add two first valid sequences
This commit is contained in:
@@ -0,0 +1,32 @@
|
||||
// préambule asymptote
|
||||
usepackage("amsmath,amssymb");
|
||||
usepackage("inputenc","utf8");
|
||||
usepackage("icomma");
|
||||
|
||||
import lib_jl;
|
||||
|
||||
unitsize(1cm,1cm);
|
||||
|
||||
limits(-5.5,5.5);
|
||||
ylimits(-5.5,5.5);
|
||||
|
||||
xaxis(BottomTop,xmin=-5.5,xmax=5.5,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
yaxis(LeftRight,ymin=-5.5,ymax=5.5,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
|
||||
real F(real x) {return 1/10*x^3+1/10*x^2-1/5*x+1;}
|
||||
draw(graph(F,-6,6,n=400),linewidth(1pt)+red+solid);
|
||||
|
||||
real G(real x) {return 0.3*(x-1)+1;}
|
||||
draw(graph(G,-6,6,n=400),linewidth(1pt)+darkblue+solid);
|
||||
|
||||
xlimits(-5.5,5.5,Crop);
|
||||
ylimits(-5.5,5.5,Crop);
|
||||
|
||||
xaxis(axis=YEquals(0),xmin=-5.5,xmax=5.5,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
yaxis(axis=XEquals(0),ymin=-5.5,ymax=5.5,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
|
||||
label(scale(1.25)*"$\mathcal{C}_f$", (4,5));
|
||||
label(scale(1.25)*"$\mathcal{T}$", (4,2), N);
|
||||
|
||||
shipout(bbox(0.1cm,0.1cm,white));
|
||||
|
||||
@@ -0,0 +1,23 @@
|
||||
<?xml version="1.0" encoding="UTF-8"?>
|
||||
<Courbes>
|
||||
<UnitX>1</UnitX>
|
||||
<Xmin>-3.5</Xmin>
|
||||
<Xmax>10.5</Xmax>
|
||||
<UnitY>1</UnitY>
|
||||
<Ymin>-.75</Ymin>
|
||||
<Ymax>8.5</Ymax>
|
||||
<GradX>1</GradX>
|
||||
<GradY>1</GradY>
|
||||
<GrilleX>1</GrilleX>
|
||||
<GrilleY>1</GrilleY>
|
||||
<Axes>1</Axes>
|
||||
<Labels>1</Labels>
|
||||
<Repere>0</Repere>
|
||||
<Grille>1</Grille>
|
||||
<Supplement></Supplement>
|
||||
<Fonctions>x^2#sqrt(x)</Fonctions>
|
||||
<Varmins>-4#0</Varmins>
|
||||
<Varmaxs>11#11</Varmaxs>
|
||||
<Couleurs>noir#noir</Couleurs>
|
||||
<Styles>ligne#ligne</Styles>
|
||||
</Courbes>
|
||||
Binary file not shown.
Binary file not shown.
|
After Width: | Height: | Size: 85 KiB |
File diff suppressed because it is too large
Load Diff
|
After Width: | Height: | Size: 168 KiB |
Binary file not shown.
|
After Width: | Height: | Size: 43 KiB |
Binary file not shown.
|
After Width: | Height: | Size: 53 KiB |
@@ -0,0 +1,30 @@
|
||||
// préambule asymptote
|
||||
usepackage("amsmath,amssymb");
|
||||
usepackage("inputenc","utf8");
|
||||
usepackage("icomma");
|
||||
|
||||
import lib_jl;
|
||||
|
||||
unitsize(1cm,1cm);
|
||||
xlimits(-5,5);
|
||||
ylimits(-5,3);
|
||||
|
||||
xaxis(BottomTop,xmin=-5,xmax=5,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
yaxis(LeftRight,ymin=-5,ymax=3,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
|
||||
real F(real x) {return log(x+1);}
|
||||
draw(graph(F,-0.9999999999,6,n=400),linewidth(1.5pt)+black+solid);
|
||||
|
||||
point pA=(-1,-1), pB=(-1,1);
|
||||
draw(line(pA,pB),linewidth(1.5pt)+red+dashed);
|
||||
label(rotate(90)*"$\boldsymbol{ x=-1 }$", (-1,-4)-.5, fontsize(12pt)+red);
|
||||
|
||||
xlimits(-5,5,Crop);
|
||||
ylimits(-5,5,Crop);
|
||||
|
||||
xaxis(axis=YEquals(0),xmin=-5,xmax=5,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=10,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
yaxis(axis=XEquals(0),ymin=-5,ymax=3,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
|
||||
|
||||
shipout(bbox(0.1cm,0.1cm,white));
|
||||
|
||||
Binary file not shown.
