% (find-LATEX "2019-2-C2-VS.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2019-2-C2-VS.tex" :end))
% (defun d () (interactive) (find-pdf-page "~/LATEX/2019-2-C2-VS.pdf"))
% (defun e () (interactive) (find-LATEX "2019-2-C2-VS.tex"))
% (defun u () (interactive) (find-latex-upload-links "2019-2-C2-VS"))
% (find-pdf-page   "~/LATEX/2019-2-C2-VS.pdf")
% (find-sh0 "cp -v  ~/LATEX/2019-2-C2-VS.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2019-2-C2-VS.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2019-2-C2-VS.pdf
%               file:///tmp/2019-2-C2-VS.pdf
%           file:///tmp/pen/2019-2-C2-VS.pdf
% http://angg.twu.net/LATEX/2019-2-C2-VS.pdf
% (find-LATEX "2019.mk")

\documentclass[oneside]{book}
\usepackage[colorlinks,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{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")
%
% (find-es "tex" "geometry")
\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


{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 2
\par PURO-UFF - 2019.2 - Eduardo Ochs
\par VS - 19/dez/2019
\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


% (find-TH "2019.1-C2" "provas-antigas")
% (find-pdf-page "~/LATEX/2017-1-C2-P1.pdf")
% (find-pdf-page "~/LATEX/2017-1-C2-P2.pdf")
% (find-pdf-page "~/LATEX/2017-1-C2-VS.pdf")
% (find-pdf-page "~/LATEX/2017-2-C2-P1.pdf")
% (find-pdf-page "~/LATEX/2017-2-C2-P2.pdf")
% (find-pdf-page "~/LATEX/2017-2-C2-VS.pdf")
% (find-pdf-page "~/LATEX/2018-2-C2-P1.pdf")
% (find-pdf-page "~/LATEX/2018-2-C2-P1fake.pdf")
% (find-pdf-page "~/LATEX/2018-2-C2-P2.pdf")
% (find-pdf-page "~/LATEX/2018-2-C2-VS.pdf")
% (find-pdf-page "~/LATEX/2019-1-C2-P1.pdf")
% (find-pdf-page "~/LATEX/2019-1-C2-P2.pdf")
% (find-pdf-page "~/LATEX/2019-1-C2-VR.pdf")
% (find-pdf-page "~/LATEX/2019-1-C2-VS.pdf")


1) \T(Total: 2.0 pts) Seja $(*)$ esta EDO: $y^3\,dx = e^{2x}\,dx$.

a) \B(1.0 pts) Encontre a solução geral de $(*)$.

b) \B(1.0 pts) Teste a sua resposta.

\bsk
\bsk
\bsk

2) \T(Total: 3.0 pts) Calcule $$\intx {\frac{x^2}{x^2 + 3x - 10}}$$
%
e teste a sua resposta.



\bsk
\bsk
\bsk


3) \T(Total: 5.0 pts) Calcule $$\intx {x^3 \sqrt{1-x^2}^3}$$
%
e teste a sua resposta.

% Dica: $\sen \arccos c = \sqrt{1-c^2}$.


\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk
\bsk

Algumas definições, fórmulas e substituições:

$\begin{array}[t]{l}
 c = \cos θ \\
 s = \sen θ \\
 t = \tan θ \\
 z = \sec θ \\
 E = e^{iθ} \\
 \end{array}
 %
 \begin{array}[t]{l}
 c^2+s^2=1 \\
 z^2=t^2+1 \\
 \sqrt{1-s^2} = c \\
 \sqrt{t^2+1} = z \\
 \sqrt{z^2-1} = t \\
 \end{array}
 %
 \begin{array}[t]{l}
 \frac{ds}{dθ} = c \\
 \frac{dc}{dθ} = -s \\
 \frac{dt}{dθ} = z^2 \\
 \frac{dz}{dθ} = zt \\
 \end{array}
 %
 \begin{array}[t]{l}
 E = c+is \\
 c = \frac{E+E¹}{2} \\
 s = \frac{E-E¹}{2i} \\
 e^{ikθ} + e^{-ikθ} = 2 \cos kθ \\
 e^{ikθ} - e^{-ikθ} = 2i \sen kθ \\
 \end{array}
$







% Baseada em:
% (find-angg "LATEX/2018-2-C2-P1fake.tex")



\end{document}

% Local Variables:
% coding: utf-8-unix
% ee-tla: "NONE"
% End: