% (find-angg "LATEX/2019-1-C2-VS.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2019-1-C2-VS.tex"))
% (defun d () (interactive) (find-pdf-page "~/LATEX/2019-1-C2-VS.pdf"))
% (defun b () (interactive) (find-zsh "bibtex 2019-1-C2-VS; makeindex 2019-1-C2-VS"))
% (defun e () (interactive) (find-LATEX "2019-1-C2-VS.tex"))
% (defun u () (interactive) (find-latex-upload-links "2019-1-C2-VS"))
% (find-xpdfpage "~/LATEX/2019-1-C2-VS.pdf")
% (find-sh0 "cp -v  ~/LATEX/2019-1-C2-VS.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2019-1-C2-VS.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2019-1-C2-VS.pdf
%               file:///tmp/2019-1-C2-VS.pdf
%           file:///tmp/pen/2019-1-C2-VS.pdf
% http://angg.twu.net/LATEX/2019-1-C2-VS.pdf
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
%\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{edrx15}               % (find-LATEX "edrx15.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
\begin{document}

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

% %L dofile "edrxtikz.lua"  -- (find-LATEX "edrxtikz.lua")
% %L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
% \pu

\def\EDOA{\ensuremath{({*})}}
\def\EDOB{\ensuremath{({*}{*})}}
\def\EDOC{\ensuremath{({*}{*}{*})}}

{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 2
\par PURO-UFF - 2019.1
\par VS - 12/julho/2019 - Eduardo Ochs
\par Respostas sem justificativas não serão aceitas.
\par Proibido usar quaisquer aparelhos eletrônicos.

}

\bsk
\bsk

\setlength{\parindent}{0em}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\B       (#1 pts){{\bf(#1 pts)}}
% Usage:
% 1) \T(Total: 2.34 pts) Foo
% a) \B(0.45 pts) Bar


% \bsk
% \bsk

% (c2q)
% (find-TH "2019.1-C2" "provas-antigas")


1) \T(Total: 1.0 pts) Calcule $$\Intx{0}{4} {|x^2-1|}.$$

\bsk

2) \T(Total: 2.0 pts) Calcule $$\intx {x^3 \sqrt{1-x^2}}.$$

\bsk

3) \T(Total: 2.0 pts) Calcule $$\intx {(x+2)\sqrt{x+3}}.$$

\bsk

4) \T(Total: 1.0 pts) Teste a sua solução da questão 2.

\bsk
\bsk

5) \T(Total: 1.0 pts) Qual é a solução geral da EDO $f'(x) =
(x+2)\sqrt{x+3}$?

Teste a sua resposta.

\bsk
\bsk

6) \T(Total: 3.0 pts) Seja \EDOA{} esta EDO: $f'(x) = \frac{x}{x-2}e^{3f(x)}$.

a) \B(1.0 pts) Encontre a solução geral de \EDOA{}.

b) \B(1.0 pts) Teste a sua solução.

c) \B(1.0 pts) Encontre a solução que passa pelo ponto $(4,5)$.









\end{document}

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