Binary file not shown.
|
After Width: | Height: | Size: 41 KiB |
File diff suppressed because it is too large
Load Diff
|
After Width: | Height: | Size: 100 KiB |
@@ -0,0 +1,35 @@
|
||||
// préambule asymptote
|
||||
usepackage("amsmath,amssymb");
|
||||
usepackage("inputenc","utf8");
|
||||
usepackage("icomma");
|
||||
|
||||
import lib_jl;
|
||||
|
||||
unitsize(0.5cm,0.125cm);
|
||||
xlimits(-3,6);
|
||||
ylimits(-20,20);
|
||||
|
||||
xaxis(BottomTop,xmin=-3,xmax=6,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(.8)+dotted);
|
||||
yaxis(LeftRight,ymin=-20,ymax=20,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(.8)+dotted);
|
||||
|
||||
real F(real x) {return 2/(x-3)+5;}
|
||||
draw(graph(F,-4,2.999999,n=400),linewidth(1.5pt)+black+solid);
|
||||
real G(real x) {return 2/(x-3)+5;}
|
||||
draw(graph(G,3.000001,6,n=400),linewidth(1.5pt)+black+solid);
|
||||
|
||||
point pA=(3,-10), pB=(3,10);
|
||||
draw(line(pA,pB),linewidth(1.5pt)+red+dashed);
|
||||
label(rotate(90)*"$\boldsymbol{x=3}$", (3,-10)+.5, fontsize(8pt)+red);
|
||||
point pA=(-3,5), pB=(3,5);
|
||||
draw(line(pA,pB),linewidth(1.5pt)+heavygreen+dashed);
|
||||
label("$\boldsymbol{y=5}$", (-2,6), fontsize(8pt)+heavygreen);
|
||||
|
||||
xlimits(-3,6,Crop);
|
||||
ylimits(-20,20,Crop);
|
||||
|
||||
xaxis(axis=YEquals(0),xmin=-3,xmax=6,Ticks(scale(.4)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
yaxis(axis=XEquals(0),ymin=-20,ymax=20,Ticks(scale(.4)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=10,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
|
||||
|
||||
shipout(bbox(0.1cm,0.1cm,white));
|
||||
|
||||
Binary file not shown.
Binary file not shown.
|
After Width: | Height: | Size: 39 KiB |
@@ -0,0 +1,116 @@
|
||||
<?xml version="1.0" standalone="no"?>
|
||||
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"
|
||||
"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
|
||||
<svg version="1.0" xmlns="http://www.w3.org/2000/svg"
|
||||
width="582.000000pt" height="640.000000pt" viewBox="0 0 582.000000 640.000000"
|
||||
preserveAspectRatio="xMidYMid meet">
|
||||
<metadata>
|
||||
Created by potrace 1.16, written by Peter Selinger 2001-2019
|
||||
</metadata>
|
||||
<g transform="translate(0.000000,640.000000) scale(0.100000,-0.100000)"
|
||||
fill="#000000" stroke="none">
|
||||
<path d="M1628 6209 c-19 -11 -25 -49 -8 -49 6 0 10 9 10 20 0 24 25 27 34 4
|
||||
7 -18 -4 -42 -33 -68 -30 -28 -26 -36 19 -36 35 0 40 3 39 23 0 12 -3 16 -6
|
||||
10 -2 -7 -14 -13 -26 -13 -20 0 -19 1 6 28 32 33 35 67 8 82 -23 12 -22 12
|
||||
-43 -1z"/>
|
||||
<path d="M1728 6208 c-9 -7 -19 -29 -23 -48 -10 -61 33 -110 70 -80 21 17 20
|
||||
104 -1 124 -19 19 -25 20 -46 4z m37 -64 c0 -38 -4 -49 -17 -52 -15 -3 -18 4
|
||||
-18 46 0 27 3 52 7 56 16 16 28 -4 28 -50z"/>
|
||||
<path d="M1922 6158 c3 -20 10 -23 56 -26 28 -2 52 -7 52 -12 0 -25 -32 -154
|
||||
-55 -220 -39 -110 -40 -119 -19 -127 13 -5 26 4 51 33 l33 39 0 -567 0 -567
|
||||
-57 -3 c-54 -3 -58 -5 -58 -28 0 -23 4 -25 58 -28 l57 -3 0 -709 0 -710 -270
|
||||
0 -270 0 0 48 c0 50 -13 74 -36 65 -10 -3 -14 -22 -14 -59 l0 -54 -270 0 -270
|
||||
0 0 49 c0 56 -19 82 -45 61 -10 -8 -15 -30 -15 -61 l0 -49 -265 0 -265 0 0 49
|
||||
c0 56 -19 82 -45 61 -12 -10 -15 -38 -15 -134 0 -66 5 -128 10 -136 14 -22 44
|
||||
0 48 35 l4 28 165 -6 c92 -4 210 -7 263 -7 l97 0 7 -31 c5 -25 10 -30 28 -27
|
||||
17 2 24 11 26 32 l4 29 111 -6 c62 -4 181 -7 265 -7 l152 0 10 -25 c12 -31 40
|
||||
-33 47 -4 6 22 7 22 202 15 108 -3 229 -9 269 -13 l72 -6 0 -663 0 -664 -61 0
|
||||
c-57 0 -60 -1 -57 -23 3 -19 10 -22 61 -25 l57 -3 0 -709 0 -709 -57 -3 c-51
|
||||
-3 -58 -6 -61 -25 -3 -23 -3 -23 137 -23 86 0 142 4 146 10 13 22 -17 40 -66
|
||||
