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-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp140
1 files changed, 92 insertions, 48 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 559dd1f58ce..0ac35f7a1c8 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -2,10 +2,7 @@ input tableauVariation;
verbatimtex
%&latex
\documentclass{article}
-%\usepackage[upright]{fourier}% ou mathpazo, lmodern, etc. ou rien !
-\usepackage[boldsans]{ccfonts}
-\usepackage{beton,euler}
-\usepackage{luximono}
+\usepackage[upright]{fourier}% ou mathpazo, lmodern, etc. ou rien !
\usepackage{amsmath}
\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas
\renewcommand\cdot{ } % idem pour les cdot
@@ -136,13 +133,11 @@ 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 $\alpha_2$ etex);val(btex $1$ etex);val(btex $\alpha_3$ 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;valBarre(btex $ $ etex);moins;nonDefBarre;moins;valBarre(btex $ $ etex);moins;
+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;
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);valPos(btex
- $ 10 $ etex,0.5);
- limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex
+ 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;
@@ -158,7 +153,35 @@ 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(13) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+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;
+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(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);
+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(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;
+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(16) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $ 0.212584$ etex);
val(btex $ 0.584635$ etex);
val(btex $+\infty $ etex);
@@ -170,7 +193,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no
valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(14) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(17) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -180,7 +203,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
etex,0);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(15) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(18) 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);
@@ -200,7 +223,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(16) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(19) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
@@ -227,7 +250,7 @@ valPos(btex $\frac{16}{3}$
endTableau;
- beginTableau(17)
+ beginTableau(20)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
@@ -237,7 +260,7 @@ 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(18)
+ beginTableau(21)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
@@ -286,7 +309,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
endTableau;
- beginTableau(19)
+ beginTableau(22)
newLigneVariables(btex $ {x}$ etex);
val(btex $-15$ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -303,7 +326,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
endTableau;
-beginTableau(20)
+beginTableau(23)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
@@ -342,7 +365,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
endTableau;
-beginTableau(21)
+beginTableau(24)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -359,7 +382,7 @@ endTableau;
-beginTableau(22)
+beginTableau(25)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $-5$ etex);
val(btex $10$ etex);
@@ -370,7 +393,7 @@ endTableau;
-beginTableau(23)
+beginTableau(26)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $2$ etex);
val(btex $5$ etex);
@@ -381,7 +404,7 @@ endTableau;
-beginTableau(24)
+beginTableau(27)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex);
val(btex $\pi $ etex);
@@ -394,8 +417,8 @@ 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 $-50$ etex);val(btex $\frac{-2}{3}$ etex);
+val(btex $\frac{(-\left(\sqrt{5}\right))}{5}$ etex);
val(btex $\frac{\sqrt{5}}{5}$ etex);
val(btex $50$ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex);
@@ -413,8 +436,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex);
endTableau;
-
-beginTableau(25) 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(28) 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 $-1$
@@ -422,7 +444,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(29) 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 $0$
@@ -430,20 +452,20 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(27) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(30) 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(29) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(32) 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(30) 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(33) 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 $1$
@@ -451,7 +473,7 @@ 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(31) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
val(btex $2 \pi $ etex);
@@ -461,13 +483,27 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex)
valPos(btex $1$ etex,1);
endTableau;
-beginTableau(32) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
+beginTableau(35) 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(36) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\mbox{atan}\left(7\right)$ 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(33) 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(37) 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(38) 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 $\frac{3 \sqrt{3}}{4}$
@@ -475,7 +511,7 @@ 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(34) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -484,7 +520,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no
etex,1);valPos(btex $-\infty$ etex,0);
endTableau;
- beginTableau(35)
+ beginTableau(40)
newLigneVariables(btex $ {x}$ etex);
val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ etex);
@@ -526,7 +562,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
endTableau;
- beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(41) 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 $-\left(e^{-4}\right)-1$
@@ -534,7 +570,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
$ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(42) 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 $2$
@@ -542,7 +578,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$
$ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(44) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -551,13 +587,21 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
etex,1);valPos(btex $0$ etex,0);
endTableau;
-beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+beginTableau(45) 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(41) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
+nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$
+ etex,1);valPos(btex
+ $ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0);
+endTableau;
+
+beginTableau(47) 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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$
@@ -567,7 +611,7 @@ endTableau;
-beginTableau(42)
+beginTableau(48)
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);
@@ -575,7 +619,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
valBarre(btex 0 etex);
endTableau;
-beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(49) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
@@ -586,7 +630,7 @@ 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(44) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -595,7 +639,7 @@ 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(45) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(51) 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);
@@ -615,7 +659,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(46) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(52) 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);
@@ -635,7 +679,7 @@ valPos(btex $0$
etex,0.5);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(47) 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 $\frac{5}{2}$ etex);
@@ -647,7 +691,7 @@ 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);valPos(btex$\sqrt{21}$etex,1);limGauche(btex $\sqrt{15}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{35}$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(48) 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 $\frac{\pi }{6}$ etex);
val(btex $\frac{3 \pi }{8}$ etex);
@@ -666,7 +710,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
- beginTableau(49)
+ beginTableau(55)
newLigneVariables(btex $ {x}$ etex);
val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);
val(btex $\frac{\pi }{3}$ etex);
@@ -693,7 +737,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f (x)}$ etex);
endTableau;
- beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $+\infty $ etex);
+ beginTableau(56) 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);