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% (find-LATEX "2022-2-C2-mathologermovel.tex")
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% (defun C () (interactive) (find-LATEXsh "lualatex 2022-2-C2-mathologermovel.tex" "Success!!!"))
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% (code-eec-LATEX "2022-2-C2-mathologermovel")
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% (find-sh0 "cp -v ~/LATEX/2022-2-C2-mathologermovel.pdf /tmp/")
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% file:///home/edrx/LATEX/2022-2-C2-mathologermovel.pdf
% file:///tmp/2022-2-C2-mathologermovel.pdf
% file:///tmp/pen/2022-2-C2-mathologermovel.pdf
% http://angg.twu.net/LATEX/2022-2-C2-mathologermovel.pdf
% (find-LATEX "2019.mk")
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% (find-CN-aula-links "2022-2-C2-mathologermovel" "2" "c2m222mm" "c2mm")
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% <videos>
% Video (not yet):
% (find-ssr-links "c2m222mm" "2022-2-C2-mathologermovel")
% (code-eevvideo "c2m222mm" "2022-2-C2-mathologermovel")
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\usepackage{amsfonts}
\usepackage{amssymb}
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%
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%
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%
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% (find-es "tex" "geometry")
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top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
]{geometry}
%
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%L dofile "Piecewise1.lua" -- (find-LATEX "Piecewise1.lua")
%L dofile "QVis1.lua" -- (find-LATEX "QVis1.lua")
%L dofile "Pict3D1.lua" -- (find-LATEX "Pict3D1.lua")
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% (find-LATEX "edrx21.sty")
\def\u#1{\par{\footnotesize \url{#1}}}
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\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
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%
% «title» (to ".title")
% (c2m222mmp 1 "title")
% (c2m222mma "title")
\thispagestyle{empty}
\begin{center}
\vspace*{1.2cm}
{\bf \Large Cálculo 2 - 2022.2}
\bsk
Aula 2: derivação e integração com o Mathologermóvel
\bsk
Eduardo Ochs - RCN/PURO/UFF
\url{http://angg.twu.net/2022.2-C2.html}
\end{center}
\newpage
% (c2m221p1p 7 "escadas-defs")
% (c2m221p1a "escadas-defs")
%L hx = function (x, y) return format(" (%s,%s)c--(%s,%s)o", x-1,y, x,y) end
%L hxs = function (ys)
%L local str = ""
%L for x,y in ipairs(ys) do str = str .. hx(x, y) end
%L return str
%L end
%L mtintegralspec = function (specf, xmax, y0)
%L local pws = PwSpec.from(specf)
%L local f = pws:fun()
%L local ys = {[0] = y0}
%L for x=1,xmax do
%L PP("FOO", x, f(x-0.5), ys)
%L ys[x] = ys[x - 1] + f(x - 0.5)
%L end
%L local strx = function (x) return tostring(v(x, ys[x])) end
%L local specF = mapconcat(strx, seq(0, xmax), "--")
%L return specF
%L end
%L
%L ysf = {1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 1, 0}
%L specf = hxs(ysf)
%L ysg = {0, 1, 2, 3, -2, -1, 0, -1, -2, 3, 2, 1, 0}
%L specg = hxs(ysg)
%L specF = mtintegralspec(specf, #ysf, 0)
%L specG = mtintegralspec(specf, #ysf, -3)
%L specI = mtintegralspec(specg, #ysg, 0)
%L pwsf = PwSpec.from(specf)
%L pwsg = PwSpec.from(specg)
%L pwsF = PwSpec.from(specF)
%L pwsG = PwSpec.from(specG)
%L pwsI = PwSpec.from(specI)
%L pf = pwsf:topict():setbounds(v(0,-2), v(#ysf,2)):pgat("pgatc")
%L pg = pwsg:topict():setbounds(v(0,-2), v(#ysg,3)):pgat("pgatc")
%L pF = pwsF:topict():setbounds(v(0,-0), v(#ysf,4)):pgat("pgatc")
%L pG = pwsG:topict():setbounds(v(0,-3), v(#ysf,1)):pgat("pgatc")
%L pI = pwsI:topict():setbounds(v(0,0), v(#ysg,6)):pgat("pgatc")
%L pf:sa("Fig f"):output()
%L pg:sa("Fig g"):output()
%L pF:sa("Fig F"):output()
%L pG:sa("Fig G"):output()
%L pI:sa("Fig I"):output()
%L
%L PictList{}:setbounds(v(0,-4),v(13,4)):pgat("pgatc"):sa("respgrid"):output()
%L
%L mtintegralspec2 = function (x0, y0, Dys, dot0, dot1)
%L local mkxy = function (x,y) return format("(%d,%d)", x, y) end
%L local xys = { mkxy(x0,y0) .. (dot0 or "") }
%L local x,y = x0,y0
%L for i,Dy in ipairs(Dys) do
%L x = x + 1
%L y = y + Dy
%L table.insert(xys, mkxy(x,y))
%L end
%L xys[#xys] = xys[#xys] .. (dot1 or "")
%L return table.concat(xys, "--")
%L end
%L
%L -- = mtintegralspec2(10, 20, {1, 2, -3, -3}, "a", "b")
%L ysf = {1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 1, 0}
%L ysf_ = {1, 2, 1, 0, -1, -2, -1}
%L ysg = {0, 1, 2, 3, -2, -1, 0, -1, -2, 3, 2, 1, 0}
%L ysg_ = {-1, -2, 3, 2, 1}
%L specH = mtintegralspec2(0, -4, ysf_, "", "o\n") ..
%L mtintegralspec2(7, 1, ysg_, "o", "")
%L specM = mtintegralspec2(0, -4, ysf_, "", "o\n") ..