40 l-49 0 0 710 0 710 49 0 c49 0 79 18 66 40 -3 5 -31 10 -61 10 l-54 0 0
|
||||
666 0 665 53 -5 c28 -3 93 -8 142 -11 367 -24 696 -79 861 -143 34 -14 50 -26
|
||||
52 -41 4 -23 22 -29 22 -7 0 9 7 12 20 9 27 -7 25 -16 -10 -56 -16 -19 -30
|
||||
-37 -30 -41 0 -3 18 -6 40 -6 35 0 40 3 39 23 0 12 -3 16 -6 10 -2 -7 -14 -13
|
||||
-26 -13 -20 0 -20 0 3 25 13 14 28 25 34 25 25 0 129 -95 175 -160 50 -72 103
|
||||
-195 140 -325 51 -182 97 -613 121 -1155 8 -179 29 -862 30 -948 0 -8 9 -12
|
||||
23 -10 21 3 22 6 22 118 -1 163 -15 617 -30 975 -21 469 -80 962 -131 1084 -8
|
||||
19 -17 48 -20 65 -8 50 -78 187 -127 252 -120 157 -336 259 -657 310 -163 25
|
||||
-150 19 -150 75 l0 49 270 0 269 0 3 -57 c3 -50 6 -58 23 -58 17 0 20 8 23 58
|
||||
l3 57 269 0 269 0 3 -57 c3 -50 6 -58 23 -58 17 0 20 8 23 58 l3 57 269 0 270
|
||||
0 0 -55 c0 -42 4 -57 16 -62 23 -8 34 14 34 70 l0 47 270 0 269 0 3 -57 c3
|
||||
-50 6 -58 23 -58 17 0 20 8 23 58 l3 57 126 0 126 0 -36 -27 c-35 -27 -47 -56
|
||||
-27 -68 5 -3 49 8 97 25 81 29 205 60 238 60 10 0 15 -16 17 -52 3 -45 6 -53
|
||||
23 -53 19 0 20 8 23 134 1 74 -1 138 -6 143 -5 5 -19 4 -34 -2 -18 -9 -86 -7
|
||||
-284 9 -490 39 -770 104 -942 218 -224 148 -322 419 -377 1037 -29 327 -38
|
||||
484 -50 896 -3 107 -8 238 -9 290 -2 52 -4 157 -5 233 l-1 137 -25 0 -25 0 0
|
||||
-127 c0 -153 16 -632 30 -938 27 -566 79 -975 151 -1182 72 -210 189 -352 359
|
||||
-436 130 -64 316 -113 533 -142 l47 -6 0 -50 0 -49 -270 0 -270 0 0 48 c0 50
|
||||
-13 74 -36 65 -10 -3 -14 -22 -14 -59 l0 -54 -270 0 -270 0 0 54 c0 40 -4 55
|
||||
-16 60 -27 10 -34 -3 -34 -60 l0 -54 -270 0 -270 0 0 49 c0 49 -18 79 -40 66
|
||||
-5 -3 -10 -31 -10 -61 l0 -54 -270 0 -270 0 0 54 c0 40 -4 55 -16 60 -27 10
|
||||
-34 -3 -34 -60 l0 -54 -270 0 -270 0 0 710 0 710 49 0 c56 0 82 19 61 45 -8
|
||||
10 -30 15 -61 15 l-49 0 0 563 1 562 27 -33 c31 -37 62 -43 62 -11 0 12 -15
|
||||
65 -34 118 -19 53 -37 118 -41 145 -4 27 -9 55 -12 62 -4 11 7 14 50 14 41 0
|
||||
56 4 61 16 3 9 4 20 0 25 -3 5 -68 9 -145 9 -140 0 -140 0 -137 -22z m3243
|
||||
-2848 c23 0 44 -11 76 -40 l44 -40 -122 0 -123 0 0 46 0 47 46 -7 c26 -3 61
|
||||
-6 79 -6z m382 -30 c28 0 33 -3 33 -24 l0 -23 -87 18 c-133 27 -156 41 -59 34
|
||||
43 -3 94 -5 113 -5z m-4744 -107 c-29 -2 -78 -2 -110 0 -32 2 -8 3 52 3 61 0
|
||||
87 -1 58 -3z m647 -3 c0 -11 -199 -12 -410 -1 -119 7 -103 8 138 9 176 1 272
|
||||
-2 272 -8z m590 -16 c0 -25 -2 -26 -37 -21 -21 4 -143 9 -270 13 -185 6 -233
|
||||
10 -233 21 0 10 50 13 270 13 l270 0 0 -26z m590 -19 c0 -53 20 -50 -202 -30
|
||||
-90 8 -202 17 -250 20 -85 7 -88 8 -88 31 l0 24 270 0 270 0 0 -45z"/>
|
||||
<path d="M1630 4725 c-19 -11 -21 -14 -7 -15 14 0 17 -9 17 -49 0 -30 -5 -51
|
||||
-12 -54 -7 -3 5 -5 27 -5 22 0 32 2 23 5 -13 3 -18 18 -20 68 l-3 63 -25 -13z"/>
|
||||
<path d="M1728 4728 c-9 -7 -19 -29 -23 -48 -10 -61 33 -110 70 -80 21 17 20
|
||||
104 -1 124 -19 19 -25 20 -46 4z m37 -64 c0 -38 -4 -49 -17 -52 -15 -3 -18 4
|
||||
-18 46 0 27 3 52 7 56 16 16 28 -4 28 -50z"/>
|
||||
<path d="M348 2909 c-20 -11 -25 -43 -5 -36 6 2 11 10 10 16 -2 6 4 11 12 11
|
||||
8 0 15 -9 15 -20 0 -11 -7 -20 -15 -20 -22 0 -18 -17 6 -23 28 -7 21 -41 -9
|
||||
-45 -16 -3 -20 0 -16 12 4 11 1 16 -10 16 -20 0 -20 -14 0 -34 19 -19 48 -21
|
||||
62 -3 16 19 10 116 -8 127 -18 12 -21 12 -42 -1z"/>
|
||||
<path d="M1530 2905 c-19 -11 -21 -14 -7 -15 14 0 17 -9 17 -49 0 -30 -5 -51
|
||||
-12 -54 -7 -3 5 -5 27 -5 22 0 32 2 23 5 -13 3 -18 18 -20 68 l-3 63 -25 -13z"/>
|
||||
<path d="M2636 2904 c-11 -8 -14 -14 -8 -14 17 0 16 -97 0 -103 -7 -3 5 -5 27
|
||||
-5 22 0 32 2 23 5 -13 3 -18 18 -20 68 -3 61 -4 63 -22 49z"/>
|
||||
<path d="M3808 2909 c-19 -11 -25 -39 -8 -39 6 0 10 7 10 15 0 8 7 15 15 15 8
|
||||
