frct_001.tex

%% format               (plain.tex + fichiers de macro) OU (jpv.tex)
%% fichiers de macro    basejpv.tex + columns.tex
%% sujet                primitive, polynome, rationnelle
%% date                 27-11-97
%% auteur               jp vignault 
 
\exo{Recherche de primitives}
 
Déterminer une primitive pour chacune des fonctions suivantes~:
 
\columns 3
 
\def \myalph{%
   \alph \tvi height 10pt depth 10pt}
 
\raggedbottom
 
\myalph\ 
$\displaystyle{
   f (x) = x^4 + 5x^3 + 3x^2 - 2
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {1 \over x^2} + {1 \over \sqrt x}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = (x+1)^3
}$
 
\myalph\ 
$\displaystyle{
   f (x) = (2x + 3)^4
}$
 
\myalph\ 
$\displaystyle{
   f (x) = x (x^2 + 1)^3
}$
 
\myalph\ 
$\displaystyle{
   f (x) = (x^2 + {1\over3}) (x^3 + x)^4
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {2x + 1 \over (x^2 + x - 2)^2}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {4x^2 \over (x^3 + 8)^3}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = x - {1 \over (3x + 1)^2}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {3 \over \sqrt x} + 1
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {1 \over \sqrt{x-1}}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {2 \over 1-x}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {2x \over x^2 - 1}
}$
 
\myalph\ 
$\displaystyle{
   f (x) = {2x + 5 \over x^2 + 5x - 6}
}$
 
\endcolumns
 
\finexo