119:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000
x:@0.841253:0.170627:0.846721:0.170627:0.846721:0.158803:0.841253:0.158803:0.000000
1:@0.737976:0.175658:0.743987:0.175658:0.743987:0.163834:0.737976:0.163834:0.000000
2:@0.737976:0.186219:0.743987:0.186219:0.743987:0.174395:0.737976:0.174395:0.000000
0:@0.775677:0.175531:0.781688:0.175531:0.781688:0.163707:0.775677:0.163707:0.000000
decrece:@0.649943:0.140141:0.694368:0.140141:0.694368:0.127899:0.649943:0.127899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crece:@0.778174:0.140141:0.808149:0.140141:0.808149:0.127899:0.778174:0.127899:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.793223:0.206401:0.804704:0.206401:0.804704:0.196377:0.793223:0.196377:0.000000
 :@0.804704:0.207109:0.807585:0.207109:0.807585:0.195632:0.804704:0.195632:0.000000
Figura 3.4.:@0.807585:0.207109:0.856154:0.207109:0.856154:0.195632:0.807585:0.195632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.791218:0.935210:0.802699:0.935210:0.802699:0.925186:0.791218:0.925186:0.000000
 :@0.802699:0.935918:0.805580:0.935918:0.805580:0.924441:0.802699:0.924441:0.000000
Figura 3.5.:@0.805580:0.935918:0.854149:0.935918:0.854149:0.924441:0.805580:0.924441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.689856:0.789981:0.695757:0.789981:0.695757:0.779070:0.689856:0.779070:0.000000
2:@0.729234:0.789981:0.735134:0.789981:0.735134:0.779070:0.729234:0.779070:0.000000
3:@0.768611:0.789981:0.774512:0.789981:0.774512:0.779070:0.768611:0.779070:0.000000
4:@0.807989:0.789981:0.813889:0.789981:0.813889:0.779070:0.807989:0.779070:0.000000
–1:@0.634465:0.810256:0.647353:0.810256:0.647353:0.799344:0.634465:0.799344:0.000000:0.000000
–2:@0.634465:0.839809:0.647353:0.839809:0.647353:0.828898:0.634465:0.828898:0.000000:0.000000
–3:@0.634465:0.869363:0.647353:0.869363:0.647353:0.858452:0.634465:0.858452:0.000000:0.000000
–4:@0.634465:0.898917:0.647353:0.898917:0.647353:0.888005:0.634465:0.888005:0.000000:0.000000
y:@0.641553:0.746486:0.646903:0.746486:0.646903:0.735574:0.641553:0.735574:0.000000
x:@0.843416:0.786097:0.848854:0.786097:0.848854:0.775186:0.843416:0.775186:0.000000
0:@0.641553:0.789991:0.647454:0.789991:0.647454:0.779079:0.641553:0.779079:0.000000
y = –(x–2)²:@0.789525:0.828485:0.845579:0.828485:0.845579:0.817574:0.789525:0.817574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.684804:0.244762:0.831589:0.244762:0.831589:0.229290:0.684804:0.229290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.685042:0.273812:0.777055:0.273812:0.777055:0.258340:0.685042:0.258340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e Ingeniería:@0.638498:0.289654:0.720098:0.289654:0.720098:0.274182:0.638498:0.274182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las funciones cuadráticas son :@0.638498:0.312202:0.833638:0.312202:0.833638:0.297139:0.638498:0.297139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ampliamente usadas en la cien-:@0.638498:0.328044:0.840799:0.328044:0.840799:0.312981:0.638498:0.312981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cia, los negocios y la ingeniería. :@0.638498:0.343886:0.839535:0.343886:0.839535:0.328823:0.638498:0.328823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La parábola puede describir :@0.638498:0.359728:0.821517:0.359728:0.821517:0.344665:0.638498:0.344665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trayectorias de chorros de agua :@0.638498:0.375570:0.844228:0.375570:0.844228:0.360507:0.638498:0.360507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en una fuente y el botar una :@0.638498:0.391412:0.824669:0.391412:0.824669:0.376349:0.638498:0.376349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pelota o definir la curvatura en :@0.638498:0.407254:0.841466:0.407254:0.841466:0.392191:0.638498:0.392191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estructuras como reflectores y :@0.638498:0.423096:0.837682:0.423096:0.837682:0.408033:0.638498:0.408033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
antenas parabólicas que forman, :@0.638498:0.438938:0.850447:0.438938:0.850447:0.423875:0.638498:0.423875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
respectivamente, los faros de :@0.638498:0.454780:0.828134:0.454780:0.828134:0.439717:0.638498:0.439717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los carros y la base de los platos :@0.638498:0.470622:0.845316:0.470622:0.845316:0.455559:0.638498:0.455559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