0 15 -9 15 -20 0 -11 -7 -20 -15 -20 -22 0 -18 -17 6 -23 28 -7 21 -41 -9 -45
|
||||
-16 -3 -20 0 -16 12 4 11 1 16 -10 16 -20 0 -20 -14 0 -34 19 -19 48 -21 62
|
||||
-3 16 19 10 116 -8 127 -18 12 -21 12 -42 -1z"/>
|
||||
<path d="M4990 2876 c0 -34 2 -37 16 -25 13 10 17 10 25 -2 5 -8 8 -23 7 -34
|
||||
-3 -23 -38 -34 -38 -11 0 8 -4 18 -10 21 -6 3 -10 -5 -10 -19 0 -29 29 -42 60
|
||||
-26 27 15 27 65 0 80 -11 6 -25 8 -30 5 -6 -3 -10 1 -10 9 0 8 10 16 22 18 33
|
||||
5 32 23 -2 23 -28 0 -30 -2 -30 -39z"/>
|
||||
<path d="M5594 2902 c-27 -22 -35 -45 -27 -83 7 -37 44 -59 68 -39 30 25 13
|
||||
90 -24 90 -11 0 -11 -4 3 -19 20 -22 18 -56 -4 -56 -11 0 -15 13 -17 47 -1 44
|
||||
15 78 25 50 5 -17 32 -15 32 2 0 8 -7 17 -16 20 -19 7 -15 9 -40 -12z"/>
|
||||
<path d="M927 2904 c-11 -11 -8 -44 3 -44 6 0 10 9 10 20 0 24 25 27 34 4 7
|
||||
-18 -4 -42 -33 -68 -30 -28 -26 -36 19 -36 35 0 40 3 39 23 0 12 -3 16 -6 10
|
||||
-2 -7 -14 -13 -26 -13 -20 0 -19 2 7 29 37 39 33 75 -9 79 -17 2 -34 0 -38 -4z"/>
|
||||
<path d="M4411 2866 c-17 -25 -31 -47 -31 -50 0 -3 12 -6 26 -6 19 0 25 -4 20
|
||||
-15 -4 -11 2 -15 20 -15 16 0 23 4 18 11 -3 6 0 15 7 20 10 6 11 9 2 9 -8 0
|
||||
-13 15 -13 39 0 22 -4 42 -9 45 -4 3 -22 -14 -40 -38z m29 -16 c0 -23 -4 -30
|
||||
-20 -30 -20 0 -20 1 -5 30 9 17 18 30 20 30 3 0 5 -13 5 -30z"/>
|
||||
<path d="M170 2830 c0 -6 28 -10 65 -10 37 0 65 4 65 10 0 6 -28 10 -65 10
|
||||
-37 0 -65 -4 -65 -10z"/>
|
||||
<path d="M760 2830 c0 -6 28 -10 65 -10 37 0 65 4 65 10 0 6 -28 10 -65 10
|
||||
-37 0 -65 -4 -65 -10z"/>
|
||||
<path d="M1360 2830 c0 -6 28 -10 65 -10 37 0 65 4 65 10 0 6 -28 10 -65 10
|
||||
-37 0 -65 -4 -65 -10z"/>
|
||||
<path d="M1630 1785 c-19 -11 -21 -14 -7 -15 14 0 17 -9 17 -49 0 -30 -5 -51
|
||||
-12 -54 -7 -3 5 -5 27 -5 22 0 32 2 23 5 -13 3 -18 18 -20 68 l-3 63 -25 -13z"/>
|
||||
<path d="M1728 1788 c-9 -7 -19 -29 -23 -48 -10 -61 33 -110 70 -80 21 17 20
|
||||
104 -1 124 -19 19 -25 20 -46 4z m37 -64 c0 -38 -4 -49 -17 -52 -15 -3 -18 4
|
||||
-18 46 0 27 3 52 7 56 16 16 28 -4 28 -50z"/>
|
||||
<path d="M1465 1710 c-4 -6 17 -10 54 -10 34 0 61 4 61 10 0 6 -24 10 -54 10
|
||||
-30 0 -58 -4 -61 -10z"/>
|
||||
<path d="M1628 309 c-19 -11 -25 -39 -8 -39 6 0 10 7 10 15 0 20 26 19 34 -1
|
||||
7 -18 -4 -42 -33 -68 -30 -28 -26 -36 19 -36 35 0 40 3 39 23 0 12 -3 16 -6
|
||||
10 -2 -7 -14 -13 -26 -13 -20 0 -19 1 6 28 32 33 35 67 8 82 -23 12 -22 12
|
||||
-43 -1z"/>
|
||||
<path d="M1728 308 c-9 -7 -19 -29 -23 -48 -10 -61 33 -110 70 -80 21 17 20
|
||||
104 -1 124 -19 19 -25 20 -46 4z m37 -64 c0 -38 -4 -49 -17 -52 -15 -3 -18 4
|
||||
-18 46 0 27 3 52 7 56 16 16 28 -4 28 -50z"/>
|
||||
<path d="M1450 230 c0 -6 28 -10 65 -10 37 0 65 4 65 10 0 6 -28 10 -65 10
|
||||
-37 0 -65 -4 -65 -10z"/>
|
||||
</g>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 7.4 KiB |
@@ -0,0 +1,30 @@
|
||||
// préambule asymptote
|
||||
usepackage("amsmath,amssymb");
|
||||
usepackage("inputenc","utf8");
|
||||
usepackage("icomma");
|
||||
|
||||
import lib_jl;
|
||||
|
||||
unitsize(1cm,1cm);
|
||||
xlimits(-2,7);
|
||||
ylimits(-3,5);
|
||||
|
||||
xaxis(BottomTop,xmin=-2,xmax=7,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
yaxis(LeftRight,ymin=-3,ymax=5,Ticks("%",extend=true,Step=1),p=linewidth(1pt)+gray(0)+dotted);
|
||||
|
||||
real F(real x) {return x-3+1/x;}
|
||||
draw(graph(F,-0.9999999999,8,n=400),linewidth(1.5pt)+black+solid);
|
||||
real G(real x) {return x-3;}
|
||||
draw(graph(G,-0.9999999999,8,n=400),linewidth(1.5pt)+red+solid+dashed);
|
||||
|
||||
label(rotate(45)*"$\boldsymbol{ y = x-3 }$", (5,2)+.5, fontsize(12pt)+red);
|
||||
|
||||
xlimits(-2,7,Crop);
|
||||
ylimits(-3,5,Crop);
|
||||
|
||||
xaxis(axis=YEquals(0),xmin=-2,xmax=7,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=10,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
yaxis(axis=XEquals(0),ymin=-3,ymax=5,Ticks(scale(.7)*Label(),beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
|
||||
|
||||
|
||||
shipout(bbox(0.1cm,0.1cm,white));
|
||||
|
||||
Binary file not shown.
Binary file not shown.
|
After Width: | Height: | Size: 5.2 KiB |
File diff suppressed because it is too large
Load Diff
|
After Width: | Height: | Size: 68 KiB |
Binary file not shown.
@@ -0,0 +1 @@
|
||||
../images/
|
||||
@@ -0,0 +1,93 @@
|
||||
% !TeX root = prof_-_etude_de_fonction_-_2023.1.tex
|
||||
|
||||
\partie{Rappels : dérivation}
|
||||
|
||||
\sspartie{Nombre dérivé, tangente}
|
||||
|
||||
\noindent
|
||||
\begin{multicols}{2}
|
||||
\noindent
|
||||
On considère une fonction $f$ définie sur un intervalle $I$, sa courbe représentative $\ronde{C}_f$ dans un repère orthogonal, et un réel $a$ dans $I$.
|
||||
|
||||
Si $\ronde{C}_f$ admet une tangente $\mathsf{T}$ au point d'abscisse $a$ non parallèle à l'axe des abscisses, on dit que $f$ est dérivable en $a$.
|
||||
|
||||
Le coefficient directeur de la tangente $\mathsf{T}$ au point $a$ est le nombre dérivé $f^{\prime}(a)$.\\\\
|
||||
\columnbreak
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=.6]{fig1.pdf}
|
||||
\end{center}
|
||||
\end{multicols}
|
||||
|
||||
\medskip
|
||||
|
||||
\begin{propriete}[équation de la tangente]
|
||||
La tangente $\mathsf{T}$ à $\ronde{C}_f$ au point de coordonnées $\coord{a, f(a)}$ a pour équation $y = f^{\prime}(a)(x - a) + f(a)$.
|
||||
\end{propriete}
|
||||
|
||||
\sspartie{Fonction dérivée et dérivées usuelles}
|
||||
|
||||
\noindent
|
||||
On dit que la fonction \textbf{$\boldsymbol{f}$ est dérivable sur l'intervalle $I$} si elle est dérivable en tout point $a$ de $I$.\\
|
||||
|
||||
\noindent
|
||||
La \textbf{fonction dérivée de $\boldsymbol{f}$} est notée $f^{\prime}$ et correspond à la fonction qui à tout réel $x$ de $I$, associe le nombre $f^{\prime}(x)$.
|
||||
|
||||
\medskip
|
||||
|
||||
\ssspartie{Dérivées des fonctions usuelles}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabularx}{.7\textwidth}{| C{4.5cm} | >{\centering\arraybackslash}X | C{4.5cm} |}
|
||||
\hline
|
||||
\textbf{\small$ \boldsymbol{f(x)} $} & \textbf{\footnotesize est dérivable sur ...}\vspace{.2em} & \textbf{\small$ \boldsymbol{f^{\prime}(x)} $} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex} $ k $ (constante) & $ \mathbb{R} $ & \rule[-1ex]{0pt}{5ex}$ 0 \vspace{1ex}$ \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ x $ & $ \mathbb{R} $ & \rule[-1ex]{0pt}{5ex}$ 1 \vspace{1ex}$ \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ x^n $ où $ n \ge 1 $ & $ \mathbb{R} $& \rule[-1ex]{0pt}{5ex}$ nx^{n-1} $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \dfrac{1}{x} $ & $ \mathbb{R}^{*} $& \rule[-1ex]{0pt}{5ex}$ -\dfrac{1}{x^2} $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \sqrt{x} $ & $ ]0\; ;\; +\infty[ $ & \rule[-1ex]{0pt}{5ex}$ \dfrac{1}{2\sqrt{x}} $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \ln x $ & $]0\ ;\ +\infty[$ & \rule[-1ex]{0pt}{5ex}$\dfrac1{x}$\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \e^{x} $ & $\R$ & \rule[-1ex]{0pt}{5ex}$\e^{x}$\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \cos x $ & $\R$ & \rule[-1ex]{0pt}{5ex}$-\sin x$\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \sin x $ & $\R$ & \rule[-1ex]{0pt}{5ex}$\cos x$\vspace{1ex} \\
|
||||
\hline
|
||||
\end{tabularx}
|
||||
\end{center}
|
||||
|
||||
\ssspartie{Opérations sur les fonctions dérivées}
|
||||
|
||||
\noindent
|
||||
On considère $u$ et $v$ deux fonctions dérivables sur un intervalle $I$ de $\R$.
