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diff --git a/macros/latex/contrib/tablor/Figures/tablor_Tab.mp b/macros/latex/contrib/tablor/Figures/tablor_Tab.mp new file mode 100644 index 0000000000..260b9b876d --- /dev/null +++ b/macros/latex/contrib/tablor/Figures/tablor_Tab.mp @@ -0,0 +1,727 @@ +input tableauVariation; +verbatimtex +%&latex +\documentclass{article} +\usepackage[upright]{kpfonts}% ou mathpazo, lmodern, etc. ou rien ! +%\usepackage{amsmath} +\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas +\renewcommand\cdot{ } % idem pour les cdot +\begin{document} +\catcode`\@=0 % pour utiliser le @ +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 $0$ etex); +val(btex $2$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex $4$ etex,1); +endTableau; + + +beginTableau(3) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $\frac{-3}{5}$ etex); +val(btex $2$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -45 x-27}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 2-x}$ etex); plus;barre;plus;valBarre(btex 0 etex);moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi(x)}$ etex); plus;valBarre(btex 0 etex); moins;nonDefBarre;plus; +endTableau; + +beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-5$ etex); +val(btex $0$ etex); +val(btex $7$ etex); + +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $25$ etex,1); valPos(btex $0$ + etex,0); +valPos(btex $49$ etex,1); +endTableau; + +beginTableau(5) 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; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex $0$ + etex,0); +valPos(btex $+\infty $ etex,1); +endTableau; + + + +beginTableau(6) 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(7) 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(8) 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(9) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,0); valPos(btex $5$etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1); +endTableau; + +beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1); +endTableau; + +beginTableau(11) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);limGauche(btex $+\infty $ etex,1);nonDefBarre; +endTableau; + +beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @varphi}$ 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(13) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\frac{5}{2}$ etex); +val(btex $4$ etex); +val(btex $6$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;valBarre(btex 0 etex);moins;debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(14) 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); +valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); 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 + $ 10 $ etex,0.5); + valPos(btex $1$ etex,0); +endTableau; + +beginTableau(15) 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); +valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex + $ -1 $ etex,0.5); + valPos(btex $0$ + etex,1);valPos(btex + $ -1 $ etex,0.5); + limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); +endTableau; + +beginTableau(16) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{10}\right))}{3}$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\frac{\sqrt{10}}{3}$ 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); +valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); 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 + $ 10 $ etex,0.5); + valPos(btex $1$ etex,0); +endTableau; + +beginTableau(17) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\frac{(-\left(\sqrt{2}\right))}{2}$ etex);val(btex $0$ etex);val(btex $\frac{\sqrt{2}}{2}$ 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); +valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex + $ -1 $ etex,0.5); + valPos(btex $0$ + etex,1);valPos(btex + $ -1 $ etex,0.5); + limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); +endTableau; + +beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\frac{(-\pi )}{3}$ etex);val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);val(btex $\pi $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex); +valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ + etex,1);valPos(btex + $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0); +endTableau; + +beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $ 0.156422$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(x)}$ etex);nonDefBarre;moins; valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); valPos(btex $ -1.145392$ + etex,0); +valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +val(btex $0$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);moins; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $1$ etex,1); valPos(btex + $0$ + etex,0);valPos(btex $1$ etex,1); +endTableau; + +beginTableau(21) 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 $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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 $\frac{(-\left(\sqrt{3}\right))}{2}$ + etex,0.5);valPos(btex $-1$ + etex,0); +valPos(btex $0$ etex,1); +endTableau; + +beginTableau(22) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +val(btex $-4$ etex); +val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $2$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex); moins;valBarre(btex $0$ etex);plus;nonDefBarre;plus;valBarre(btex $0$ etex);moins;nonDefBarre;moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\frac{8}{9}$ + 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); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex); moins;valBarre(btex $\frac{-64}{9}$ etex);moins;nonDefBarre;moins;valBarre(btex $0$ etex);plus;valBarre(btex $\frac{44}{9}$ etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $+\infty $ etex,1);valPos(btex $\frac{32}{3}$ + etex,0.5);limGauche(btex + $-\infty$ + etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $0$ + etex,0); +valPos(btex $\frac{16}{3}$ + etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + + + beginTableau(23) + newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex); +val(btex $5$etex); +val(btex $+\infty$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;valBarre(btex 0 etex);moins;barre;moins; +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(24) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\sqrt{2}$ etex); +val(btex $\frac{3}{2}$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;valBarre(btex 0 etex);moins; + + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-1}$ etex); + plus;barre; + plus; + valBarre(btex 0 etex);moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+1}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex); + moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-2}$ etex); + plus; + valBarre(btex 0 etex);moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins; + +endTableau; + + beginTableau(25) +newLigneVariables(btex $ {x}$ etex); + val(btex $-15$ 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 $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex); + plus;valBarre(btex 0 etex); moins; + valBarre(btex 0 etex); +endTableau; + + +beginTableau(26) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $-4$ etex); +val(btex $\frac{5}{4}$ etex); +val(btex $\frac{3}{2}$ etex); +val(btex $2$ etex); +val(btex $4$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); plus;barre;plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -4 x+5}$ etex); plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-16}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins;valBarre(btex 0 etex);plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex); moins;barre;moins;barre;moins;barre;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(27) +newLigneVariables(btex $ {x}$ etex); + val(btex $-10$ etex);val(btex $-3$ etex); +val(btex $5$ etex); +val(btex $10$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex); moins;barre;moins;barre;moins; + valBarre(btex 0 etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-5}$ etex); moins;barre;moins;valBarre(btex 0 etex);plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex); valBarre(btex 0 etex);plus;barre;plus;barre;plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+3}$ etex); moins; valBarre(btex 0 etex);plus;barre;plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);nonDefBarre;moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex); +endTableau; + + + +beginTableau(28) +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); + plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex); +endTableau; + + + +beginTableau(29) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $-10$ etex);val(btex $2$ etex); +val(btex $5$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \frac{(x+10)}{(x-5) (x-2)}}$ etex); + valBarre(btex 0 etex); plus;nonDefBarre;moins;nonDefBarre; +endTableau; + + + +beginTableau(30) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex); +val(btex $\pi $ etex); +val(btex $\frac{3 \pi }{2}$ etex); +val(btex $2 \pi $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \tan\left(x\right)}$ etex); + valBarre(btex 0 etex); plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex); +endTableau; + + beginTableau(105) +newLigneVariables(btex $ {x}$ etex); + val(btex $-50$ etex);val(btex $-\frac{2}{3}$ etex); +val(btex $-\frac{\sqrt{5}}{5}$ etex); +val(btex $\frac{\sqrt{5}}{5}$ etex); +val(btex $50$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex); + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +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; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; + +endTableau; + + beginTableau(31) 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 $-1$ + etex,0);valPos(btex + $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(32) 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 $0$ + etex,0);valPos(btex + $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @ln'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ + $ etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @ln}$ etex); +nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -@ln'(x)}$ etex); moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle -@ln}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(36) 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 $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex); +valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ + etex,1);valPos(btex + $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0); +endTableau; + +beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $\pi $ etex); +val(btex $2 \pi $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex);valPos(btex $1$ etex,1); valPos(btex $-1$ + etex,0); +valPos(btex $1$ etex,1); +endTableau; + +beginTableau(38) 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 $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$ + $ etex);plus; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @tan}$ 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(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\mathrm{atan}\left(7\right)$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$ + $ etex);plus; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @tan}$ 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(40) 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 $\frac{3 \sqrt{3}}{4}$ + etex,1);valPos(btex + $ 1 $ etex,0.5);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $ -0.839287$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ 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 $\frac{3 \sqrt{3}}{4}$ + etex,1);valPos(btex + $ 1 $ etex,0.5);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-\infty$ etex,0); valPos(btex $0$ + etex,1);valPos(btex $-\infty$ etex,0); +endTableau; + + beginTableau(43) +newLigneVariables(btex $ {x}$ etex); + val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex); +val(btex $-1$ 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 $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;valBarre(btex 0 etex);moins; + + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex); + moins;barre; + moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex); + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex); + plus; + valBarre(btex 0 etex);moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex); + plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins; + +endTableau; + + beginTableau(44) 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 $-\left(e^{-4}\right)-1$ + etex,0);valPos(btex + $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(45) 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 $2$ + etex,1);valPos(btex + $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $1$ 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 $0$ etex,0); valPos(btex $\ln\left(\frac{(e^{1}+1)}{e^{1}}\right)$ + etex,1);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(48) 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(49) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ 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 $\frac{1}{4}$ + etex,1);valPos(btex + $ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $e^{\frac{(-\left(\sqrt{5}\right)+1)}{2}}$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ etex);val(btex $e^{\frac{(\sqrt{5}+1)}{2}}$ 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 $\frac{1}{4}$ + etex,1);valPos(btex + $ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + + + +beginTableau(51) +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); + valBarre(btex 0 etex);moins; + valBarre(btex 0 etex); +endTableau; + +beginTableau(52) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-\left(\sqrt{2}\right)$ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\sqrt{2}$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;debutNonDefStrict;finNonDefStrict;moins;valBarre(btex 0 etex);plus; +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(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(54) 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 $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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 $\frac{(-\left(\sqrt{3}\right))}{2}$ + etex,0.5);valPos(btex $-1$ + etex,0); +valPos(btex $0$ etex,1); +endTableau; + +beginTableau(55) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{3}$ etex); +val(btex $\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 $\frac{(\pi -3 \sqrt{3})}{3}$ + etex,0); +valPos(btex $\pi $ + 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 $0$ + etex,0.5);valPos(btex $-3$ + etex,0); +valPos(btex $0$ + etex,0.5);valPos(btex $1$ etex,1); +endTableau; + +beginTableau(56) 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); + +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 $-3 \cos\left(\frac{\pi }{8}\right)$ 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); +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 $0$ etex,1); +endTableau; + + beginTableau(57) +newLigneVariables(btex $ {x}$ etex); + val(btex $0$ 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);moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex); + 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); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; + +endTableau; + +
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