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;