|
||||
\begin{center}
|
||||
\begin{tabularx}{.7\textwidth}{| C{4.5cm} | >{\centering\arraybackslash}X | C{4.5cm} |}
|
||||
\hline
|
||||
\textbf{$ \boldsymbol{f} $} & \textbf{\footnotesize est dérivable ...}\vspace{.2em} & \textbf{$ \boldsymbol{f^{\prime}} $} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ k \times u $ ($k$ constante)& sur $I$ & \rule[-1ex]{0pt}{5ex}$ k \times u' $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ u + v $ & sur $I$ & \rule[-1ex]{0pt}{5ex}$ u' + v' $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ u \times v $ & sur $I$ & \rule[-1ex]{0pt}{5ex}$ u' \times v + u \times v' $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \dfrac{u}{v} $ & si $v(x) \neq 0$ & \rule[-1ex]{0pt}{5ex}$ \dfrac{u' \times v - u \times v'}{v^2} \vspace{1ex}$ \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \dfrac{1}{v} $ & si $v(x) \neq 0$ & \rule[-1ex]{0pt}{5ex}$ \dfrac{-v'}{v^2} \vspace{1ex}$ \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ u^n $ avec $n \ge 1$ & sur $I$ & \rule[-1ex]{0pt}{5ex}$ n \times u^{\prime} \times u^{n-1} \vspace{1ex}$ \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \ln(u) $ & si $u(x) > 0$ & \rule[-1ex]{0pt}{5ex}$ \dfrac{u^{\prime}}{u} $\vspace{1ex} \\
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$ \e^{u} $ & sur $I$ & \rule[-1ex]{0pt}{5ex}$ u^{\prime} \times \e^{u} $\vspace{1ex} \\
|
||||
\hline
|
||||
\end{tabularx}
|
||||
\end{center}
|
||||
|
||||
@@ -0,0 +1,153 @@
|
||||
% !TeX root = prof_-_etude_de_fonction_-_2023.1.tex
|
||||
|
||||
\partie{Rappels : limites et asymptotes}
|
||||
|
||||
\sspartie{Limites des fonctions de références}
|
||||
|
||||
\ssspartie{Limite en $\boldsymbol{\infty}$}
|
||||
|
||||
\begin{center}
|
||||
% \resizebox{\textwidth}{!}{%
|
||||
\begin{tabular}{|>{\columncolor[HTML]{B5B5B5}}c|c|c|c|c|c|c|c|}
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$f(x)$ & $x^n$ & $\dfrac1{x^n}$ & $\sqrt{x}$ & $\dfrac1{\sqrt{x}}$ & $e^{x}$ & $e^{ax}$ & $\ln(x)$ \\[2ex] \hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$\lim\limits_{x \to +\infty}f(x)=$ & $+\infty$ & $0$ & $+\infty$ & $0$ & $+\infty$ &
|
||||
\begin{tabular}{lr}
|
||||
$+\infty$ & si $a>0$ \\
|
||||
$0$ & si $a<0$
|
||||
\end{tabular} & $+\infty$ \\ \hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$\lim\limits_{x \to -\infty}f(x)=$
|
||||
&
|
||||
\begin{tabular}{lr}
|
||||
$-\infty$ & si $n$ impair \\
|
||||
$+\infty$ & si $n$ pair
|
||||
\end{tabular}
|
||||
& $0$ & non définie & non définie & $0$ &
|
||||
\begin{tabular}{lr}
|
||||
$0$ & si $a>0$ \\
|
||||
$+\infty$ & si $a<0$
|
||||
\end{tabular} & non définie \\ \hline
|
||||
\end{tabular}%
|
||||
% }
|
||||
\end{center}
|
||||
|
||||
\vspace{-.2cm}
|
||||
|
||||
\ssspartie{Limite en $\boldsymbol{0}$}
|
||||
|
||||
\begin{center}
|
||||
% \resizebox{\textwidth}{!}{%
|
||||
\begin{tabular}{|>{\columncolor[HTML]{B5B5B5}} c|c|c|c|}
|
||||
\hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$f(x)$ & $\dfrac1{x^n}$ & $\dfrac1{\sqrt{x}}$ & $\ln(x)$ \\[2ex] \hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$\lim\limits_{\substack{x \to 0 \\ x > 0}}f(x)=$ & $+\infty$ & $+\infty$ & $-\infty$ \\[2ex] \hline
|
||||
\rule[-1ex]{0pt}{2.5ex}$\lim\limits_{\substack{x \to 0 \\ x < 0}}f(x)=$
|
||||
&
|
||||
\begin{tabular}{lr}
|
||||
$-\infty$ & si $n$ impair \\
|
||||
$+\infty$ & si $n$ pair
|
||||
\end{tabular}
|
||||
& non définie & non définie \\ \hline
|
||||
\end{tabular}%
|
||||
% }
|
||||
\end{center}
|
||||
|
||||
\vspace{-.2cm}
|
||||
|
||||
\ssspartie{Opérations sur les limites}
|
||||
|
||||
\begin{tasks}[style=itemize](4)
|
||||
\task $ f $ et $ g $ sont deux fonctions ;
|
||||
\task $A$ est soit $+\infty$, soit $-\infty$ ou un réel ;
|
||||
\task \textsf{\textbf{F. I.}} : Forme indéterminée ;
|
||||
\task \textup{*} : règle des signes.
|
||||
\end{tasks}
|
||||
|
||||
\begin{multicols}{2}
|
||||
~
|
||||
\vspace{-1.3cm}
|
||||
\begin{center}
|
||||
% \resizebox{\textwidth}{!}{%
|
||||
\begin{tabular}{|>{\columncolor[HTML]{FFFFFF}}c |c|c|c|c|c|>{\columncolor[HTML]{EFEFEF}}c|}
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}f(x)=$ & $\ell$ & $\ell$ & $\ell$ & $+\infty$ & $-\infty$ & {$+\infty$} \\
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}g(x)=$ & $\ell'$ & $+\infty$ & $-\infty$ & $+\infty$ & $-\infty$ & {$-\infty$} \\
|
||||
\hline
|
||||
alors $\lim\limits_{x \to A}f(x)+g(x)=$ & $\ell + \ell'$ & $+\infty$ & $-\infty$ & $+\infty$ & $-\infty$ & {\textsf{\textbf{F. I}}} \\
|
||||
\hline
|
||||
\end{tabular}%
|
||||
% }
|
||||
\end{center}
|
||||
|
||||
\columnbreak
|
||||
|
||||
\begin{center}
|
||||
% \resizebox{\textwidth}{!}{%
|
||||
\begin{tabular}{|>{\columncolor[HTML]{FFFFFF}}c |c|c|>{\columncolor[HTML]{EFEFEF}}c|c|}
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}f(x)=$ & $\ell$ & $\ell \neq0 $ & {$0$} & $\infty$ \\
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}g(x)=$ & $\ell'$ & $\infty$ & {$\infty$} & $\infty$ \\
|
||||
\hline
|
||||
alors $\lim\limits_{x \to A}f(x) \times g(x)=$ & $\ell \times \ell'$ & $\infty^{*}$ & {\textsf{\textbf{F. I.}}} & $\infty^{*}$ \\
|
||||
\hline
|
||||
\end{tabular}%
|
||||
% }
|
||||
\end{center}
|
||||
\end{multicols}
|
||||
|
||||
\begin{center}
|
||||
% \resizebox{\textwidth}{!}{%
|
||||
\begin{tabular}{|>{\columncolor[HTML]{FFFFFF}}c |c|c|>{\columncolor[HTML]{EFEFEF}}c|c|c|>{\columncolor[HTML]{EFEFEF}}c|}
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}f(x)=$ & $\ell$ & $\ell \neq 0$ & {$0$} & $\ell$ & $\infty$ & {$\infty$} \\
|
||||
\hline
|
||||
Si $\lim\limits_{x \to A}g(x)=$ & $\ell' \neq 0$ & $0$ & {$0$} & $\infty$ & $\ell'$ & {$\infty$} \\
|
||||
\hline
|
||||
alors $\lim\limits_{x \to A}\dfrac{f(x)}{g(x)}=$ & $\dfrac{\ell}{\ell'}$ & $\infty^{*}$ & {\textsf{\textbf{F. I.}}} & $0$ & $\infty^{*}$ & {\textsf{\textbf{F. I.}}} \\
|
||||
\hline
|
||||
\end{tabular}%
|
||||
% }
|
||||
\end{center}
|
||||
|
||||
\sspartie{Comportement asymptotique}
|
||||
|
||||
\noindent
|
||||
On considère une fonction $f$, sa courbe $\ronde{C}_f$, $a$ et $\ell$ des nombres réels.
|
||||
|
||||
\vspace{.4cm}
|
||||
|
||||
\begin{definition}[existence d'asymptote horizontale]
|
||||
\bi
|
||||
\item Lorsque $ \lim\limits_{x \to +\infty} f(x) = \ell $, on dit que la courbe $\ronde{C}_f$ admet la droite d'équation $y=\ell$ comme asymptote horizontale en $+\infty$.
|
||||
\item Lorsque $ \lim\limits_{x \to a} f(x) = +\infty $, on dit que la courbe $\ronde{C}_f$ admet la droite d'équation $x=a$ comme asymptote verticale.
|
||||
\item Lorsque $ \lim\limits_{x \to +\infty} f(x) - (mx+p)= \ell $, on dit que la courbe $\ronde{C}_f$ admet la droite d'équation $y=mx+p$ comme asymptote oblique en $+\infty$.
|
||||
\ei
|
||||
\end{definition}
|
||||
|
||||
\vspace{.2cm}
|
||||
|
||||
\noindent
|
||||
On retrouve les même situations lorsque $x$ tend vers $-\infty$.
