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%               file:///tmp/2016-2-C2-P1.pdf
%           file:///tmp/pen/2016-2-C2-P1.pdf
% http://angg.twu.net/LATEX/2016-2-C2-P1.pdf
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%   ____      _                    _ _           
%  / ___|__ _| |__   ___  ___ __ _| | |__   ___  
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% | |__| (_| | |_) |  __/ (_| (_| | | | | | (_) |
%  \____\__,_|_.__/ \___|\___\__,_|_|_| |_|\___/ 
%                                                

{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 2
\par PURO-UFF - 2016.2
\par P1 - 16/nov/2016 - Eduardo Ochs
% \par Versão: 14/mar/2016
\par Links importantes:
\par \url{http://angg.twu.net/2016.2-C2.html} (página do curso)
\par \url{http://angg.twu.net/2016.2-C2/2016.2-C2.pdf} (quadros)
% \par \url{http://angg.twu.net/LATEX/2016-1-C2-material.pdf}
\par {\tt eduardoochs@gmail.com} (meu e-mail)
}

\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

1) \T(Total: 1.0 pts) Lembre do truque para derivar o arcsen:

$c = \cos θ, s = \sen θ, θ = \arcsen s$,

$\frac{ds}{dθ} = c = \sqrt{1-s^2},
 \frac{dθ}{ds} = \frac1c = \frac{1}{\sqrt{1-s^2}},
 \frac{d}{ds} \arcsen s = \frac{1}{\sqrt{1-s^2}}.
$,

Use algo parecido para calcular $\frac{d}{dx} \arctan x$.

\bsk

2) \T(Total: 1.0 pts) Explique por que $$\Intx{-1}{1}{x^{-4}} ≠ \Difx{-1}{1} {\frac{x^{-3}}{-3}}.$$

3) \T(Total: 2.0 pts) Calcule $$\Intx{-1}{2}{\frac{1}{1+|x|}}.$$

4) \T(Total: 2.0 pts) Calcule $$\intx {\frac{x^2}{x^2 - 4x - 5}}.$$

5) \T(Total: 3.0 pts) Calcule por substituição trigonométrica:

a) \B(1.0 pts) $$\intx {\frac{1}{1+x^2}}$$

b) \B(2.0 pts) $$\intx {\frac{x^2}{\sqrt{1-4x^2}}}$$

% 6) \T(Total: 1.0 pts) Calcule $$\intx {(2x+3) \sen (4x+5)}.$$
6) \T(Total: 1.0 pts) Calcule $$\intx {x \sen (4x+5)}.$$



% (find-books "__analysis/__analysis.el" "stewart")
% (find-stewart7page (+ 32 518) "7.5. Strategy for Integration")
% (find-stewart7page (+ 32 523) "7.5. Exercises")




\end{document}

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