// fltk 7Fl_Tile 44 -1001 714 31 [ // fltk N4xcas23Comment_Multiline_InputE 44 -1001 714 30 Methode de Newton pour trouver une valeur approchee de sqrt(2) , // fltk N4xcas10Log_OutputE 44 -971 714 1 ] , // fltk 7Fl_Tile 44 -968 714 167 [ // fltk N4xcas19Multiline_Input_tabE 44 -968 714 30 f(x):=x**2-2 , // fltk N4xcas10Log_OutputE 44 -938 714 84 // Parsing f£// Success compiling f££ , // fltk N4xcas8EquationE 44 -854 714 53 (x)->x^2-2 ] , // fltk 7Fl_Tile 44 -799 714 31 [ // fltk N4xcas23Comment_Multiline_InputE 44 -799 714 30 On trace la tangente au graphe de f en x0 et l'intersection avec l'axe des x -> x1 , // fltk N4xcas10Log_OutputE 44 -769 714 1 ] , // fltk N4xcas6FigureE 44 -766 714 369 // fltk N4xcas12History_PackE 46 -1094 218 697 [ // fltk 7Fl_Tile 61 -1094 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -1094 203 30 assume(x0=0.6) , // fltk N4xcas10Log_OutputE 61 -1064 203 1 , // fltk 9Fl_Scroll 61 -1063 203 50 [ // fltk N4xcas10Gen_OutputE 61 -1063 214 25 parameter(x0,-5.0,5.0,0.6) , // fltk 12Fl_Scrollbar 51 76 206 16 [] , // fltk 12Fl_Scrollbar 257 42 16 34 [] ] ] , // fltk 7Fl_Tile 61 -1011 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -1011 203 30 F:=plotfunc(f(x)) , // fltk N4xcas10Log_OutputE 61 -981 203 1 , // fltk 9Fl_Scroll 61 -980 203 50 [ // fltk N4xcas10Gen_OutputE 61 -980 278 25 [plot(pnt[x+(i)*(x^2-2),x,-5.0,5.0])] , // fltk 12Fl_Scrollbar 51 62 206 16 [] , // fltk 12Fl_Scrollbar 257 28 16 34 [] ] ] , // fltk 7Fl_Tile 61 -928 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -928 203 30 M1:=couleur(element(F,x0),vert) , // fltk N4xcas10Log_OutputE 61 -898 203 1 , // fltk 9Fl_Scroll 61 -897 203 50 [ // fltk N4xcas10Gen_OutputE 61 -897 139 25 point(x0,x0^2-2) , // fltk 12Fl_Scrollbar 51 86 206 16 [] , // fltk 12Fl_Scrollbar 257 36 16 50 [] ] ] , // fltk 7Fl_Tile 61 -845 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -845 203 30 T1:=couleur(tangent(F,M1),vert) , // fltk N4xcas10Log_OutputE 61 -815 203 1 , // fltk 9Fl_Scroll 61 -814 203 50 [ // fltk N4xcas10Gen_OutputE 61 -814 436 25 polygone(point(x0,x0^2-2),point(x0+1,x0^2-2+2*x0)) , // fltk 12Fl_Scrollbar 51 86 206 16 [] , // fltk 12Fl_Scrollbar 257 52 16 34 [] ] ] , // fltk 7Fl_Tile 61 -762 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -762 203 30 N1:=inter_droite(T1,droite(y=0)) , // fltk N4xcas10Log_OutputE 61 -732 203 1 , // fltk 9Fl_Scroll 61 -731 203 50 [ // fltk N4xcas10Gen_OutputE 61 -731 198 25 point((x0^2+2)/(2*x0),0) , // fltk 12Fl_Scrollbar 61 396 203 16 [] , // fltk 12Fl_Scrollbar 264 346 16 50 [] ] ] , // fltk 7Fl_Tile 61 -679 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -679 203 30 x1:=abscisse(N1) , // fltk N4xcas10Log_OutputE 61 -649 203 1 , // fltk 9Fl_Scroll 61 -648 203 50 [ // fltk N4xcas10Gen_OutputE 61 -648 115 25 (x0^2+2)/2/x0 , // fltk 12Fl_Scrollbar 61 479 203 16 [] , // fltk 12Fl_Scrollbar 264 429 16 50 [] ] ] , // fltk 7Fl_Tile 61 -596 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -596 203 30 M2:=couleur(element(F,x1),cyan) , // fltk N4xcas10Log_OutputE 61 -566 203 1 , // fltk 9Fl_Scroll 61 -565 203 50 [ // fltk N4xcas10Gen_OutputE 61 -565 333 25 point((x0^2+2)/2/x0,((x0^2+2)/2/x0)^2-2) , // fltk 12Fl_Scrollbar 61 63 203 16 [] , // fltk 12Fl_Scrollbar 264 29 16 34 [] ] ] , // fltk 7Fl_Tile 61 -513 203 81 [ // fltk N4xcas19Multiline_Input_tabE 61 -513 203 30 T2:=couleur(tangent(F,M2),cyan) , // fltk N4xcas10Log_OutputE 61 -483 203 1 , // fltk 9Fl_Scroll 61 -482 203 50 [ // fltk N4xcas10Gen_OutputE 61 -482 915 25 polygone(point((x0^2+2)/2/x0,((x0^2+2)/2/x0)^2-2),point((x0^2+2)/2/x0+1,((x0^2+2)/2/x0)^2-2+2*(x0^2+2)/2/x0)) , // fltk 12Fl_Scrollbar 61 71 203 16 [] , // fltk 12Fl_Scrollbar 264 37 16 34 [] ] ] , // fltk 7Fl_Tile 61 -430 203 31 [ // fltk N4xcas19Multiline_Input_tabE 61 -430 203 30 , // fltk N4xcas10Log_OutputE 61 -400 203 1 ] ] // fltk N4xcas8GeometryE 282 -740 386 343 -5,5,-3.5,5.25,[parameter(x0,-5.0,5.0,0.6),seq[pnt(pnt[curve(group[pnt[x+(i)*(x^2-2),x,-5.0,5.0],group[-5.0+23*i,-4.92125984252+22.2187984376*i,-4.84251968504+21.4499969*i,-4.76377952756+20.6935953872*i,-4.68503937008+19.9495938992*i,-4.6062992126+19.217992436*i,-4.52755905512+18.4987909976*i,-4.44881889764+17.791989584*i,-4.37007874016+17.0975881952*i,-4.29133858268+16.4155868312*i,-4.2125984252+15.745985492*i,-4.13385826772+15.0887841776*i,-4.05511811024+14.443982888*i,-3.97637795276+13.8115816232*i,-3.89763779528+13.1915803832*i,-3.8188976378+12.583979168*i,-3.74015748031+11.9887779776*i,-3.66141732283+11.405976812*i,-3.58267716535+10.8355756712*i,-3.50393700787+10.2775745551*i,-3.42519685039+9.73197346395*i,-3.34645669291+9.19877239754*i,-3.26771653543+8.67797135594*i,-3.18897637795+8.16957033914*i,-3.11023622047+7.67356934714*i,-3.03149606299+7.18996837994*i,-2.95275590551+6.71876743753*i,-2.87401574803+6.25996651993*i,-2.79527559055+5.81356562713*i,-2.71653543307+5.37956475913*i,-2.63779527559+4.95796391593*i,-2.55905511811+4.54876309753*i,-2.48031496063+4.15196230392*i,-2.40157480315+3.76756153512*i,-2.32283464567+3.39556079112*i,-2.24409448819+3.03596007192*i,-2.16535433071+2.68875937752*i,-2.08661417323+2.35395870792*i,-2.00787401575+2.03155806312*i,-1.92913385827+1.72155744311*i,-1.85039370079+1.42395684791*i,-1.77165354331+1.13875627751*i,-1.69291338583+0.865955731911*i,-1.61417322835+0.60555521111*i,-1.53543307087+0.357554715109*i,-1.45669291339+0.121954243909*i,-1.37795275591-0.101246202492*i,-1.29921259843-0.312046624093*i,-1.22047244094-0.510447020894*i,-1.14173228346-0.696447392895*i,-1.06299212598-0.870047740095*i,-0.984251968504-1.0312480625*i,-0.905511811024-1.1800483601*i,-0.826771653543-1.3164486329*i,-0.748031496063-1.4404488809*i,-0.669291338583-1.5520491041*i,-0.590551181102-1.6512493025*i,-0.511811023622-1.7380494761*i,-0.433070866142-1.8124496249*i,-0.354330708661-1.8744497489*i,-0.275590551181-1.9240498481*i,-0.196850393701-1.9612499225*i,-0.11811023622-1.9860499721*i,-0.0393700787402-1.9984499969*i,0.0393700787402-1.9984499969*i,0.11811023622-1.9860499721*i,0.196850393701-1.9612499225*i,0.275590551181-1.9240498481*i,0.354330708661-1.8744497489*i,0.433070866142-1.8124496249*i,0.511811023622-1.7380494761*i,0.590551181102-1.6512493025*i,0.669291338583-1.5520491041*i,0.748031496063-1.4404488809*i,0.826771653543-1.3164486329*i,0.905511811024-1.1800483601*i,0.984251968504-1.0312480625*i,1.06299212598-0.870047740095*i,1.14173228346-0.696447392895*i,1.22047244094-0.510447020894*i,1.29921259843-0.312046624093*i,1.37795275591-0.101246202492*i,1.45669291339+0.121954243908*i,1.53543307087+0.357554715109*i,1.61417322835+0.60555521111*i,1.69291338583+0.865955731911*i,1.77165354331+1.13875627751*i,1.85039370079+1.42395684791*i,1.92913385827+1.72155744311*i,2.00787401575+2.03155806312*i,2.08661417323+2.35395870792*i,2.16535433071+2.68875937752*i,2.24409448819+3.03596007192*i,2.32283464567+3.39556079112*i,2.40157480315+3.76756153512*i,2.48031496063+4.15196230392*i,2.55905511811+4.54876309753*i,2.63779527559+4.95796391593*i,2.71653543307+5.37956475913*i,2.79527559055+5.81356562713*i,2.87401574803+6.25996651993*i,2.95275590551+6.71876743753*i,3.03149606299+7.18996837994*i,3.11023622047+7.67356934714*i,3.18897637795+8.16957033914*i,3.26771653543+8.67797135594*i,3.34645669291+9.19877239754*i,3.42519685039+9.73197346395*i,3.50393700787+10.2775745551*i,3.58267716535+10.8355756712*i,3.66141732283+11.405976812*i,3.74015748031+11.9887779776*i,3.8188976378+12.583979168*i,3.89763779528+13.1915803832*i,3.97637795276+13.8115816232*i,4.05511811024+14.443982888*i,4.13385826772+15.0887841776*i,4.2125984252+15.745985492*i,4.29133858268+16.4155868312*i,4.37007874016+17.0975881952*i,4.44881889764+17.791989584*i,4.52755905512+18.4987909976*i,4.6062992126+19.217992436*i,4.68503937008+19.9495938992*i,4.76377952756+20.6935953872*i,4.84251968504+21.4499969*i,4.92125984252+22.2187984376*i,5+23*i]]),0,"F"])],pnt(pnt[x0+(i)*(x0^2-2),vert,"M1"]),pnt(pnt[line[x0+(i)*(x0^2-2),x0+(i)*(x0^2-2)+1+(2*i)*x0],vert,"T1"]),pnt(pnt[(x0^2+2)/(2*x0),0,"N1"]),(x0^2+2)/2/x0,pnt(pnt[(x0^2+2)/2/x0+(i)*(((x0^2+2)/2/x0)^2-2),cyan,"M2"]),pnt(pnt[line[(x0^2+2)/2/x0+(i)*(((x0^2+2)/2/x0)^2-2),(x0^2+2)/2/x0+(i)*(((x0^2+2)/2/x0)^2-2)+1+(2*i)*(x0^2+2)/2/x0],cyan,"T2"])] , // fltk 7Fl_Tile 44 -395 714 31 [ // fltk N4xcas23Comment_Multiline_InputE 44 -395 714 30 On cree la fonction permettant de passer de x0 a x1 , // fltk N4xcas10Log_OutputE 44 -365 714 1 ] , // fltk 7Fl_Tile 44 -362 714 108 [ // fltk N4xcas19Multiline_Input_tabE 44 -362 714 30 g:=unapply(x1,x0) , // fltk N4xcas10Log_OutputE 44 -332 714 1 , // fltk N4xcas8EquationE 44 -331 714 77 (x0)->(x0^2+2)/(x0*2) ] , // fltk 7Fl_Tile 44 -252 714 31 [ // fltk N4xcas23Comment_Multiline_InputE 44 -252 714 30 Tableau des valeurs de la suite (tableseq) , // fltk N4xcas10Log_OutputE 44 -222 714 1 ] , // fltk 7Fl_Tile 44 -219 714 370 [ // fltk N4xcas13Tableur_GroupE 44 -219 714 369 1 1 1 0 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, // fltk N4xcas10Log_OutputE 44 150 714 1 ] , // fltk 7Fl_Tile 44 153 714 31 [ // fltk N4xcas23Comment_Multiline_InputE 44 153 714 30 On calcule en mode exact la valeur de x6 , // fltk N4xcas10Log_OutputE 44 183 714 1 ] , // fltk 7Fl_Tile 44 186 714 98 [ // fltk N4xcas19Multiline_Input_tabE 44 186 714 30 rac2:=(g@@6)(6/10) , // fltk N4xcas10Log_OutputE 44 216 714 1 , // fltk N4xcas8EquationE 44 217 714 67 7866894008096762401289293893700543019909459533970334696439476481/5562734100001039200031789201027619926968247165965440118056504640 ] , // fltk 7Fl_Tile 44 286 714 74 [ // fltk N4xcas19Multiline_Input_tabE 44 286 714 30 evalf(f(rac2)) , // fltk N4xcas10Log_OutputE 44 316 714 1 , // fltk N4xcas8EquationE 44 317 714 43 5.34060217077e-25 ] , // fltk 7Fl_Tile 44 362 714 50 [ // fltk N4xcas23Comment_Multiline_InputE 44 362 714 49 Donc (thm des accroissements finis) rac2 est une valeur approchee de sqrt(2) £avec 24 decimales , // fltk N4xcas10Log_OutputE 44 411 714 1 ] , // fltk 7Fl_Tile 44 414 714 31 [ // fltk N4xcas19Multiline_Input_tabE 44 414 714 30 , // fltk N4xcas10Log_OutputE 44 444 714 1 ]