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% (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!!!")) % (defun D () (interactive) (find-pdf-page "~/LATEX/2023-1-C2-volumes.pdf")) % (defun d () (interactive) (find-pdftools-page "~/LATEX/2023-1-C2-volumes.pdf")) % (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")) % (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g)) % (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") % «.defs-T-and-B» (to "defs-T-and-B") % «.defs-caepro» (to "defs-caepro") % «.defs-pict2e» (to "defs-pict2e") % «.title» (to "title") % «.links» (to "links") % % «.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} \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") % % (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/2023-1-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") \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)}} % «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 = "%" \def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}} \def\pictaxesstyle{\linethickness{0.5pt}} \def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}} \celllower=2.5pt \pu % _____ _ _ _ % |_ _(_) |_| | ___ _ __ __ _ __ _ ___ % | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \ % | | | | |_| | __/ | |_) | (_| | (_| | __/ % |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___| % |_| |___/ % % «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} % Local Variables: % coding: utf-8-unix % ee-tla: "c2vo" % ee-tla: "c2m231volumes" % End: