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Diffstat (limited to 'Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp')
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1 files changed, 112 insertions, 63 deletions
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 7542f5b669b..6fae90d5590 100644 --- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp +++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp @@ -107,7 +107,19 @@ valPos(btex $\frac{3}{2}$ etex,1);valPos(btex $\frac{1}{2}$ etex,0); endTableau; -beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(8) 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(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,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $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);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(11) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -116,7 +128,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi'(x)}$ etex);mo 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(9) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $\frac{5}{2}$ etex); @@ -128,8 +140,9 @@ 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);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(10) 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; +beginTableau(13) 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 @@ -137,7 +150,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte valPos(btex $1$ etex,0); endTableau; -beginTableau(11) 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(14) 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 @@ -148,8 +161,9 @@ 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(12) 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; +beginTableau(15) 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 @@ -157,7 +171,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte valPos(btex $1$ etex,0); endTableau; -beginTableau(13) 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); +beginTableau(16) 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 @@ -168,16 +182,18 @@ 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(14) 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; +beginTableau(17) 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(15) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $ 0.337860$ etex);val(btex $\alpha_2$ etex);val(btex $ 1.745534$ etex);val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g''(x)}$ etex);nonDefBarre;moins;valBarre(btex$ $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus;valBarre(btex 0 etex);moins; +beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $ 0.337860$ etex);val(btex $\alpha_2$ etex);val(btex $ 1.745534$ etex);val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g''(x)}$ etex);nonDefBarre;moins;valBarre(btex$ + $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus;valBarre(btex 0 etex);moins; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g'}$ etex); nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 0 $ etex,0.5); valPos(btex $ -0.530055$ etex,0);valPos(btex @@ -185,7 +201,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 0 $ etex,0.5); valPo etex,1); valPos(btex $0$ etex,0); endTableau; -beginTableau(16) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $ 0.212584$ etex); val(btex $ 0.584635$ etex); val(btex $+\infty $ etex); @@ -197,7 +213,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(17) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $ 0.001000$ etex); val(btex $ 0.002000$ etex); val(btex $+\infty $ etex); @@ -208,7 +224,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(18) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +beginTableau(21) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); val(btex $0$ etex); val(btex $+\infty $ etex); @@ -218,7 +234,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va etex,0);valPos(btex $1$ etex,1); endTableau; -beginTableau(19) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +beginTableau(22) 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); @@ -238,7 +254,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va valPos(btex $0$ etex,1); endTableau; -beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +beginTableau(23) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); val(btex $-4$ etex); val(btex $-1$ etex); val(btex $0$ etex); @@ -265,7 +281,7 @@ valPos(btex $\frac{16}{3}$ endTableau; - beginTableau(21) + beginTableau(24) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex); val(btex $5$etex); @@ -275,7 +291,7 @@ 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(22) + beginTableau(25) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex); val(btex $-1$ etex); @@ -324,7 +340,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex); endTableau; - beginTableau(23) + beginTableau(26) newLigneVariables(btex $ {x}$ etex); val(btex $-15$ etex);val(btex $-10$ etex); val(btex $10$ etex); @@ -341,7 +357,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex); endTableau; -beginTableau(24) +beginTableau(27) newLigneVariables(btex $ {x}$ etex); val(btex $-\infty $ etex);val(btex $-4$ etex); val(btex $\frac{5}{4}$ etex); @@ -359,7 +375,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex); moins;no endTableau; -beginTableau(25) +beginTableau(28) newLigneVariables(btex $ {x}$ etex); val(btex $-10$ etex);val(btex $-3$ etex); val(btex $5$ etex); @@ -374,7 +390,7 @@ endTableau; -beginTableau(26) +beginTableau(29) newLigneVariables(btex $\displaystyle {x}$ etex); val(btex $-10$ etex);val(btex $-5$ etex); val(btex $10$ etex); @@ -385,7 +401,7 @@ endTableau; -beginTableau(27) +beginTableau(30) newLigneVariables(btex $\displaystyle {x}$ etex); val(btex $-10$ etex);val(btex $2$ etex); val(btex $5$ etex); @@ -396,7 +412,7 @@ endTableau; -beginTableau(28) +beginTableau(31) newLigneVariables(btex $\displaystyle {x}$ etex); val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex); val(btex $\pi $ etex); @@ -407,15 +423,38 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \tan\left(x\right)}$ e valBarre(btex 0 etex); plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex); endTableau; -beginTableau(29) 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; + 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(32) 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(30) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +beginTableau(33) 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 $0$ @@ -423,28 +462,30 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$ $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(31) 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; +beginTableau(34) 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(33) newLigneVariables(btex $x$ etex);val(btex $1$ etex); +beginTableau(36) 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(34) 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; +beginTableau(37) 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(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $\pi $ etex); val(btex $2 \pi $ etex); @@ -454,35 +495,39 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex) valPos(btex $1$ etex,1); endTableau; -beginTableau(36) 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; +beginTableau(39) 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(37) 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; +beginTableau(40) 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(38) 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; +beginTableau(41) 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(39) 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; +beginTableau(42) 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(40) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); +beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); val(btex $0$ etex); val(btex $+\infty $ etex); @@ -491,7 +536,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no etex,1);valPos(btex $-\infty$ etex,0); endTableau; - beginTableau(41) + beginTableau(44) newLigneVariables(btex $ {x}$ etex); val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex); val(btex $-1$ etex); @@ -533,7 +578,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex); endTableau; - beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); + beginTableau(45) 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 $-\left(e^{-4}\right)-1$ @@ -541,7 +586,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$ $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +beginTableau(46) 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 $2$ @@ -549,7 +594,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$ $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0); endTableau; -beginTableau(45) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +beginTableau(48) newLigneVariables(btex $x$ etex);val(btex $0$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -558,22 +603,25 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va etex,1);valPos(btex $0$ etex,0); endTableau; -beginTableau(46) 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; +beginTableau(49) 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(47) 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; +beginTableau(50) 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(48) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $e^{\frac{(-\left(\sqrt{5}\right)+1)}{2}}$ etex);val(btex $e^{\frac{1}{2}}$ 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; +beginTableau(51) 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 @@ -582,7 +630,7 @@ endTableau; -beginTableau(49) +beginTableau(52) 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); @@ -590,7 +638,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex); valBarre(btex 0 etex); endTableau; -beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-\left(\sqrt{2}\right)$ etex); val(btex $-1$ etex); val(btex $1$ etex); @@ -601,7 +649,7 @@ 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(51) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(54) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $+\infty $ etex); @@ -610,7 +658,7 @@ 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);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(52) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +beginTableau(55) 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); @@ -630,7 +678,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va valPos(btex $0$ etex,1); endTableau; -beginTableau(53) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +beginTableau(56) 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); @@ -650,7 +698,7 @@ valPos(btex $0$ etex,0.5);valPos(btex $1$ etex,1); endTableau; -beginTableau(54) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +beginTableau(57) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); val(btex $-1$ etex); val(btex $1$ etex); val(btex $4$ etex); @@ -661,7 +709,7 @@ 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 $\sqrt{35}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{15}$ etex,0);limGauche(btex $\sqrt{15}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{35}$ etex,0);valPos(btex $+\infty $ etex,1); endTableau; -beginTableau(55) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +beginTableau(58) 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); @@ -680,7 +728,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va valPos(btex $0$ etex,1); endTableau; - beginTableau(56) + beginTableau(59) newLigneVariables(btex $ {x}$ etex); val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex); val(btex $\frac{7 \pi }{6}$ etex); @@ -704,8 +752,9 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f (x)}$ etex); endTableau; - beginTableau(57) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $+\infty $ etex); -newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g''(x)}$ etex);nonDefBarre;moins;valBarre(btex$ $ etex);moins; nonDefBarre;plus; + beginTableau(60) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g''(x)}$ etex);nonDefBarre;moins;valBarre(btex$ + $ etex);moins; nonDefBarre;plus; newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g'}$ etex); nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 0 $ etex,0.5); limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1); endTableau; |