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-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp187
1 files changed, 77 insertions, 110 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 0ac35f7a1c8..7542f5b669b 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -45,16 +45,11 @@ newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $\frac{-3}{5}$ etex);
val(btex $2$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(45 x\right)-27}$ etex);
- plus;
- valBarre(btex 0 etex);moins;barre;moins;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(45 x\right)-27}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 2-x}$ etex);
- plus;barre;
- plus;valBarre(btex 0 etex);moins;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 2-x}$ etex); plus;barre;plus;valBarre(btex 0 etex);moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi(x)}$ etex);
- plus;valBarre(btex 0 etex); moins;nonDefBarre;plus;
+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);
@@ -181,6 +176,15 @@ 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(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;
+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(16) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $ 0.212584$ etex);
val(btex $ 0.584635$ etex);
@@ -193,7 +197,18 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no
valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(17) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(17) 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(18) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -203,7 +218,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
etex,0);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(18) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(19) 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);
@@ -223,7 +238,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(19) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
@@ -250,7 +265,7 @@ valPos(btex $\frac{16}{3}$
endTableau;
- beginTableau(20)
+ beginTableau(21)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
@@ -260,7 +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(21)
+ beginTableau(22)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
@@ -309,7 +324,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
endTableau;
- beginTableau(22)
+ beginTableau(23)
newLigneVariables(btex $ {x}$ etex);
val(btex $-15$ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -326,7 +341,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
endTableau;
-beginTableau(23)
+beginTableau(24)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
@@ -334,55 +349,32 @@ val(btex $\frac{3}{2}$ etex);
val(btex $2$ etex);
val(btex $4$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
- plus;barre;
- plus;barre;
- plus;
- valBarre(btex 0 etex);moins;barre;
- moins;barre;moins;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex); plus;barre;plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex);
- plus;barre;
- plus;
- valBarre(btex 0 etex);moins;barre;
- moins;barre;
- moins;barre;moins;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex); plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-16}$ etex);
- plus;
- valBarre(btex 0 etex);moins;barre;
- moins;barre;
- moins;barre;
- moins;valBarre(btex 0 etex);plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex);
- moins;barre;
- moins;barre;
- moins;barre;
- moins;
- valBarre(btex 0 etex);plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
- moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;nonDefBarre;plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-16}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins;valBarre(btex 0 etex);plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex); moins;barre;moins;barre;moins;barre;moins; valBarre(btex 0 etex);plus;barre;plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex); moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;nonDefBarre;plus;
endTableau;
-beginTableau(24)
+beginTableau(25)
newLigneVariables(btex $ {x}$ etex);
- val(btex $-\infty $ etex);val(btex $-10$ etex);
+ val(btex $-10$ etex);val(btex $-3$ etex);
+val(btex $5$ etex);
val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex);
- moins;barre;moins;
-
- 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);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex); moins;barre;moins;barre;moins;
+ valBarre(btex 0 etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-5}$ etex); moins;barre;moins;valBarre(btex 0 etex);plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex); valBarre(btex 0 etex);plus;barre;plus;barre;plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+3}$ etex); moins; valBarre(btex 0 etex);plus;barre;plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);nonDefBarre;moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);
endTableau;
-beginTableau(25)
+beginTableau(26)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $-5$ etex);
val(btex $10$ etex);
@@ -393,7 +385,7 @@ endTableau;
-beginTableau(26)
+beginTableau(27)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $2$ etex);
val(btex $5$ etex);
@@ -404,7 +396,7 @@ endTableau;
-beginTableau(27)
+beginTableau(28)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex);
val(btex $\pi $ etex);
@@ -415,28 +407,7 @@ 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(105)
-newLigneVariables(btex $ {x}$ 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);
- 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(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);
+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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPos(btex $-1$
@@ -444,7 +415,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+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);
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 $0$
@@ -452,20 +423,20 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(30) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+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;
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(32) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(33) 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(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);
+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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex);
valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$
@@ -473,7 +444,7 @@ 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(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
val(btex $2 \pi $ etex);
@@ -483,19 +454,19 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex)
valPos(btex $1$ etex,1);
endTableau;
-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);
+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;
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);
+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;
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 $x$ 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(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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$
@@ -503,7 +474,7 @@ 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(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);
+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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$
@@ -511,7 +482,7 @@ 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(39) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -520,7 +491,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no
etex,1);valPos(btex $-\infty$ etex,0);
endTableau;
- beginTableau(40)
+ beginTableau(41)
newLigneVariables(btex $ {x}$ etex);
val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ etex);
@@ -562,7 +533,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
endTableau;
- beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(42) 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 $-\left(e^{-4}\right)-1$
@@ -570,7 +541,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
$ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(43) 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 $2$
@@ -578,7 +549,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$
$ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(44) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(45) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -587,13 +558,13 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
etex,1);valPos(btex $0$ etex,0);
endTableau;
-beginTableau(45) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+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;
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(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);
+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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$
@@ -601,7 +572,7 @@ nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPo
$ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(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);
+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;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$
@@ -611,7 +582,7 @@ endTableau;
-beginTableau(48)
+beginTableau(49)
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);
@@ -619,7 +590,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
valBarre(btex 0 etex);
endTableau;
-beginTableau(49) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
@@ -630,7 +601,7 @@ 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(50) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(51) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -639,7 +610,7 @@ 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(51) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(52) 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);
@@ -659,7 +630,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(52) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(53) 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);
@@ -679,19 +650,18 @@ valPos(btex $0$
etex,0.5);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(53) 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 $\frac{5}{2}$ etex);
val(btex $4$ etex);
val(btex $6$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;valBarre(btex 0 etex);moins;debutNonDefStrict;finNonDefStrict;plus;
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $\sqrt{35}$ 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);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;debutNonDefStrict;finNonDefStrict;plus;
+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(54) 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 $\frac{\pi }{6}$ etex);
val(btex $\frac{3 \pi }{8}$ etex);
@@ -710,34 +680,31 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
valPos(btex $0$ etex,1);
endTableau;
- beginTableau(55)
+ beginTableau(56)
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;
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;
+ plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
endTableau;
- beginTableau(56) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $+\infty $ etex);
+ 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;
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);