%L mtintegralspec2(7, 2, ysg_, "o", "")
%L -- = specH
%L -- = specM
%L pwsH = PwSpec.from(specH)
%L pwsM = PwSpec.from(specM)
%L pH = pwsH:topict():setbounds(v(0,-4), v(12,4)):pgat("pgatc")
%L pM = pwsM:topict():setbounds(v(0,-4), v(12,5)):pgat("pgatc")
%L pH:sa("Fig H"):output()
%L pM:sa("Fig M"):output()
\pu
\newpage
Este PDF vai ser refeito depois!
Por enquanto:
\msk
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1) assista a parte do vídeo do Mathologer sobre como usar um carro pra
derivar e integrar --- essa parte começa no 3:12. Link:
\ssk
{\footnotesize
% http://angg.twu.net/mathologer-calculus-easy.html#03:08
\url{http://angg.twu.net/mathologer-calculus-easy.html\#03:08}
}
\ssk
Repare que ele sempre põe o gráfico da distância em cima e o gráfico
da velocidade embaixo; quando ele fala de derivação ele começa com uma
função ``original'', $f$, em cima e ele desenha, ou escreve, a
derivada dela, $f'$, embaixo.
\msk
% «item-2» (to ".item-2")
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% (c2m222mma "item-2")
2) O Leithold define a inclinação de uma reta na página 17 (no
capítulo 1) e na página 150 (no capítulo 3) ele discute a derivada da
função $|x|$. Leia estes trechos.
% (find-books "__analysis/__analysis.el" "leithold")
% (find-leitholdptpage (+ 17 17) "inclinação")
% (find-leitholdptpage (+ 17 150) "|x|")
\newpage
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{\bf Item 3}
\ssk
Considere que a função $G(x)$ do exercício 4 daqui
\ssk
{\footnotesize
% (c2m221tfc1p 10 "exercicio-4")
% (c2m221tfc1a "exercicio-4")
% http://angg.twu.net/LATEX/2022-1-C2-TFC1.pdf#page=10
\url{http://angg.twu.net/LATEX/2022-1-C2-TFC1.pdf#page=10}
}
\ssk
é um gráfico da posição do mathologermóvel no tempo. Copie esse
gráfico num papel e abaixo dele faça o gráfico correspondente da
velocidade do mathologermóvel no tempo.
\msk
Tem uma espécie de gabarito desse exercício aqui:
\ssk
{\footnotesize
% (c2m212mt3p 4 "gabarito")
% (c2m212mt3a "gabarito")
% http://angg.twu.net/LATEX/2021-2-C2-MT3.pdf#page=4
\url{http://angg.twu.net/LATEX/2021-2-C2-MT3.pdf#page=4}
}
\newpage
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{\bf Item 4}
\scalebox{0.9}{\def\colwidth{12.5cm}\firstcol{
Na P1 do semestre passado --- link:
\ssk
{\footnotesize
% (c2m221p1p 7 "escadas")
% (c2m221p1a "escadas")
% http://angg.twu.net/LATEX/2022-1-C2-P1.pdf#page=7
\url{http://angg.twu.net/LATEX/2022-1-C2-P1.pdf\#page=7}
}
\ssk
eu defini as funções $f(x)$ e $g(x)$ desta forma:
\unitlength=9pt
\bsk
$f(x) = \ga{Fig f}
\qquad
g(x) = \ga{Fig g}
$
% $
% \ga{Fig F}
% \ga{Fig G}
% \ga{Fig I}
% \ga{Fig M}
% $
\msk
Interprete esses gráficos da $f(x)$ e da $g(x)$ como dois gráficos
diferentes da velocidade do mathologermóvel no tempo. Copie elas num
papel e acima de cada um deles faça o gráfico correspondente da
posição do mathologermóvel no tempo.
\msk
Tem uma espécie de gabarito disso aqui:
\ssk
{\footnotesize
% (c2m221p1p 8 "escadas-gab")
% (c2m221p1a "escadas-gab")
% http://angg.twu.net/LATEX/2022-1-C2-P1.pdf#page=8
\url{http://angg.twu.net/LATEX/2022-1-C2-P1.pdf\#page=8}
}
}\anothercol{
}}
\newpage
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% (c2m222mmp 5 "item-5")
% (c2m222mma "item-5")
{\bf Item 5}
\ssk
Faça o exercício 1 daqui:
\ssk
{\footnotesize
% (c2m221tfc1p 7 "exercicio-1")
% (c2m221tfc1a "exercicio-1")
% http://angg.twu.net/LATEX/2022-1-C2-TFC1.pdf#page=7
\url{http://angg.twu.net/LATEX/2022-1-C2-TFC1.pdf\#page=7}
}
\ssk
Pra fazer ele você vai ter que interpretar o gráfico da $f(x)$ como um
gráfico de velocidade, e você vai que interpretar expressões como esta aqui
%
$$\Intx{1.5}{2}{f(x)}$$
%
como o quanto a posição do mathologermóvel varia entre o ``instante
inicial'', que é $t=1.5$, e o ``instante final'', que é $t=2$.
% (find-TH "mathologer-calculus-easy" "legendas")
% (find-TH "mathologer-calculus-easy" "legendas" "03:08")
%\printbibliography
\GenericWarning{Success:}{Success!!!} % Used by `M-x cv'
\end{document}
% __ __ _
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% | |\/| |/ _` | |/ / _ \
% | | | | (_| | < __/
% |_| |_|\__,_|_|\_\___|
%
% <make>
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2022-2-C2-mathologermovel veryclean
make -f 2019.mk STEM=2022-2-C2-mathologermovel pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2mm"
% ee-tla: "c2m222mm"
% End: