diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex')
56 files changed, 8791 insertions, 7692 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp index d0549eeb9cf..0f84f2a3c09 100644 --- a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp +++ b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp @@ -4,12 +4,12 @@ newLigneVariables(btex $ {x}$ etex); val(btex $-\frac{\sqrt{5}}{5}$ etex); val(btex $\frac{\sqrt{5}}{5}$ etex); val(btex $50$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex); moins; valBarre(btex 0 etex);plus;barre; plus;barre;plus; -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex); plus;barre; plus; valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0 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+510.18356 0 lineto stroke newpath 0 -86.73239 moveto -356.62201 -86.73239 lineto stroke +510.18356 -86.73239 lineto stroke 0.5 0 dtransform exch truncate exch idtransform pop setlinewidth newpath 0 0 moveto 0 -86.73239 lineto stroke -newpath 356.62201 0 moveto -356.62201 -86.73239 lineto stroke +newpath 510.18356 0 moveto +510.18356 -86.73239 lineto stroke showpage %%EOF diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp index 5797a66cf34..fa53635eeb2 100644 --- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp +++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp @@ -8,7 +8,39 @@ verbatimtex \renewcommand\cdot{ } % idem pour les cdot \begin{document} etex -beginTableau(0) newLigneVariables(btex $x$ etex);val(btex $-5$ etex); +beginTableau(0) newLigneVariables(btex $t$ etex);val(btex $-10$ etex); +val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex + $+\infty $ + etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ + etex,1);limGauche(btex + $-\infty$ + etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); + +endTableau; + +beginTableau(1) newLigneVariables(btex $t$ etex);val(btex $-10$ etex); +val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex + $+\infty $ + etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ + etex,1);limGauche(btex + $-\infty$ + etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); + +endTableau; + +beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-5$ etex); val(btex $0$ etex); val(btex $7$ etex); @@ -17,7 +49,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va valPos(btex $49$ etex,1); endTableau; -beginTableau(1) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(3) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $0$ etex); val(btex $+\infty $ etex); @@ -29,14 +61,14 @@ endTableau; -beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $0$ etex); val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus; endTableau; -beginTableau(3) newLigneVariables(btex $t$ etex);val(btex $-10$ etex); +beginTableau(5) newLigneVariables(btex $t$ etex);val(btex $-10$ etex); val(btex $-1$ etex); val(btex $0$ etex); val(btex $1$ etex); @@ -52,7 +84,20 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va endTableau; -beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(6) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex); +val(btex $\frac{(-\pi )}{2}$ etex); +val(btex $\frac{\pi }{2}$ etex); +val(btex $\pi $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); moins; valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{1}{2}$ etex,1); valPos(btex $\frac{-1}{2}$ + etex,0); +valPos(btex $\frac{3}{2}$ + etex,1);valPos(btex $\frac{1}{2}$ etex,0); + +endTableau; + +beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -61,7 +106,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $0$ etex,0);debutNonDef;finNonDef;limDroite(btex $0$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $\frac{5}{2}$ etex); @@ -73,7 +118,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(6) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); +beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ $ etex);plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;valBarre(btex $ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); @@ -83,7 +128,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte valPos(btex $1$ etex,0); endTableau; -beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex); +beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus; nonDefBarre;plus;valBarre(btex $ $ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;nonDefBarre;moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); @@ -95,7 +140,7 @@ valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefB limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); endTableau; -beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $ 0.212584$ etex); val(btex $ 0.584635$ etex); val(btex $+\infty $ etex); @@ -107,27 +152,27 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(10) newLigneVariables(btex $t$ etex);val(btex $0$ etex); -val(btex $\frac{1}{8} \times \pi $ etex); -val(btex $\frac{1}{3} \times \pi $ etex); -val(btex $\frac{3}{8} \times \pi $ etex); +beginTableau(13) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{8}$ etex); +val(btex $\frac{\pi }{3}$ etex); +val(btex $\frac{3 \pi }{8}$ etex); val(btex $\frac{\pi }{2}$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex); -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3\pi }{8}\right)$ +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3 \pi }{8}\right)$ etex,0.5);valPos(btex $-1$ etex,0); valPos(btex $-\left(\cos\left(\frac{\pi }{8}\right)\right)$ etex,0.5);valPos(btex $0$ etex,1); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex); newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$ - etex,1);valPos(btex $-\left(\frac{1}{2} \times \sqrt{3}\right)$ + etex,1);valPos(btex $\frac{(-\left(\sqrt{3}\right))}{2}$ etex,0.5);valPos(btex $-1$ etex,0); valPos(btex $0$ etex,1); endTableau; -beginTableau(11) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +beginTableau(14) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); val(btex $-4$ etex); val(btex $-1$ etex); val(btex $0$ etex); @@ -155,7 +200,7 @@ valPos(btex $\frac{16}{3}$ endTableau; - beginTableau(12) + beginTableau(15) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex); val(btex $5$etex); @@ -165,7 +210,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;val newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -x+5}$ etex);plus;barre;plus;valBarre(btex 0 etex);moins; newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle {(-2x+3)(-x+5)}}$ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; endTableau; - beginTableau(13) + beginTableau(16) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex); val(btex $-1$ etex); @@ -173,7 +218,7 @@ val(btex $1$ etex); val(btex $\sqrt{2}$ etex); val(btex $\frac{3}{2}$ etex); val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex); plus;barre; plus;barre; plus;barre; @@ -214,7 +259,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex); endTableau; - beginTableau(14) + beginTableau(17) newLigneVariables(btex $ {x}$ etex); val(btex $-15$ etex);val(btex $-10$ etex); val(btex $10$ etex); @@ -231,7 +276,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex); endTableau; -beginTableau(15) +beginTableau(18) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty $ etex);val(btex $-4$ etex); val(btex $\frac{5}{4}$ etex); @@ -239,14 +284,14 @@ val(btex $\frac{3}{2}$ etex); val(btex $2$ etex); val(btex $4$ etex); val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex); plus;barre; plus;barre; plus; valBarre(btex 0 etex);moins;barre; moins;barre;moins; -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4x\right)+5}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex); plus;barre; plus; valBarre(btex 0 etex);moins;barre; @@ -266,32 +311,16 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex); moins; valBarre(btex 0 etex);plus;barre;plus; newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex); - moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;nonDefBarre;plus; -endTableau; - - -beginTableau(16) -newLigneVariables(btex $ {x}$ etex); - val(btex $-\infty $ etex);val(btex $-10$ etex); -val(btex $10$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex); - moins;barre;moins; - - valBarre(btex 0 etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex); - moins;valBarre(btex 0 etex);plus; -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex); - plus;nonDefBarre; moins; - valBarre(btex 0 etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex);plus; endTableau; -beginTableau(17) +beginTableau(19) newLigneVariables(btex $\displaystyle {x}$ etex); val(btex $-10$ etex);val(btex $-5$ etex); val(btex $10$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+5)}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+5)}$ etex); plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex); endTableau; @@ -301,12 +330,12 @@ newLigneVariables(btex $ {x}$ etex); val(btex $-\frac{\sqrt{5}}{5}$ etex); val(btex $\frac{\sqrt{5}}{5}$ etex); val(btex $50$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex); moins; valBarre(btex 0 etex);plus;barre; plus;barre;plus; -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex); plus;barre; plus; valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; @@ -316,7 +345,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex); endTableau; - beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); + beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;moins;valBarre(btex$ $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPos(btex $-1$ @@ -324,7 +353,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +beginTableau(21) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$ @@ -332,13 +361,13 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$ $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $1$ etex); +beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $1$ etex); val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins; @@ -346,7 +375,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va endTableau; -beginTableau(23) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex); +beginTableau(25) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins;valBarre(btex$ $ etex);moins; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ @@ -354,9 +383,9 @@ valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0); endTableau; -beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $\pi $ etex); -val(btex $2\pi $ etex); +val(btex $2 \pi $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $1$ etex,1); valPos(btex $-1$ @@ -364,22 +393,22 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va valPos(btex $1$ etex,1); endTableau; -beginTableau(25) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex); +beginTableau(27) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle h'(t)}$ etex); plus;valBarre(btex$ $ etex);plus; nonDefBarre;plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle h}$ etex); valPos(btex $0$ etex,0);valPos(btex $ 7 $ etex,0.5); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1); endTableau; -beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex); +beginTableau(28) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); -valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3}{4} \times \sqrt{3}$ +valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$ etex,1);valPos(btex $ 1 $ etex,0.5);valPos(btex $0$ etex,0); endTableau; -beginTableau(27) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); +beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); val(btex $0$ etex); val(btex $+\infty $ etex); @@ -389,15 +418,15 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no endTableau; - beginTableau(28) + beginTableau(30) newLigneVariables(btex $ {x}$ etex); - val(btex $-10$ etex);val(btex $-\left(\frac{1}{2} \times \sqrt{5}\right)+\frac{-3}{2}$ etex); + val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex); val(btex $-1$ etex); -val(btex $\frac{1}{2} \times \sqrt{5}+\frac{-3}{2}$ etex); +val(btex $\frac{(\sqrt{5}-3)}{2}$ etex); val(btex $1$ etex); val(btex $\frac{3}{2}$ etex); val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex); plus;barre; plus;barre; plus;barre; @@ -419,7 +448,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex); plus;barre; plus;barre;plus; -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3x+1}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex); plus; valBarre(btex 0 etex);moins;barre; moins; @@ -431,7 +460,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex); endTableau; - beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); + beginTableau(31) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$ @@ -439,7 +468,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$ $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(30) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); valPos(btex $1$ etex,0); valPos(btex $2$ @@ -447,7 +476,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$ $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0); endTableau; -beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -457,13 +486,13 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va endTableau; -beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex); +beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;valBarre(btex$ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); valPos(btex $1$ etex,1);valPos(btex $ 0 $ etex,0.5);valPos(btex $-\pi -1$ etex,0); endTableau; -beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); +beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$ @@ -473,15 +502,15 @@ endTableau; -beginTableau(35) +beginTableau(37) newLigneVariables(btex $\displaystyle {x}$ etex); val(btex $-10$ etex);val(btex $10$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+10)}$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex); valBarre(btex 0 etex);plus; valBarre(btex 0 etex); endTableau; -beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-\left(\sqrt{2}\right)$ etex); val(btex $-1$ etex); val(btex $1$ etex); @@ -492,7 +521,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; v newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex$-2$etex,0);limGauche(btex $0$ etex,1);debutNonDef;finNonDef;limDroite(btex $0$ etex,1);valPos(btex$-2$etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -501,38 +530,38 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(38) newLigneVariables(btex $t$ etex);val(btex $0$ etex); -val(btex $\frac{1}{8} \times \pi $ etex); -val(btex $\frac{1}{3} \times \pi $ etex); -val(btex $\frac{3}{8} \times \pi $ etex); +beginTableau(40) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{8}$ etex); +val(btex $\frac{\pi }{3}$ etex); +val(btex $\frac{3 \pi }{8}$ etex); val(btex $\frac{\pi }{2}$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex); -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3\pi }{8}\right)$ +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3 \pi }{8}\right)$ etex,0.5);valPos(btex $-1$ etex,0); valPos(btex $-\left(\cos\left(\frac{\pi }{8}\right)\right)$ etex,0.5);valPos(btex $0$ etex,1); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex); newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$ - etex,1);valPos(btex $-\left(\frac{1}{2} \times \sqrt{3}\right)$ + etex,1);valPos(btex $\frac{(-\left(\sqrt{3}\right))}{2}$ etex,0.5);valPos(btex $-1$ etex,0); valPos(btex $0$ etex,1); endTableau; -beginTableau(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex); -val(btex $\frac{1}{3} \times \pi $ etex); +beginTableau(41) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{3}$ etex); val(btex $\pi $ etex); -val(btex $\frac{5}{3} \times \pi $ etex); -val(btex $2\pi $ etex); +val(btex $\frac{5 \pi }{3}$ etex); +val(btex $2 \pi $ etex); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $-1$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-1$ etex); -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\left(\sqrt{3}\right)-\left(\frac{1}{-3} \times \pi \right)$ +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex $\frac{(\pi +-3 \sqrt{3})}{3}$ etex,0); valPos(btex $\pi $ - etex,0.5);valPos(btex $\sqrt{3}+\frac{5}{3} \times \pi $ - etex,1);valPos(btex $2\pi $ etex,0); + etex,0.5);valPos(btex $\frac{(5 \pi +3 \sqrt{3})}{3}$ + etex,1);valPos(btex $2 \pi $ etex,0); newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(\sqrt{3}\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $\sqrt{3}$ etex);plus;valBarre(btex $0$ etex); newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $1$ etex,1);valPos(btex $0$ @@ -542,7 +571,7 @@ valPos(btex $0$ etex,0.5);valPos(btex $1$ etex,1); endTableau; -beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $\frac{5}{2}$ etex); @@ -554,75 +583,51 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $\sqrt{35}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{15}$ etex,0);valPos(btex$\sqrt{21}$etex,1);limGauche(btex $\sqrt{15}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{35}$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-5$ etex); -val(btex $\frac{2}{5}$ etex); -val(btex $10$ etex); - -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $\frac{169}{2}$ etex,1); valPos(btex $\frac{58}{5}$ - etex,0); -valPos(btex $242$ etex,1); -endTableau; - -beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-20$ etex); -val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex); -val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex); -val(btex $20$ etex); - -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-26047$ etex,0); valPos(btex $\frac{14}{243} \times \sqrt{7}+\frac{-1681}{243}$ - etex,1);valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{-1681}{243}$ - etex,0); -valPos(btex $22033$ etex,1); -endTableau; +beginTableau(43) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{8}$ etex); +val(btex $\frac{\pi }{6}$ etex); +val(btex $\frac{3 \pi }{8}$ etex); +val(btex $\frac{\pi }{2}$ etex); -beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-20$ etex); -val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex); -val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex); -val(btex $20$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(t)}$ etex);valBarre(btex $3$ etex);plus;valBarre(btex $3 \cos\left(\frac{3 \pi }{8}\right)$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \cos\left(\frac{\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex $\sin\left(\frac{3 \pi }{8}\right)$ + etex,0.5);valPos(btex $1$ + etex,1);valPos(btex $-\left(\sin\left(\frac{\pi }{8}\right)\right)$ + etex,0.5);valPos(btex $-1$ etex,0); -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $26047$ etex,1); valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{1681}{243}$ +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$ + etex,1);valPos(btex $\frac{\sqrt{3}}{2}$ + etex,0.5);valPos(btex $-1$ etex,0); -valPos(btex $\frac{14}{243} \times \sqrt{7}+\frac{1681}{243}$ - etex,1);valPos(btex $-22033$ etex,0); - +valPos(btex $0$ etex,1); endTableau; - - -beginTableau(44) -newLigneVariables(btex $\displaystyle {x}$ etex); - val(btex $-20$ etex);val(btex $ 1.942052$ etex); -val(btex $20$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(3x^{3}\right)+5x^{2}-\left(2x\right)+7}$ etex); - plus;valBarre(btex 0 etex); moins; + beginTableau(44) +newLigneVariables(btex $ {x}$ etex); + val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex); +val(btex $\frac{\pi }{3}$ etex); +val(btex $\frac{7 \pi }{6}$ etex); +val(btex $\frac{5 \pi }{3}$ etex); +val(btex $\frac{11 \pi }{6}$ etex); +val(btex $2 \pi $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \cos\left(x\right)+\frac{1}{-2}}$ etex); + plus; + valBarre(btex 0 etex);plus; + valBarre(btex 0 etex);moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; -endTableau; - - - -beginTableau(45) -newLigneVariables(btex $\displaystyle {x}$ etex); - val(btex $-20$ etex);val(btex $ 1.942052$ etex); -val(btex $20$ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x^{3}-\left(5x^{2}\right)+2x-7}$ etex); - moins;valBarre(btex 0 etex); plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex); + plus;barre; + plus;barre; + plus; + valBarre(btex 0 etex);moins;barre; + moins;valBarre(btex 0 etex);plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f (x)}$ etex); + plus;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; endTableau; -beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $ 0.000000$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f''(x)}$ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f'}$ etex); -valPos(btex $\frac{1}{2}$ etex,0); valPos(btex $ 1.000000$ - etex,1);valPos(btex - $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0); -endTableau; - -beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); -val(btex $ 0.639232$ etex); -val(btex $+\infty $ etex); - -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus; valBarre(btex 0 etex);moins; -newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-\infty$ etex,0); valPos(btex $ 0.967397$ - etex,1);valPos(btex $-\infty$ etex,0); - -endTableau; - +
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.pdf b/Master/texmf-dist/doc/latex/tablor/tablor.pdf Binary files differindex db5ac600269..e79dbbf0274 100644 --- a/Master/texmf-dist/doc/latex/tablor/tablor.pdf +++ b/Master/texmf-dist/doc/latex/tablor/tablor.pdf diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.tex b/Master/texmf-dist/doc/latex/tablor/tablor.tex index dcc593424ab..fd514f0f77e 100644 --- a/Master/texmf-dist/doc/latex/tablor/tablor.tex +++ b/Master/texmf-dist/doc/latex/tablor/tablor.tex @@ -48,11 +48,11 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com % petits environnements bclogo \newenvironment{DANGER}[1]{% -\begin{bclogo}{\attention}{#1}{0.9white}{0.1}} +\begin{bclogo}{\attention}{#1}{0.9white}{0.1}{0}} {\end{bclogo}} \newenvironment{Idee}[1]{% -\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}} +\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}{0}} {\end{bclogo}} @@ -72,24 +72,6 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com -%%%% Macros pour un Vrai-Faux - -\usepackage{pifont} - -\newcommand{\Q}{\mbox{\ding{114}\hspace{-.7em}\raisebox{.2ex}[1ex]{\ding{51}}}} - -\newcommand{\VF}{% - \hfill\makebox[1cm][s]{\bf V\hfill F} - } - -\newcommand{\Rep}[1][]{% - \ifthenelse{\equal{#1}{v}}{% - \hfill\makebox[1cm][s]{\Q\hfill \ding{114}}}{% - \ifthenelse{\equal{#1}{f}}{% - \hfill\makebox[1cm][s]{\ding{114} \hfill\Q}}{% - \hfill\makebox[1cm][s]{\ding{114} \hfill\ding{114}}}}} - - % titre \title{\texttt{tablor.sty} \\La machine à créer des tableaux de signes et de variations } @@ -98,7 +80,7 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com avec l'efficace participation de Jean-Michel \textsc{Boucart}\\ Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gconnan.free.fr/punbb/upload/index.php}} -\date{14 juin 2008 - Version 3.00} +\date{8 octobre 2008 - Version 4.00} @@ -129,6 +111,37 @@ Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gcon Il s'agit d'obtenir rapidement un tableau de signe ou un tableau de variation en entrant un minimum de commandes. +\section{Nouveautés} + +\subsection{Changements depuis la version 3.00} + +La version 4.00 n'est malheureusement plus compatible avec les versions +antérieures car une option supplémentaire a été ajoutée pour traiter les +fonctions trigonométriques. + +Une possibilité a de plus été ajoutée pour réduire la taille des +tableaux. + + +\subsection{Professor.sty} + + +\texttt{tablor.sty} a fait des petits... Grâce à une efficace +collaboration avec Denis \textsc{LE FUR}, vous disposez à présent de +toute une panoplie d'outils similaires pour tracer des courbes, des +histogrammes, des arbres de probabilités, des graphes probabilistes, des +lissages par moyennes mobiles et j'en passe et des meilleures... Allez +découvrir ces trésors sur +\href{http://mathsp.tuxfamily.org/spip.php?rubrique46}{http://mathsp.tuxfamily.org/spip.php?rubrique46}. + + + + + + + + + \section{Comment ça marche~?} \subsection{Principe général} @@ -200,7 +213,7 @@ fclose(sortie); // on ferme XCasmpfc.mp -\begin{figure} +\begin{figure}[!h] \begin{Idee}{Autres collaborations XCAS/\LaTeX{}} On peut suivre ce même principe pour créer d'autres associations de vos outils préférés. Voir par exemple~: @@ -219,6 +232,17 @@ et \section{De quoi a-t-on besoin~?} +\begin{figure}[!h] + \begin{Idee}{Conseils en lignes} + N'hésitez pas à explorer la page suivante : + +\href{http://mathsp.tuxfamily.org/spip.php?article186}{http://mathsp.tuxfamily.org/spip.php?article186} + +surtout si vous êtes sur XP :-) + \end{Idee} + \end{figure} + + \begin{itemize} \item Il faut avoir installé \texttt{XCAS}, logiciel multi-plateforme de calcul et de programmation~: @@ -266,7 +290,7 @@ pour installer une nouvelle extension \LaTeX{}. \end{itemize} -\begin{figure} +\begin{figure}[!h] \begin{Idee}{shell-escape} Pour les utilisateurs de TeXnicCenter, observez cette @@ -294,7 +318,7 @@ et là il faut ajouter \end{figure} -\begin{figure} +\begin{figure}[!h] \begin{DANGER}{Conflit d'extensions} L'extension \verb+fancybox+ rentre en conflit avec \verb+fancyvrb+ qu'utilise \verb+tablor+ car elles définissent toutes deux différemment l'environnement \verb+VerbatimOut+. @@ -314,14 +338,14 @@ et là il faut ajouter -% \begin{figure} +% \begin{figure}[!h] % %\begin{DANGER} % Le fichier \texttt{tablor.sty} est codé en \texttt{latin-1}. Les utilisateurs de % \texttt{utf-8} devront donc utiliser \texttt{tablorutf8.sty} à la place. % %\end{DANGER} % \end{figure} -\pagebreak +%\pagebreak \section{Comment l'utiliser~?} @@ -343,7 +367,7 @@ Le préambule sera toujours~: -% \begin{figure} +% \begin{figure}[!h] % \begin{Idee} % Les fontes utilisées dans les tableaux sont \verb+[upright]{fourier}+. Il est tout à % fait possible d'utiliser d'autres fontes. Il suffit de modifier le fichier @@ -581,7 +605,55 @@ ou bien, selon les cas~: \end{lstlisting} +\section{Facteur de réduction} +Si vous trouvez le tableau trop grand, vous pouvez utilisez la commande +\verb+\ech{nombre}+ où \texttt{nombre} représente le coefficienr de +réduction ou d'agrandissement du tableau. + +Par exemple, comparez~: + + \begin{lstlisting} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} + \end{lstlisting} + + \begin{center} + + +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} + +\end{center} + +et + + \begin{lstlisting} +\ech{0.7} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} +\ech{1} + \end{lstlisting} + + \begin{center} + + \ech{0.7} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} +\ech{1} + +\end{center} + +\begin{figure}[!h] + \begin{DANGER}{Remise à l'échelle 1} + N'oubliez pas de remettre à l'échelle 1 en entrant à la + suite de l'environnement \verb+\ech{1}+ + \end{DANGER} + \end{figure} \section{Tableaux des variations} @@ -594,7 +666,7 @@ L'environnement s'appelle \texttt{TV}. On utilise une commande au format \texttt \xcas \begin{lstlisting} -TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,\tv) +TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,lignes,trigo,\tv) \end{lstlisting} \begin{itemize} @@ -602,16 +674,18 @@ TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expr \item \texttt{[borne inf,borne sup]} désigne les bornes de l'ensemble de définition. On note $+\infty$~:~\texttt{+infinity} et $-\infty$~:~\texttt{-infinity}. N'oubliez pas les crochets~! -\item \texttt{[valeurs interdites]} désigne la liste des valeurs interdites; +\item \texttt{[valeurs interdites]} désigne la liste des valeurs interdites~; \item \texttt{"nom fonction"} désigne la lettre représentant la fonction telle que vous voulez qu'elle apparaisse : $f$, $g$, $\varphi$, etc. \item \texttt{"nom variable"}~:~même chose pour la variable, selon que vous voulez la désigner par $x$, $t$, etc. N'oubliez pas les guillemets~! \item \texttt{expression en fonction de x} désigne l'expression de la fonction. Attention~! Utilisez - ici toujours $x$ pour désigner la variable; -\item le paramètre \texttt{t} est à remplacer par 1 si vous voulez voir apparaître une ligne + ici toujours $x$ pour désigner la variable~; +\item le paramètre \texttt{lignes} est à remplacer par 1 si vous voulez voir apparaître une ligne avec le signe de la dérivée, par 0 si vous ne voulez pas de cette ligne et par 2 si vous ne voulez - que le signe de la dérivée. + que le signe de la dérivée~; +\item le paramètre \texttt{trigo} est à remplacer par \texttt{t} si la + fonction étudiée est trigonométrique et par tout autre symbole sinon~; \item on termine par \verb+\tv+, une commande permettant de numéroter les tableaux en interne. \end{itemize} @@ -627,7 +701,7 @@ Voyons à présent quelques exemples. On obtient~: \begin{TV} -TV([-5,7],[],"f","x",x^2,0,\tv); +TV([-5,7],[],"f","x",x^2,0,n,\tv); \end{TV} @@ -635,7 +709,7 @@ après avoir entré~: \begin{lstlisting} \begin{TV} -TV([-5,7],[],"f","x",x^2,0,\tv) +TV([-5,7],[],"f","x",x^2,0,n,\tv) \end{TV} \end{lstlisting} @@ -645,12 +719,12 @@ TV([-5,7],[],"f","x",x^2,0,\tv) \begin{lstlisting} \begin{TV} -TV([-infinity,+infinity],[],"f","x",x^2,1,\tv) +TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([-infinity,+infinity],[],"f","x",x^2,1,\tv) +TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv) \end{TV} \item Avec la même fonction sur \textbf{R} avec uniquement le signe de la dérivée~: @@ -659,12 +733,12 @@ TV([-infinity,+infinity],[],"f","x",x^2,1,\tv) \begin{lstlisting} \begin{TV} -TV([-infinity,+infinity],[],"f","x",x^2,2,\tv) +TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([-infinity,+infinity],[],"f","x",x^2,2,\tv) +TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv) \end{TV} @@ -674,7 +748,7 @@ TV([-infinity,+infinity],[],"f","x",x^2,2,\tv) \begin{lstlisting} \begin{TV} -TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv) +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} \end{lstlisting} @@ -682,12 +756,30 @@ TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv) \begin{TV} -TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv) +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} \end{center} +\item Pour la fonction $x\mapsto \sin(x)+\frac{1}{2}$ on n'oublie pas le + paramètre \texttt{t}~: + + \begin{lstlisting} +\begin{TV} +TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv) +\end{TV} + \end{lstlisting} + + \begin{center} +\begin{TV} +TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv) +\end{TV} +\end{center} + + + + \item Il y aura des problèmes pour des équations $f'(x)=0$ que \texttt{XCAS} ne saurait pas résoudre de manière formelle. Il faudrait alors utiliser une résolution numérique et remplacer \texttt{resoudre} par \texttt{fsolve}. Mais dans les études demandées au Bac, l'étude des signes @@ -710,19 +802,19 @@ On utilise alors l'environnement \texttt{TVZ} (Z comme zone...). \begin{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv) \end{TVZ} \end{lstlisting} \begin{center} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv) \end{TVZ} \end{center} -\begin{figure} +\begin{figure}[!h] \begin{DANGER}{Listes des intervalles interdits} Le troisième argument est une liste d'intervalles : la liste des «~zones interdites~» qui peut éventuellemnt se réduire à un seul intervalle comme dans l'exemple précédent. @@ -735,7 +827,7 @@ Voici un exemple comportant plusieurs zones in \begin{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv) \end{TVZ} \end{lstlisting} @@ -743,7 +835,7 @@ Voici un exemple comportant plusieurs zones in \begin{center} \begin{TVZ} - TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv) \end{TVZ} \end{center} @@ -756,7 +848,7 @@ Si l'on veut mettre en évidence les solutions de l'équation $f(x)=a$, on uti La syntaxe est~: \begin{lstlisting} -TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,\tv) +TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,trigo,\tv) \end{lstlisting} Les paramètres sont les mêmes que pour \texttt{TV} mais on ajoute la valeur \texttt{a} bien sûr. @@ -766,7 +858,7 @@ Par exemple, pour $f~:~x\mapsto \frac{x^2}{x^2-1}$ et l'équation $f(x)=10$ on en \begin{lstlisting} \begin{TVI} -TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv) +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) \end{TVI} \end{lstlisting} @@ -774,7 +866,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv) et on obtient~: \begin{TVI} -TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv) +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) \end{TVI} Les solutions sont notées $\alpha_1$, $\alpha_2$, etc. @@ -784,7 +876,7 @@ Si l'équation est plutôt $f(x)=-1$~: \begin{lstlisting} \begin{TVI} -TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv) +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) \end{TVI} \end{lstlisting} @@ -792,7 +884,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv) et on obtient~: \begin{TVI} -TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv) +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) \end{TVI} @@ -823,7 +915,7 @@ On étudie d'abord la fonction $x\mapsto g'(x)$~: % \begin{TVIapp} -% TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,\tv) +% TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,n,\tv) % \end{TVIapp} \stepcounter{TVn} @@ -860,18 +952,19 @@ La syntaxe est la suivante~: \begin{lstlisting} \begin{TVP} -TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,\tv) +TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,n,\tv) \end{TVP} \end{lstlisting} avec \texttt{IE} l'intervalle d'étude, \texttt{VI} la liste des listes de valeurs interdites respectives pour les deux fonctions, \texttt{a} pour avoir un tableau complet ou partiel comme dans -les autres "TV", enfin \texttt{trigo} qui vaut 1 si interviennent des fonctions trigonométrqiues, 0 +les autres "TV", enfin \texttt{trigo} qui vaut \texttt{t} si interviennent des +fonctions trigonométrqiues, autre chose sinon. -\begin{figure}[h] +\begin{figure}[!h] \begin{DANGER}{Version de XCAS} L'utilisation de TVP implique l'utilisation d'une version de XCAS d'une date postérieure au 14 juin 2008 ! @@ -892,13 +985,13 @@ sinon. \begin{lstlisting} \begin{TVP} - TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv) + TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv) \end{TVP} \end{lstlisting} \begin{TVP} - TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv) + TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv) \end{TVP} @@ -919,14 +1012,14 @@ y(t)=\frac{t^2(t+2)}{t+1} \begin{lstlisting} \begin{TVP} -TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv) +TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv) \end{TVP} \end{lstlisting} \begin{TVP} -TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv) +TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv) \end{TVP} @@ -957,7 +1050,7 @@ TSa(-2,3,-1,5,\tv); -\begin{figure}[h] +\begin{figure}[!h] \begin{DANGER}{Nouveauté à partir de la version 2.08} Par souci de cohérence avec l'environnement TSq, on doit rajouter maintenant en premier argument le nom de la fonction produit dans l'environnement TS. @@ -977,7 +1070,7 @@ précisant l'intervalle d'étude~: \begin{lstlisting} \begin{TS} - TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv); + TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv); \end{TS} \end{lstlisting} @@ -985,7 +1078,7 @@ On obtient~: \begin{TS} - TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv); + TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv); \end{TS} @@ -994,13 +1087,13 @@ Ou bien, sur un intervalle borné~: \begin{lstlisting} \begin{TS} -TS("f",[x-10,x+10],[-15,10],\tv) +TS("f",[x-10,x+10],[-15,10],n,\tv) \end{TS} \end{lstlisting} \begin{TS} -TS("f",[x-10,x+10],[-15,10],\tv) +TS("f",[x-10,x+10],[-15,10],n,\tv) \end{TS} @@ -1012,7 +1105,7 @@ On entre dans deux listes différentes les facteurs du numérateur et du dénominat \begin{lstlisting} \begin{TSq} -TSq("nom du quotient",[liste des facteurs du numérateur],[liste des facteurs du dénominateur],[inf,sup]) +TSq("nom du quotient",[liste des facteurs du numérateur],[liste des facteurs du dénominateur],[inf,sup],trigo,\tv) \end{TSq} \end{lstlisting} @@ -1020,7 +1113,7 @@ Par exemple, pour étudier le signe de $\frac{(-2x+3)(-4x+5)}{(x^2-16)(x-2)}$ sur \begin{lstlisting} \begin{TSq} -TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv) +TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv) \end{TSq} \end{lstlisting} @@ -1028,21 +1121,21 @@ TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv) \begin{TSq} -TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv) +TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv) \end{TSq} -Sur un intervalle borné~: +% Sur un intervalle borné~: -\begin{lstlisting} -\begin{TSq} -TSq("Q",[x-10],[x+10],[-infinity,10],\tv) -\end{TSq} -\end{lstlisting} +% \begin{lstlisting} +% \begin{TSq} +% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv) +% \end{TSq} +% \end{lstlisting} -\begin{TSq} -TSq("Q",[x-10],[x+10],[-infinity,10],\tv) -\end{TSq} +% \begin{TSq} +% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv) +% \end{TSq} @@ -1055,14 +1148,14 @@ l'expression étudiée et l'intervalle considéré~: \begin{lstlisting} \begin{TSc} -TSc((x-10)*(x+5),[-10,10],\tv) +TSc((x-10)*(x+5),[-10,10],n,\tv) \end{TSc} \end{lstlisting} \begin{TSc} -TSc((x-10)*(x+5),[-10,10],\tv) +TSc((x-10)*(x+5),[-10,10],n,\tv) \end{TSc} @@ -1087,7 +1180,7 @@ Si vous tapez~: \begin{lstlisting} \begin{TV*}{100} - TV([-1,+infinity],[],"f","x",x-ln(x+1),1,\tv) + TV([-1,+infinity],[],"f","x",x-ln(x+1),1,n,\tv) \end{TV*} \end{lstlisting} @@ -1106,7 +1199,7 @@ Par exemple, je tape~: \begin{lstlisting} \begin{TS*}{100} - TS("F",[3*x+2,5*x^2-1],[-50,50],\tv) + TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv) \end{TS*} \end{lstlisting} @@ -1125,7 +1218,7 @@ automatiquement pour m'afficher le tableau voulu~: \begin{center} \begin{TS*}{105} - TS("F",[3*x+2,5*x^2-1],[-50,50],\tv) + TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv) \end{TS*} \end{center} @@ -1191,6 +1284,7 @@ dans un fichier \texttt{latex-tempo}: "\""(p "nom de la variable :")"\"," ""(p "expression de la fonction (utiliser x) :")"," ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")"," +""(p "trigo ?(t:trigo, n:non trigo) :")"," "\\tv)" n> "\\end{TV}" n> "\\end{center}" > % )) @@ -1203,6 +1297,7 @@ dans un fichier \texttt{latex-tempo}: "\""(p "nom de la variable :")"\"," ""(p "expression de la fonction (utiliser x) :")"," ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")"," +""(p "trigo ?(t:trigo, n:non trigo) :")"," ""(p "f(x)=l pour la valeur l :")"," "\\tv)" n> "\\end{TVI}" n> @@ -1212,7 +1307,8 @@ dans un fichier \texttt{latex-tempo}: "\\begin{TS}" n> "TS(\""(p "nom du produit :")"\"," "["(p "liste des facteurs (,) :")"]," - "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," +""(p "trigo ?