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Diffstat (limited to 'Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp')
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp301
1 files changed, 153 insertions, 148 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 5797a66cf34..fa53635eeb2 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -8,7 +8,39 @@ verbatimtex
\renewcommand\cdot{ } % idem pour les cdot
\begin{document}
etex
-beginTableau(0) newLigneVariables(btex $x$ etex);val(btex $-5$ 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 $-5$ etex);
val(btex $0$ etex);
val(btex $7$ etex);
@@ -17,7 +49,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
valPos(btex $49$ etex,1);
endTableau;
-beginTableau(1) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(3) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -29,14 +61,14 @@ endTableau;
-beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(4) 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(3) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+beginTableau(5) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $1$ etex);
@@ -52,7 +84,20 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
endTableau;
-beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(6) 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(7) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -61,7 +106,7 @@ 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 $0$ etex,0);debutNonDef;finNonDef;limDroite(btex $0$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\frac{5}{2}$ etex);
@@ -73,7 +118,7 @@ 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);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(6) 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(9) 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);
@@ -83,7 +128,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte
valPos(btex $1$ etex,0);
endTableau;
-beginTableau(7) 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(10) 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);
@@ -95,7 +140,7 @@ 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(9) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $ 0.212584$ etex);
val(btex $ 0.584635$ etex);
val(btex $+\infty $ etex);
@@ -107,27 +152,27 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no
valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(10) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(13) 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 $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ 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 $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ 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 $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+ 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(11) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(14) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
@@ -155,7 +200,7 @@ valPos(btex $\frac{16}{3}$
endTableau;
- beginTableau(12)
+ beginTableau(15)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
@@ -165,7 +210,7 @@ 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(13)
+ beginTableau(16)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
@@ -173,7 +218,7 @@ val(btex $1$ etex);
val(btex $\sqrt{2}$ etex);
val(btex $\frac{3}{2}$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;barre;
@@ -214,7 +259,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
endTableau;
- beginTableau(14)
+ beginTableau(17)
newLigneVariables(btex $ {x}$ etex);
val(btex $-15$ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -231,7 +276,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
endTableau;
-beginTableau(15)
+beginTableau(18)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
@@ -239,14 +284,14 @@ val(btex $\frac{3}{2}$ etex);
val(btex $2$ etex);
val(btex $4$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;
valBarre(btex 0 etex);moins;barre;
moins;barre;moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4x\right)+5}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex);
plus;barre;
plus;
valBarre(btex 0 etex);moins;barre;
@@ -266,32 +311,16 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex);
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(16)
-newLigneVariables(btex $ {x}$ etex);
- val(btex $-\infty $ 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 $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
- plus;nonDefBarre; moins;
- valBarre(btex 0 etex);
+ moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;
endTableau;
-beginTableau(17)
+beginTableau(19)
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);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+5)}$ etex);
plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);
endTableau;
@@ -301,12 +330,12 @@ newLigneVariables(btex $ {x}$ etex);
val(btex $-\frac{\sqrt{5}}{5}$ etex);
val(btex $\frac{\sqrt{5}}{5}$ etex);
val(btex $50$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex);
moins;
valBarre(btex 0 etex);plus;barre;
plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex);
+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;
@@ -316,7 +345,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex);
endTableau;
- beginTableau(18) 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(20) 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 $-1$
@@ -324,7 +353,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(21) 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 $0$
@@ -332,13 +361,13 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;
@@ -346,7 +375,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
endTableau;
-beginTableau(23) 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(25) 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 $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins;valBarre(btex$ $ etex);moins; 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 $ 1/2 $ etex,0.5); valPos(btex $1$
@@ -354,9 +383,9 @@ 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(24) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
-val(btex $2\pi $ etex);
+val(btex $2 \pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $1$ etex,1); valPos(btex $-1$
@@ -364,22 +393,22 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
valPos(btex $1$ etex,1);
endTableau;
-beginTableau(25) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
