summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/tablor/Figures/tablor_Tab.mp
blob: 260b9b876d9f5581d076b3c0762dc4ed0c8426f9 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
input tableauVariation;
verbatimtex
%&latex
\documentclass{article}
\usepackage[upright]{kpfonts}% ou mathpazo, lmodern, etc. ou rien !
%\usepackage{amsmath}
\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas
\renewcommand\cdot{ } % idem pour les cdot
\begin{document}
\catcode`\@=0 % pour utiliser le @
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 $0$ etex);
val(btex $2$ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);plus;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex $4$ etex,1);
endTableau;


beginTableau(3)
newLigneVariables(btex $ {x}$ etex);
   val(btex $-\infty $ etex);val(btex $\frac{-3}{5}$ etex);
val(btex $2$ etex);
val(btex $+\infty $ etex); 
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -45 x-27}$ 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 $\hbox{ Signe de }\atop{\displaystyle @varphi(x)}$ etex); plus;valBarre(btex 0 etex); moins;nonDefBarre;plus; 
endTableau;

beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
val(btex $0$ etex);
val(btex $7$ etex);

newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $25$ etex,1); valPos(btex          $0$
                                            etex,0);
valPos(btex $49$ etex,1);
endTableau;

beginTableau(5) 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;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex          $0$
                                            etex,0);
valPos(btex $+\infty $ etex,1);
endTableau;



beginTableau(6) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;
endTableau;

beginTableau(7) 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(8) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex);
val(btex $\frac{(-\pi )}{2}$ etex);
val(btex $\frac{\pi }{2}$ etex);
val(btex $\pi $ etex);

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(9) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,0); valPos(btex $5$etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1);
endTableau;

beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1);
endTableau;

beginTableau(11) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex);
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);limGauche(btex $+\infty $ etex,1);nonDefBarre;
endTableau;

beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @varphi}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $0$ etex,0);debutNonDef;finNonDef;limDroite(btex $0$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(13) 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 $-\infty$ 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(14) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(15) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;  nonDefBarre;plus;valBarre(btex $  $ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;nonDefBarre;moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $\frac{100}{99}$ etex,0);  limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex
                                            $ -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(16) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{10}\right))}{3}$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\frac{\sqrt{10}}{3}$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(17) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\frac{(-\left(\sqrt{2}\right))}{2}$ etex);val(btex $0$ etex);val(btex $\frac{\sqrt{2}}{2}$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;  nonDefBarre;plus;valBarre(btex $  $ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;nonDefBarre;moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $\frac{100}{99}$ etex,0);  limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex
                                            $ -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(18) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\frac{(-\pi )}{3}$ etex);val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @cos}$ etex);
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(19) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $     0.156422$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(x)}$ etex);nonDefBarre;moins; valBarre(btex 0 etex);plus;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); valPos(btex          $    -1.145392$
                                            etex,0);
valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);moins; nonDefBarre;plus;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);valPos(btex $1$ etex,1); valPos(btex
                                    $0$
                                    etex,0);valPos(btex $1$ etex,1);
endTableau;

beginTableau(21) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
val(btex $\frac{\pi }{8}$ etex);
val(btex $\frac{\pi }{3}$ etex);
val(btex $\frac{3 \pi }{8}$ etex);
val(btex $\frac{\pi }{2}$ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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          $\frac{(-\left(\sqrt{3}\right))}{2}$
                                            etex,0.5);valPos(btex          $-1$
                                            etex,0);
valPos(btex $0$ etex,1);
endTableau;

beginTableau(22) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $2$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex); moins;valBarre(btex $0$ etex);plus;nonDefBarre;plus;valBarre(btex $0$ etex);moins;nonDefBarre;moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex          $\frac{8}{9}$
                                            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);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex); moins;valBarre(btex $\frac{-64}{9}$ etex);moins;nonDefBarre;moins;valBarre(btex $0$ etex);plus;valBarre(btex $\frac{44}{9}$ etex);plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);valPos(btex $+\infty $ etex,1);valPos(btex          $\frac{32}{3}$
                                            etex,0.5);limGauche(btex
                                    $-\infty$
                                    etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex          $0$
                                            etex,0);
valPos(btex          $\frac{16}{3}$
                                            etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;


          beginTableau(23)
   newLigneVariables(btex $ {x}$ etex);
   val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
val(btex $+\infty$ etex);
  
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;valBarre(btex 0 etex);moins;barre;moins;
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(24)
newLigneVariables(btex $ {x}$ etex);
   val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\sqrt{2}$ etex);
val(btex $\frac{3}{2}$ etex);
val(btex $+\infty $ etex); 
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex);
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;valBarre(btex 0 etex);moins;
    
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-1}$ etex);
                              plus;barre;
                              plus;
                                valBarre(btex 0 etex);moins;
                                valBarre(btex 0 etex);plus;barre;
                              plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+1}$ etex);
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex);
                              moins;barre;
                              moins;barre;
                              moins;
                                valBarre(btex 0 etex);plus;barre;
                              plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-2}$ etex);
                              plus;
                                valBarre(btex 0 etex);moins;barre;
                              moins;barre;
                              moins;
                                valBarre(btex 0 etex);plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
                              moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;
                              
endTableau;

   beginTableau(25)
newLigneVariables(btex $ {x}$ etex);
   val(btex $-15$ 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 $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
                              plus;valBarre(btex 0 etex); moins;
                                valBarre(btex 0 etex);
endTableau;

 
beginTableau(26)
newLigneVariables(btex $ {x}$ etex);
   val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
val(btex $\frac{3}{2}$ etex);
val(btex $2$ etex);
val(btex $4$ etex);
val(btex $+\infty $ etex); 
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); plus;barre;plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;
     
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -4 x+5}$ 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; 
endTableau;


beginTableau(27)
newLigneVariables(btex $ {x}$ 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;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(28)
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);
                               plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);
endTableau;



beginTableau(29)
newLigneVariables(btex $\displaystyle  {x}$ etex);
   val(btex $-10$ etex);val(btex $2$ etex);
val(btex $5$ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \frac{(x+10)}{(x-5) (x-2)}}$ etex);
                                valBarre(btex 0 etex); plus;nonDefBarre;moins;nonDefBarre;
endTableau;



beginTableau(30)
newLigneVariables(btex $\displaystyle  {x}$ etex);
   val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex);
val(btex $\pi $ etex);
val(btex $\frac{3 \pi }{2}$ etex);
val(btex $2 \pi $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \tan\left(x\right)}$ etex);
                                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 $-\frac{\sqrt{5}}{5}$ 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(31) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;moins;valBarre(btex$
                                                       $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPos(btex          $-1$
                                            etex,0);valPos(btex
                                            $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;  valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $\frac{1}{4}$ etex,1);  valPos(btex          $0$
                                            etex,0);valPos(btex
                                            $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @ln'(x)}$ etex);nonDefBarre;plus;valBarre(btex$
                                                       $ etex);plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @ln}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -@ln'(x)}$ etex); moins;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle -@ln}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\infty$ etex,0);
endTableau;

beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @cos}$ etex);
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(37) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
val(btex $2 \pi $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @cos}$ etex);valPos(btex $1$ etex,1); valPos(btex          $-1$
                                            etex,0);
valPos(btex $1$ etex,1);
endTableau;

beginTableau(38) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; nonDefBarre;plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @tan}$ etex);
valPos(btex $0$ etex,0);valPos(btex $ 7 $ etex,0.5); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1);
endTableau;

beginTableau(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\mathrm{atan}\left(7\right)$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; nonDefBarre;plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle @tan}$ etex);
valPos(btex $0$ etex,0);valPos(btex $ 7 $ etex,0.5); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1);
endTableau;

beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(41) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $    -0.839287$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $1$ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(42) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);moins;
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-\infty$ etex,0); valPos(btex          $0$
                                            etex,1);valPos(btex $-\infty$ etex,0);
endTableau;

  beginTableau(43)
newLigneVariables(btex $ {x}$ etex);
   val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ 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 $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex);
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;barre;
                              plus;valBarre(btex 0 etex);moins;
    
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex);
                              moins;barre;
                              moins;barre;
                              moins;barre;
                              moins;
                                valBarre(btex 0 etex);plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex);
                              moins;barre;
                              moins;
                                valBarre(btex 0 etex);plus;barre;
                              plus;barre;
                              plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex);
                              plus;
                                valBarre(btex 0 etex);moins;barre;
                              moins;
                                valBarre(btex 0 etex);plus;barre;
                              plus;barre;plus;
                              
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
                              plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;
                              
endTableau;

 beginTableau(44) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins;  valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $-1$ etex,1);  valPos(btex          $-\left(e^{-4}\right)-1$
                                            etex,0);valPos(btex
                                            $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;

beginTableau(45) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus;  valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $1$ etex,0);  valPos(btex          $2$
                                            etex,1);valPos(btex
                                            $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;

beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ 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 $0$ etex,0); valPos(btex          $\ln\left(\frac{(e^{1}+1)}{e^{1}}\right)$
                                            etex,1);valPos(btex $0$ etex,0);
endTableau;

beginTableau(48) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;valBarre(btex$
                                                       $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $1$ etex,1);valPos(btex $ 0 $ etex,0.5);valPos(btex $-\pi -1$ etex,0);
endTableau;

beginTableau(49) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(50) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $e^{\frac{(-\left(\sqrt{5}\right)+1)}{2}}$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ etex);val(btex $e^{\frac{(\sqrt{5}+1)}{2}}$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$
                                                       $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins; 
newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
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(51)
newLigneVariables(btex $\displaystyle  {x}$ etex);
   val(btex $-10$ etex);val(btex $10$ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
                                valBarre(btex 0 etex);moins; 
                                valBarre(btex 0 etex);
endTableau;

beginTableau(52) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\sqrt{2}$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;debutNonDefStrict;finNonDefStrict;moins;valBarre(btex 0 etex);plus;
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(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;
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(54) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
val(btex $\frac{\pi }{8}$ etex);
val(btex $\frac{\pi }{3}$ etex);
val(btex $\frac{3 \pi }{8}$ etex);
val(btex $\frac{\pi }{2}$ etex);

newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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          $\frac{(-\left(\sqrt{3}\right))}{2}$
                                            etex,0.5);valPos(btex          $-1$
                                            etex,0);
valPos(btex $0$ etex,1);
endTableau;

beginTableau(55) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
val(btex $\frac{\pi }{3}$ etex);
val(btex $\pi $ etex);
val(btex $\frac{5 \pi }{3}$ etex);
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          $\frac{(\pi -3 \sqrt{3})}{3}$
                                            etex,0);
valPos(btex          $\pi $
                                            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          $0$
                                            etex,0.5);valPos(btex          $-3$
                                            etex,0);
valPos(btex          $0$
                                            etex,0.5);valPos(btex $1$ etex,1);
endTableau;

beginTableau(56) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
val(btex $\frac{\pi }{8}$ etex);
val(btex $\frac{\pi }{6}$ etex);
val(btex $\frac{3 \pi }{8}$ etex);
val(btex $\frac{\pi }{2}$ 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 $-3 \cos\left(\frac{\pi }{8}\right)$ 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);
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 $0$ etex,1);
endTableau;

  beginTableau(57)
newLigneVariables(btex $ {x}$ etex);
   val(btex $0$ 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);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;
                                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); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
                              
endTableau;