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\begin{document}
	
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\begin{center}SANS CALCULATRICE\end{center}\vskip 0cm
	
\hskip-1cm \boxit{4pt}{Minitest N°05}\rightarrowfill\quad\boxit{3pt}{Corrigé}\bigskip

Compléter avec les transformées\bigskip

Si $f(t) = te^{-t}U(t)$ alors $F(p) = {\red \dfrac{1}{(p+1)^2}}$\vskip 1cm

Si $f(t) = tU(t)-(t-3)U(t-3)$ alors $F(p) = {\red \dfrac1{p^2}(1-e^{-3p})}$\vskip 1cm

Si $f(t) = t\times e^{-3t}\times U(t)$ alors $F(p) = {\red \dfrac{1}{(p+3)^2}}$\vskip 1cm

Si $f(t) = \sin(2t)\times e^{-3t}\times U(t)$ alors $F(p) = {\red \dfrac{2}{(p+3)^2+4}}$\vskip 1cm

Si $f(t) = 2\cos(5t)\times e^{-2t}\times U(t)$ alors $F(p) = {\red \dfrac{2p+4}{(p+2)^2+25}}$\vskip 1cm



Compléter avec les originaux\bigskip

Si $F(p)=\dfrac{1}{p^2+9}$ alors $f(t) = {\red \dfrac13\times \sin(3t)\;U(t)}$\vskip 1cm

Si $F(p)=\dfrac{1}{(p+9)^2}$ alors $f(t) = {\red t\times e^{-9t}\; U(t)}$\vskip 1cm

Si $F(p)=\dfrac{1-e^{-p}}{p^2}$ alors $f(t) = {\red t\;U(t)-(t-1)\;U(t-1)}$\vskip 1cm

Si $F(p)=\dfrac{1}{p^2}(1-2e^{-p}+e^{-2p})$ alors $f(t) = {\red t\;U(t)-2(t-1)t\;U(t-1)+(t-2)\;U(t-2)}$\vskip 1cm

Si $F(p)=\dfrac{p+1}{(p+2)^2+25}$ alors $f(t) = {\red \cos(5t)e^{-2t}\;U(t)-\dfrac15\times\sin(3t)e^{-2t}\;U(t)}$\vskip 1cm


\newpage

\thispagestyle{empty}	

\begin{center}SANS CALCULATRICE\end{center}\vskip 0cm

\hskip-1cm \boxit{4pt}{Minitest N°05}\rightarrowfill\quad\boxit{3pt}{Corrigé}\bigskip

Compléter avec les transformées\bigskip

Si $f(t) = te^{-2t}U(t)$ alors $F(p) = {\red \dfrac{1}{(p+2)^2}}$\vskip 1cm

Si $f(t) = tU(t)-(t-4)U(t-4)$ alors $F(p) = {\red \dfrac{1}{p^2}\times (1-e^{-4p})}$\vskip 1cm

Si $f(t) = t\times e^{-2t}\times U(t)$ alors $F(p) = {\red \dfrac{1}{(p+2)^2}}$\vskip 1cm

Si $f(t) = \sin(3t)\times e^{-2t}\times U(t)$ alors $F(p) = {\red \dfrac{3}{(p+2)^2+9}}$\vskip 1cm

Si $f(t) = 5\cos(2t)\times e^{-2t}\times U(t)$ alors $F(p) = {\red \dfrac{5p+10}{(p+2)^2+4}}$\vskip 1cm



Compléter avec les originaux\bigskip

Si $F(p)=\dfrac{2p}{p^2+16}$ alors $f(t) = {\red 2\cos(4t)\;U(t)}$\vskip 1cm

Si $F(p)=\dfrac{1}{(p+16)^2}$ alors $f(t) = {\red t\times e^{-16t}\;U(t)}$\vskip 1cm

Si $F(p)=\dfrac{1-e^{-2p}}{p^2}$ alors $f(t) = {\red t\;U(t)-(t-2)\;U(t-2)}$\vskip 1cm

Si $F(p)=\dfrac{1}{p}(1-2e^{-p}+e^{-2p})$ alors $f(t) = {\red U(t)-2U(t-1)+U(t-2)}$\vskip 1cm

Si $F(p)=\dfrac{p+2}{(p+1)^2+25}$ alors $f(t) = {\red \cos(5t)\times e^{-t}\;U(t)+\dfrac15\sin(5t)\times e^{-t}\; U(t)}$\vskip 1cm



\end{document} 