(t:trigo, n:non trigo) :")"," "\\tv)" n> "\\end{TS}" n> "\\end{center}" > % )) @@ -1223,6 +1319,7 @@ dans un fichier \texttt{latex-tempo}: "["(p "liste des facteurs du numerateur (,) :")"]," "["(p "liste des facteurs du denominateur (,) :")"]," "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," +""(p "trigo ?(t:trigo, n:non trigo) :")"," "\\tv)" n> "\\end{TSq}" n> "\\end{center}" > % )) @@ -1238,7 +1335,7 @@ dans un fichier \texttt{latex-tempo}: "["(p "expression de la fonction x (utiliser t) :")"," ""(p "expression de la fonction y (utiliser t) :")"]," ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")"," - ""(p "1 si fonctions trigo, 0 sinon :")"," + ""(p "t si fonctions trigo, n sinon :")"," "\\tv)" n> "\\end{TVP}" n> "\\end{center}" > % )) @@ -1253,6 +1350,7 @@ dans un fichier \texttt{latex-tempo}: "\""(p "nom de la variable :")"\"," ""(p "expression de la fonction (utiliser x) :")"," ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")"," +""(p "trigo ?(t:trigo, n:non trigo) :")"," "\\tv)" n> "\\end{TV}" n> "\\end{center}" > % )) @@ -1267,133 +1365,127 @@ Voici quelques exemples de tableaux~: \begin{lstlisting} \begin{TVI} -TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv) +TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv) +TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv) \end{TVI} \begin{lstlisting} \begin{TVI} -TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv) +TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv) +TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv) \end{TVI} \begin{lstlisting} \begin{TVI} -TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv) +TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv) +TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv) \end{TVI} \stepcounter{TVn} \begin{lstlisting} \begin{TV} -TV([1,+infinity],[],"f","x",-ln(x),1,\tv) +TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([1,+infinity],[],"f","x",-ln(x),1,\tv) +TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv) \end{TV} \begin{lstlisting} \begin{TVI} -TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv) +TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv) +TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv) \end{TVI} \begin{lstlisting} \begin{TV} -TV([0,2*pi],[],"f","x",cos(x),1,\tv) +TV([0,2*pi],[],"f","x",cos(x),1,t,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([0,2*Pi],[],"f","x",cos(x),1,\tv) +TV([0,2*Pi],[],"f","x",cos(x),1,t,\tv) \end{TV} -\begin{figure} - \begin{DANGER}{Fonctions périodiques} - Il y aura des problèmes si vous demandez un tableau des variations d'une fonction - périodique sur un intervalle - d'amplitude supérieure à la période, mais est-ce vraiment utile ?... - \end{DANGER} - \end{figure} + \begin{lstlisting} \begin{TVI} -TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv) +TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv) +TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv) \end{TVI} \begin{lstlisting} \begin{TVI} -TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv) +TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv) +TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv) \end{TVI} \begin{lstlisting} \begin{TV} -TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv) +TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv) +TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv) \end{TV} \begin{lstlisting} \begin{TS} -TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv); +TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv); \end{TS} \end{lstlisting} \begin{TS} -TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv); +TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv); \end{TS} \begin{lstlisting} \begin{TVI} -TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv) +TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv) +TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv) \end{TVI} @@ -1401,12 +1493,12 @@ TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv) \begin{lstlisting} \begin{TVI} -TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv) +TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv) +TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv) \end{TVI} \stepcounter{TVn} @@ -1414,12 +1506,12 @@ TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv) \begin{lstlisting} \begin{TV} -TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv) +TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv) \end{TV} \end{lstlisting} \begin{TV} -TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv) +TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv) \end{TV} @@ -1428,91 +1520,91 @@ TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv) \begin{lstlisting} \begin{TVI} -TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv) +TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv) +TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv) \end{TVI} \begin{lstlisting} \begin{TVI} -TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv) +TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv) \end{TVI} \end{lstlisting} \begin{TVI} -TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv) +TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv) \end{TVI} \begin{lstlisting} \begin{TSc} -TSc((x-10)*(x+10),[-10,10],\tv) +TSc((x-10)*(x+10),[-10,10],n,\tv) \end{TSc} \end{lstlisting} \begin{TSc} -TSc((x-10)*(x+10),[-10,10],\tv) +TSc((x-10)*(x+10),[-10,10],n,\tv) \end{TSc} \begin{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv) \end{TVZ} \end{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv) \end{TVZ} \begin{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv) \end{TVZ} \end{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv) \end{TVZ} \begin{lstlisting} \begin{TVP} -TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv) +TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv) \end{TVP} \end{lstlisting} \begin{TVP} -TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv) +TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv) \end{TVP} \begin{lstlisting} \begin{TVP} -TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv) +TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv) \end{TVP} \end{lstlisting} \begin{TVP} -TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv) +TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv) \end{TVP} \begin{lstlisting} \begin{TVZ} - TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv) \end{TVZ} \end{lstlisting} @@ -1520,175 +1612,212 @@ TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv) \begin{center} \begin{TVZ} - TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,\tv) + TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,n,\tv) \end{TVZ} \end{center} -\lat + \begin{lstlisting} -\begin{enumerate} -\item + \begin{TVP} + TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv) + \end{TVP} +\end{lstlisting} + + +\begin{center} + \begin{TVP} + TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv) + \end{TVP} + \end{center} + +\begin{lstlisting} +\begin{TS} + TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv) +\end{TS} +\end{lstlisting} + - Selon le tableau de variation de la fonction $f$ - ci-dessous, on peut affirmer que \ldots +\begin{center} +\begin{TS} + TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv) +\end{TS} +\end{center} + + + + + + + + + + +% \lat + +% \begin{lstlisting} +% \begin{enumerate} +% \item + +% Selon le tableau de variation de la fonction $f$ +% ci-dessous, on peut affirmer que \ldots -\begin{TV} - TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv) -\end{TV} +% \begin{TV} +% TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv) +% \end{TV} -\VF -\begin{itemize} +% \VF +% \begin{itemize} - \item[\ldots] 5 n'a pas d'antécédent \Rep - \item[\ldots] 5 n'a pas d'image \Rep - \item[\ldots] 5 a deux antécédents \Rep - \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep +% \item[\ldots] 5 n'a pas d'antécédent \Rep +% \item[\ldots] 5 n'a pas d'image \Rep +% \item[\ldots] 5 a deux antécédents \Rep +% \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep -\end{itemize} +% \end{itemize} -\item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent - correspondre à $f$~: +% \item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent +% correspondre à $f$~: -\VF +% \VF - \begin{enumerate} +% \begin{enumerate} - \item Tableau 1 \Rep +% \item Tableau 1 \Rep -\begin{TV} - TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv) -\end{TV} +% \begin{TV} +% TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv) +% \end{TV} -\item Tableau 2 \Rep +% \item Tableau 2 \Rep -\begin{TV} - TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv) -\end{TV} +% \begin{TV} +% TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv) +% \end{TV} -\item Tableau 3 \Rep +% \item Tableau 3 \Rep -\begin{TSc} - TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv) -\end{TSc} +% \begin{TSc} +% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv) +% \end{TSc} -\item Tableau 4 \Rep +% \item Tableau 4 \Rep -\begin{TSc} - TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv) -\end{TSc} +% \begin{TSc} +% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv) +% \end{TSc} -\end{enumerate} +% \end{enumerate} -\end{enumerate} +% \end{enumerate} -\end{lstlisting} +% \end{lstlisting} -\begin{enumerate} -\item +% \begin{enumerate} +% \item - Selon le tableau de variation de la fonction $f$ - ci-dessous, on peut affirmer que \ldots +% Selon le tableau de variation de la fonction $f$ +% ci-dessous, on peut affirmer que \ldots -\begin{TV} - TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv) -\end{TV} +% \begin{TV} +% TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv) +% \end{TV} -\VF -\begin{itemize} +% \VF +% \begin{itemize} - \item[\ldots] 5 n'a pas d'antécédent \Rep - \item[\ldots] 5 n'a pas d'image \Rep - \item[\ldots] 5 a deux antécédents \Rep - \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep +% \item[\ldots] 5 n'a pas d'antécédent \Rep +% \item[\ldots] 5 n'a pas d'image \Rep +% \item[\ldots] 5 a deux antécédents \Rep +% \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep -\end{itemize} +% \end{itemize} -\item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent-ils - correspondre à la fonction $f$~: +% \item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent-ils +% correspondre à la fonction $f$~: -\VF +% \VF - \begin{enumerate} +% \begin{enumerate} - \item Tableau 1 \Rep +% \item Tableau 1 \Rep -\begin{TV} - TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv) -\end{TV} +% \begin{TV} +% TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv) +% \end{TV} -\item Tableau 2 \Rep +% \item Tableau 2 \Rep -\begin{TV} - TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv) -\end{TV} +% \begin{TV} +% TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv) +% \end{TV} -\item Tableau 3 \Rep +% \item Tableau 3 \Rep -\begin{TSc} - TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv) -\end{TSc} +% \begin{TSc} +% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv) +% \end{TSc} -\item Tableau 4 \Rep +% \item Tableau 4 \Rep -\begin{TSc} - TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv) -\end{TSc} +% \begin{TSc} +% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv) +% \end{TSc} -\end{enumerate} +% \end{enumerate} -\end{enumerate} +% \end{enumerate} -\begin{lstlisting} -On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ +% \begin{lstlisting} +% On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ -Étudions sa dérivée~: +% Étudions sa dérivée~: -\begin{TVIapp} - TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) - \end{TVIapp} +% \begin{TVIapp} +% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) +% \end{TVIapp} -On en déduit le tableau de variation de $f$ +% On en déduit le tableau de variation de $f$ -\begin{TVapp} - TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv) - \end{TVapp} -\end{lstlisting} +% \begin{TVapp} +% TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv) +% \end{TVapp} +% \end{lstlisting} -On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ +% On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ -Étudions sa dérivée~: +% Étudions sa dérivée~: -\begin{TVIapp} - TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) - \end{TVIapp} +% \begin{TVIapp} +% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) +% \end{TVIapp} -On en déduit le tableau de variation de $f$ +% On en déduit le tableau de variation de $f$ -\begin{TVapp} - TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv) - \end{TVapp} +% \begin{TVapp} +% TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv) +% \end{TVapp} |