))
% (defun o () (interactive) (find-LATEX "2023-2-C2-P1.tex"))
% (defun o () (interactive) (find-LATEX "2023-2-C2-P2.tex"))
% (defun u () (interactive) (find-latex-upload-links "2023-2-C2-VS"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2023-2-C2-VS.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (code-eec-LATEX "2023-2-C2-VS")
% (find-pdf-page "~/LATEX/2023-2-C2-VS.pdf")
% (find-sh0 "cp -v ~/LATEX/2023-2-C2-VS.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2023-2-C2-VS.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2023-2-C2-VS.pdf")
% file:///home/edrx/LATEX/2023-2-C2-VS.pdf
% file:///tmp/2023-2-C2-VS.pdf
% file:///tmp/pen/2023-2-C2-VS.pdf
% http://anggtwu.net/LATEX/2023-2-C2-VS.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2023-2-C2-VS" "C2" "c2m232vs" "c2vs")
% «.defs» (to "defs")
% «.defs-T-and-B» (to "defs-T-and-B")
% «.defs-caepro» (to "defs-caepro")
% «.defs-pict2e» (to "defs-pict2e")
% «.defs-maxima» (to "defs-maxima")
% «.title» (to "title")
% «.links» (to "links")
%
% «.djvuize» (to "djvuize")
% <videos>
% Video (not yet):
% (find-ssr-links "c2m232vs" "2023-2-C2-VS")
% (code-eevvideo "c2m232vs" "2023-2-C2-VS")
% (code-eevlinksvideo "c2m232vs" "2023-2-C2-VS")
% (find-c2m232vsvideo "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")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
]{geometry}
%
\begin{document}
% «defs» (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")
\def\drafturl{http://anggtwu.net/LATEX/2023-2-C2.pdf}
\def\drafturl{http://anggtwu.net/2023.2-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")
\long\def\ColorDarkOrange#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){\ColorDarkOrange{\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 dofile "Piecewise2.lua" -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua" -- (find-LATEX "Escadas1.lua")
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\celllower=2.5pt
% «defs-maxima» (to ".defs-maxima")
%L dofile "Maxima2.lua" -- (find-angg "LUA/Maxima2.lua")
\pu
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
% | | | | |_| | __/ | |_) | (_| | (_| | __/
% |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
% |_| |___/
%
% «title» (to ".title")
% (c2m232vsp 1 "title")
% (c2m232vsa "title")
\thispagestyle{empty}
\begin{center}
\vspace*{1.2cm}
{\bf \Large Cálculo 2 - 2023.2}
\bsk
Prova suplementar (VS)
\bsk
Eduardo Ochs - RCN/PURO/UFF
\url{http://anggtwu.net/2023.2-C2.html}
\end{center}
\newpage
% «links» (to ".links")
% (c2m232vsp 2 "links")
% (c2m232vsa "links")
%{\bf Links}
%
%\scalebox{0.6}{\def\colwidth{9cm}\firstcol{
%}\anothercol{
%}}
\newpage
\scalebox{0.49}{\def\colwidth{11cm}\firstcol{
%\vspace*{-0.4cm}
{\bf Questão 1}
\T(Total: 4.0 pts)
Resolva esta integral por substituição trigonométrica
%
$$\intx{x^3\sqrt{1-25x^2}}
$$
e teste o seu resultado.
\bsk
\bsk
{\bf Questão 2}
\T(Total: 4.0 pts)
Resolva esta integral
%
$$\intx{\frac{x^3}{(x-1)(x+2)}}
$$
e teste o seu resultado.
\bsk
\bsk
{\bf Questão 3}
\T(Total: 4.0 pts)
Seja:
%
$$f(x) \;=\; \sum_{n=1}^{∞} \frac{(2x-3)^n}{n}
$$
a) \B (0.1 pts) Descubra se $f(\frac32)$ converge.
b) \B (0.4 pts) Descubra se $f(2)$ converge.
c) \B (3.5 pts) Descubra em que intervalo $f(x)$ converge.
\vspace*{-5cm}
}\anothercol{
{}
% (find-books "__analysis/__analysis.el" "stewart-pt" "662" "O Teste da Razão")
% (find-books "__analysis/__analysis.el" "stewart-pt" "664" "O Teste da Raiz")
Dicas pra questão 3:
No teste da razão a gente calcula isto aqui,
%
$$\lim_{n→∞} \left|\frac{a_{n+1}}{a_n}\right|$$
e no teste da raiz a gente calcula isto:
%
$$\lim_{n→∞} \sqrt[n]{|a_n|}$$
Na questão 3 você vai ter que imaginar que você está escrevendo pra um
leitor que sabe bem pouco sobre sequências e séries -- como você era
até poucos dias atrás -- e você vai ter que explicar todos os passos
mais difíceis. Tente administrar o seu tempo pra dar explicações mais
detalhas nos passos mais difíceis e explicações menos detalhadas nos
passos menos difíceis!!!
\bsk
\bsk
Dica gerais: lembre dos critérios de correção que eu estou usando no
curso! Em todas as questões desta prova eu vou corrigir as respostas
de vocês como se eu fosse o ``colega menos seu amigo e sem paciência
pra adivinhar nada'' da Dica 7 e do slide sobre contextos... por
exemplo, se você escrever só ``$a=42$'' eu vou interpretar isso como
``aqui essa pessoa tá dizendo que aqui \standout{é óbvio} que `$a=42$'
é verdade {\sl pra qualquer valor de $a$}''... ou seja, a parte em
português das questões de vocês vai ser muito importante!
% (find-es "maxima" "2022-2-C2-P2")
}}
\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 "~/2023.2-C2/")
# (find-fline "~/LATEX/2023-2-C2/")
# (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 ~/2023.2-C2/
cp -fv $1.pdf ~/LATEX/2023-2-C2/
cat <<%%%
% (find-latexscan-links "C2" "$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=2023-2-C2-VS veryclean
make -f 2019.mk STEM=2023-2-C2-VS pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2vs"
% ee-tla: "c2m232vs"
% End: