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-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor_Tab.mp146
1 files changed, 65 insertions, 81 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 905afed0cbc..260b9b876d9 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor_Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor_Tab.mp
@@ -2,8 +2,8 @@ input tableauVariation;
verbatimtex
%&latex
\documentclass{article}
-\usepackage[upright]{fourier}% ou mathpazo, lmodern, etc. ou rien !
-\usepackage{amsmath}
+\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}
@@ -39,8 +39,15 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
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(2)
+
+beginTableau(3)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $\frac{-3}{5}$ etex);
val(btex $2$ etex);
@@ -52,7 +59,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 2-x}$ etex); plus;barr
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi(x)}$ etex); plus;valBarre(btex 0 etex); moins;nonDefBarre;plus;
endTableau;
-beginTableau(3) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
+beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
val(btex $0$ etex);
val(btex $7$ etex);
@@ -61,7 +68,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
valPos(btex $49$ etex,1);
endTableau;
-beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -73,14 +80,14 @@ endTableau;
-beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+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(6) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+beginTableau(7) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $1$ etex);
@@ -95,7 +102,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
endTableau;
-beginTableau(7) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex);
+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);
@@ -107,19 +114,19 @@ valPos(btex $\frac{3}{2}$
etex,1);valPos(btex $\frac{1}{2}$ etex,0);
endTableau;
-beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
+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(9) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
+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(10) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
+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(11) 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 $+\infty $ etex);
@@ -128,7 +135,7 @@ 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(12) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(13) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\frac{5}{2}$ etex);
@@ -140,7 +147,7 @@ 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$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(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);
+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);
@@ -150,7 +157,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte
valPos(btex $1$ etex,0);
endTableau;
-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);
+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
@@ -161,7 +168,7 @@ valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefB
limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
endTableau;
-beginTableau(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);
+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);
@@ -171,7 +178,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte
valPos(btex $1$ etex,0);
endTableau;
-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);
+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
@@ -182,7 +189,7 @@ valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefB
limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
endTableau;
-beginTableau(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);
+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);
@@ -191,40 +198,17 @@ valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$
$ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0);
endTableau;
-beginTableau(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
- $ 0 $ etex,0.5);valPos(btex $ 1.534460$
- etex,1); valPos(btex $0$ etex,0);
-endTableau;
-
beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
-val(btex $ 0.212584$ etex);
-val(btex $ 0.584635$ etex);
+val(btex $ 0.156422$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);nonDefBarre;limDroite(btex $-\infty$ etex,0); valPos(btex $ -2.818394$
- etex,1);valPos(btex $ -2.944288$
+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 $x$ etex);val(btex $0$ etex);
-val(btex $ 0.001000$ etex);
-val(btex $ 0.002000$ etex);
-val(btex $+\infty $ etex);
-
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);plus;valBarre(btex 0 etex);plus;
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);nonDefBarre;limDroite(btex $ 0.000000$ etex,0); valPos(btex $ 0.000000$
- etex,0.5);valPos(btex $ 0.000000$
- etex,0.5);valPos(btex $+\infty $ etex,1);
-endTableau;
-
-beginTableau(21) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -234,7 +218,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
etex,0);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(22) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+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);
@@ -254,7 +238,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(23) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(22) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
@@ -281,7 +265,7 @@ valPos(btex $\frac{16}{3}$
endTableau;
- beginTableau(24)
+ beginTableau(23)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
@@ -291,7 +275,7 @@ 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(25)
+ beginTableau(24)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
@@ -340,7 +324,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
endTableau;
- beginTableau(26)
+ beginTableau(25)
newLigneVariables(btex $ {x}$ etex);
val(btex $-15$ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -357,7 +341,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
endTableau;
-beginTableau(27)
+beginTableau(26)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
@@ -375,7 +359,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex); moins;no
endTableau;
-beginTableau(28)
+beginTableau(27)
newLigneVariables(btex $ {x}$ etex);
val(btex $-10$ etex);val(btex $-3$ etex);
val(btex $5$ etex);
@@ -390,7 +374,7 @@ endTableau;
-beginTableau(29)
+beginTableau(28)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $-5$ etex);
val(btex $10$ etex);
@@ -401,7 +385,7 @@ endTableau;
-beginTableau(30)
+beginTableau(29)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $2$ etex);
val(btex $5$ etex);
@@ -412,7 +396,7 @@ endTableau;
-beginTableau(31)
+beginTableau(30)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex);
val(btex $\pi $ etex);
@@ -439,12 +423,12 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex);
plus;
valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (3x+2)(5x^2-1)}$ etex);
+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);
+ 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);
@@ -453,7 +437,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+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 $0$
@@ -461,21 +445,21 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+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(36) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+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(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);
+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);
@@ -484,7 +468,7 @@ valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$
$ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0);
endTableau;
-beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
val(btex $2 \pi $ etex);
@@ -494,21 +478,21 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex)
valPos(btex $1$ etex,1);
endTableau;
-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);
+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(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);
+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(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);
+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);
@@ -517,7 +501,7 @@ valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac
$ 1 $ etex,0.5);valPos(btex $0$ etex,0);
endTableau;
-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);
+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);
@@ -526,7 +510,7 @@ valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac
$ 1 $ etex,0.5);valPos(btex $0$ etex,0);
endTableau;
-beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -535,7 +519,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no
etex,1);valPos(btex $-\infty$ etex,0);
endTableau;
- beginTableau(44)
+ beginTableau(43)
newLigneVariables(btex $ {x}$ etex);
val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ etex);
@@ -577,7 +561,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
endTableau;
- beginTableau(45) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ 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 $-\left(e^{-4}\right)-1$
@@ -585,7 +569,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
$ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+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 $2$
@@ -593,7 +577,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$
$ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(48) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -602,14 +586,14 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
etex,1);valPos(btex $0$ etex,0);
endTableau;
-beginTableau(49) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+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(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);
+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);
@@ -618,7 +602,7 @@ nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPo
$ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-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);
+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);
@@ -629,7 +613,7 @@ endTableau;
-beginTableau(52)
+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);
@@ -637,7 +621,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
valBarre(btex 0 etex);
endTableau;
-beginTableau(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+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);
@@ -648,7 +632,7 @@ 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(54) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -657,7 +641,7 @@ 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(55) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+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);
@@ -677,7 +661,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(56) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+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);
@@ -697,7 +681,7 @@ valPos(btex $0$
etex,0.5);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(57) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+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);
@@ -716,7 +700,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
- beginTableau(58)
+ beginTableau(57)
newLigneVariables(btex $ {x}$ etex);
val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);
val(btex $\frac{7 \pi }{6}$ etex);