+beginTableau(27) 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 $\hbox{ Signe de }\atop{\displaystyle h'(t)}$ etex); plus;valBarre(btex$ $ etex);plus; nonDefBarre;plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle h}$ 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(26) 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(28) 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 $\frac{3}{4} \times \sqrt{3}$
+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(27) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -389,15 +418,15 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no
endTableau;
- beginTableau(28)
+ beginTableau(30)
newLigneVariables(btex $ {x}$ etex);
- val(btex $-10$ etex);val(btex $-\left(\frac{1}{2} \times \sqrt{5}\right)+\frac{-3}{2}$ etex);
+ val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ etex);
-val(btex $\frac{1}{2} \times \sqrt{5}+\frac{-3}{2}$ 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 $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;barre;
@@ -419,7 +448,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex);
plus;barre;
plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3x+1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex);
plus;
valBarre(btex 0 etex);moins;barre;
moins;
@@ -431,7 +460,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
endTableau;
- beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(31) 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 $-\left(e^{-4}\right)-1$
@@ -439,7 +468,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
$ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(30) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(32) 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 $2$
@@ -447,7 +476,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$
$ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -457,13 +486,13 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
endTableau;
-beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+beginTableau(35) 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(34) 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(36) 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 $\frac{1}{4}$
@@ -473,15 +502,15 @@ endTableau;
-beginTableau(35)
+beginTableau(37)
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);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
valBarre(btex 0 etex);plus;
valBarre(btex 0 etex);
endTableau;
-beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
@@ -492,7 +521,7 @@ 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(37) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -501,38 +530,38 @@ 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);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(38) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(40) 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 $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ 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 $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ 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 $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+ 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(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
+beginTableau(41) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{3}$ etex);
val(btex $\pi $ etex);
-val(btex $\frac{5}{3} \times \pi $ etex);
-val(btex $2\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 $-\left(\sqrt{3}\right)-\left(\frac{1}{-3} \times \pi \right)$
+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 $\sqrt{3}+\frac{5}{3} \times \pi $
- etex,1);valPos(btex $2\pi $ etex,0);
+ 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 $0$
@@ -542,7 +571,7 @@ valPos(btex $0$
etex,0.5);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\frac{5}{2}$ etex);
@@ -554,75 +583,51 @@ 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(41) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
-val(btex $\frac{2}{5}$ etex);
-val(btex $10$ etex);
-
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $\frac{169}{2}$ etex,1); valPos(btex $\frac{58}{5}$
- etex,0);
-valPos(btex $242$ etex,1);
-endTableau;
-
-beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ etex);
-
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-26047$ etex,0); valPos(btex $\frac{14}{243} \times \sqrt{7}+\frac{-1681}{243}$
- etex,1);valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{-1681}{243}$
- etex,0);
-valPos(btex $22033$ etex,1);
-endTableau;
+beginTableau(43) 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);
-beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ 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 $-\left(3 \cos\left(\frac{\pi }{8}\right)\right)$ 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);
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $26047$ etex,1); valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{1681}{243}$
+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 $\frac{14}{243} \times \sqrt{7}+\frac{1681}{243}$
- etex,1);valPos(btex $-22033$ etex,0);
-
+valPos(btex $0$ etex,1);
endTableau;
-
-
-beginTableau(44)
-newLigneVariables(btex $\displaystyle {x}$ etex);
- val(btex $-20$ etex);val(btex $ 1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(3x^{3}\right)+5x^{2}-\left(2x\right)+7}$ etex);
- plus;valBarre(btex 0 etex); moins;
+ beginTableau(44)
+newLigneVariables(btex $ {x}$ etex);
+ val(btex $0$ etex);val(btex $\frac{\pi }{3}$ 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);plus;
+ valBarre(btex 0 etex);moins;barre;
+ moins;
+ valBarre(btex 0 etex);plus;barre;plus;
-endTableau;
-
-
-
-beginTableau(45)
-newLigneVariables(btex $\displaystyle {x}$ etex);
- val(btex $-20$ etex);val(btex $ 1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x^{3}-\left(5x^{2}\right)+2x-7}$ etex);
- moins;valBarre(btex 0 etex); plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex);
+ plus;barre;
+ 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); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
endTableau;
-beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $ 0.000000$ 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 $\frac{1}{2}$ etex,0); valPos(btex $ 1.000000$
- etex,1);valPos(btex
- $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
-endTableau;
-
-beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
-val(btex $ 0.639232$ 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 $-\infty$ etex,0); valPos(btex $ 0.967397$
- etex,1);valPos(btex $-\infty$ etex,0);
-
-endTableau;
-
+ \ No newline at end of file