|
||||
|
||||
\vspace{.4cm}
|
||||
|
||||
% exemple
|
||||
\begin{exemple}
|
||||
\begin{center}
|
||||
\begin{tabular}{ccc}
|
||||
\rule[-1ex]{0pt}{2.5ex} $f(x) = \ln(x+1)$ & \hspace{.2cm} & $g(x) = \dfrac{2}{x-3}+5$ \\
|
||||
\rule[-1ex]{0pt}{2.5ex} \includegraphics[scale=.8]{fig4.pdf} & \hspace{.2cm} & \includegraphics[scale=1.25]{fig5.pdf} \\
|
||||
\rule[-1ex]{0pt}{2.5ex} la droite $x=-1$ est asymptote verticale & \hspace{.2cm} & les droites $y=5$ et $x=3$ sont asymptotes horizontale et verticale \\
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
~\vspace{.4cm}
|
||||
\begin{center}
|
||||
\begin{tabular}{ccc}
|
||||
\rule[-1ex]{0pt}{2.5ex} \hspace{.2cm} & $h(x) = \dfrac{x^2-3x+1}{x}$ & \hspace{.2cm} \\
|
||||
\rule[-1ex]{0pt}{2.5ex} \hspace{.2cm} & \includegraphics[scale=.8]{fig6.pdf} & \hspace{.2cm} \\
|
||||
\rule[-1ex]{0pt}{2.5ex} \hspace{.2cm} & la droite $y=x-3$ est asymptote oblique & \hspace{.2cm} \\
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{exemple}
|
||||
@@ -0,0 +1,45 @@
|
||||
% !TeX root = prof_-_etude_de_fonction_-_2023.1.tex
|
||||
|
||||
\newpage
|
||||
|
||||
\partie{Applications}
|
||||
|
||||
\begin{application}[calculer une dérivée]
|
||||
Déterminer la fonction dérivée de chacune des fonctions sur l'intervalle donné.
|
||||
|
||||
\begin{tasks} (2)[]
|
||||
\task\ $f_1(x) = x^2 \e^{x}$ \qquad pour $x \in \R$
|
||||
\task\ $f_2(x) = 3 \ln(x) - \dfrac5{x} + 2\sqrt{x}$ \qquad pour $ x \in ]0\ ;\ +\infty[ $
|
||||
\task\ $f_3 = \dfrac{5x+3}{x-4}$ \qquad pour $x \in ]-\infty\ ;\ 4[ \cup ]4\ ;\ +\infty[$
|
||||
\task\ $f_4(x) = \e^{x^2-x}$ \qquad pour $x \in \R$
|
||||
\task\ $f_5(x) = \ln(x^3+1)$ \qquad pour $x \in ]0\ ;\ +\infty[$
|
||||
\end{tasks}
|
||||
\end{application}
|
||||
|
||||
\vspace{.4cm}
|
||||
|
||||
\begin{application}[calculer une limite]
|
||||
Déterminer les limites suivantes:
|
||||
\begin{tasks} (4)[]
|
||||
\task\ $ \lim\limits_{x \to +\infty } 5-x^2 \e^{x} $
|
||||
\task\ $ \lim\limits_{\substack{ x \to 0 \\ x>0 }} \dfrac{3+x}{\ln x} $
|
||||
\task\ $ \lim\limits_{\substack{ x \to -2 \\ x>-2 }} \dfrac{x^2-6x+7}{4+2x} $
|
||||
\task\ $ \lim\limits_{x \to -\infty } \e^{x^2-x} $
|
||||
\end{tasks}
|
||||
\end{application}
|
||||
|
||||
\vspace{.4cm}
|
||||
|
||||
\begin{application}[étudier une fonction et ses asymptotes]
|
||||
Soit $f$ la fonction définie sur $]-\infty\ ;\ -2[\cup]-2\ ;\ +\infty[$ par $f(x)=x+3-\dfrac1{x+2}$ et $\ronde{C}_f$ sa courbe représentative.
|
||||
\begin{questions}
|
||||
\item Calculer la dérivée de la fonction $f$ et étudier ses variations.
|
||||
\item Déterminer les limites de $f$ aux bornes de son ensemble de définition.
|
||||
\item En déduire l'existence d'une asymptote verticale et préciser son équation.
|
||||
\item Montrer que la droite $D$ d'équation $y=x+3$ est asymptote oblique à la coiurbe $\ronde{C}_f$ en $-\infty$ et en $+\infty$.
|
||||
\item Déterminer la position relative de $\ronde{C}_f$ et de la droite $D$. Justifier.
|
||||
\end{questions}
|
||||
\end{application}
|
||||
|
||||
\vspace{.4cm}
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
Binary file not shown.
@@ -0,0 +1,22 @@
|
||||
\documentclass[10pt]{jl-cours}
|
||||
\usepackage{asymptote}
|
||||
|
||||
\newcolumntype{M}[1]{>{\centering}m{#1}}
|
||||
|
||||
\begin{document}
|
||||
\pagenumbering{arabic}
|
||||
|
||||
\titre{\Jd Étude de fonctions}{\Jd Étude de fonctions}
|
||||
\lohead*{BTS2E}
|
||||
\rofoot*{\anneescolaire}
|
||||
|
||||
\cofoot[\thepage]{\thepage}
|
||||
\cefoot[\thepage]{\thepage}
|
||||
|
||||
\nskip{3}
|
||||
|
||||
\import{.}{partieI.tex}
|
||||
\import{.}{partieII.tex}
|
||||
\import{.}{partieIII.tex}
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user