satelitales. :@0.638498:0.486464:0.706623:0.486464:0.706623:0.471401:0.638498:0.471401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Responde:@0.638503:0.675727:0.707210:0.675727:0.707210:0.660255:0.638503:0.660255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: ¿qué otro tipo de :@0.707175:0.675305:0.828738:0.675305:0.828738:0.660241:0.707175:0.660241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaciones tienen las funcio-:@0.638503:0.691147:0.831800:0.691147:0.831800:0.676083:0.638503:0.676083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes cuadráticas?:@0.638503:0.706989:0.742441:0.706989:0.742441:0.691925:0.638503:0.691925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 368766932:@0.870588:0.649688:0.870588:0.581514:0.859119:0.581514:0.859119:0.649688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entonces :@0.108233:0.117606:0.177374:0.117606:0.177374:0.101108:0.108233:0.101108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≤−:@0.229517:0.116985:0.254331:0.116985:0.254331:0.100704:0.229517:0.100704:0.000000:0.000000
x:@0.181084:0.116464:0.188559:0.116464:0.188559:0.099996:0.181084:0.099996:0.000000
x:@0.210772:0.116464:0.218247:0.116464:0.218247:0.099996:0.210772:0.099996:0.000000
<:@0.196997:0.116349:0.207805:0.116349:0.207805:0.099851:0.196997:0.099851:0.000000
1:@0.258415:0.106994:0.266911:0.106994:0.266911:0.090496:0.258415:0.090496:0.000000
2:@0.257787:0.127350:0.266283:0.127350:0.266283:0.110852:0.257787:0.110852:0.000000
.  Sumando    en la desigualdad, se obtiene :@0.269828:0.116349:0.586758:0.117606:0.586758:0.101108:0.269828:0.099851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.188789:0.118568:0.193706:0.118568:0.193706:0.109019:0.188789:0.109019:0.000000
2:@0.218940:0.118568:0.223858:0.118568:0.223858:0.109019:0.218940:0.109019:0.000000
1:@0.362399:0.107037:0.370895:0.107037:0.370895:0.090540:0.362399:0.090540:0.000000
2:@0.361771:0.127350:0.370267:0.127350:0.370267:0.110852:0.361771:0.110852:0.000000
1:@0.143674:0.145976:0.152170:0.145976:0.152170:0.129478:0.143674:0.129478:0.000000
2:@0.143046:0.166289:0.151542:0.166289:0.151542:0.149791:0.143046:0.149791:0.000000
<:@0.155401:0.155287:0.166209:0.155287:0.166209:0.138790:0.155401:0.138790:0.000000
1:@0.202312:0.145976:0.210808:0.145976:0.210808:0.129478:0.202312:0.129478:0.000000
2:@0.201680:0.166289:0.210176:0.166289:0.210176:0.149791:0.201680:0.149791:0.000000
0,  de donde :@0.229269:0.155287:0.321102:0.156545:0.321102:0.140048:0.229269:0.138790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.119646:0.157506:0.124563:0.157506:0.124563:0.147957:0.119646:0.147957:0.000000
2:@0.177128:0.157506:0.182045:0.157506:0.182045:0.147957:0.177128:0.147957:0.000000
+:@0.128232:0.155924:0.138809:0.155924:0.138809:0.139643:0.128232:0.139643:0.000000
+ ≤:@0.186876:0.155924:0.225816:0.155924:0.225816:0.139643:0.186876:0.139643:0.000000:0.000000:0.000000
x:@0.111958:0.155403:0.119433:0.155403:0.119433:0.138934:0.111958:0.138934:0.000000
x:@0.168964:0.155403:0.176439:0.155403:0.176439:0.138934:0.168964:0.138934:0.000000
x:@0.332184:0.153523:0.339659:0.153523:0.339659:0.137055:0.332184:0.137055:0.000000
1:@0.339878:0.155627:0.344796:0.155627:0.344796:0.146078:0.339878:0.146078:0.000000
+:@0.347104:0.154044:0.357680:0.154044:0.357680:0.137763:0.347104:0.137763:0.000000
1:@0.361553:0.144573:0.370049:0.144573:0.370049:0.128076:0.361553:0.128076:0.000000
2:@0.360917:0.164772:0.369413:0.164772:0.369413:0.148275:0.360917:0.148275:0.000000
2:@0.379091:0.134134:0.384008:0.134134:0.384008:0.124585:0.379091:0.124585:0.000000
>:@0.387938:0.153408:0.398746:0.153408:0.398746:0.136910:0.387938:0.136910:0.000000
x:@0.408879:0.153523:0.416354:0.153523:0.416354:0.137055:0.408879:0.137055:0.000000
2:@0.417045:0.155627:0.421963:0.155627:0.421963:0.146078:0.417045:0.146078:0.000000
+:@0.425421:0.154044:0.435998:0.154044:0.435998:0.137763:0.425421:0.137763:0.000000
1:@0.439870:0.144573:0.448366:0.144573:0.448366:0.128076:0.439870:0.128076:0.000000
2:@0.439234:0.164772:0.447730:0.164772:0.447730:0.148275:0.439234:0.148275:0.000000
2:@0.457408:0.134134:0.462326:0.134134:0.462326:0.124585:0.457408:0.124585:0.000000
0:@0.480599:0.153408:0.489095:0.153408:0.489095:0.136910:0.480599:0.136910:0.000000
, y :@0.507127:0.156545:0.525988:0.156545:0.525988:0.140048:0.507127:0.140048:0.000000:0.000000:0.000000:0.000000
sumando   en esta última desigualdad, se deduce :@0.108240:0.194023:0.473932:0.194017:0.473932:0.177520:0.108240:0.177525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.184131:0.184704:0.192627:0.184704:0.192627:0.168207:0.184131:0.168207:0.000000
4:@0.184131:0.205019:0.192627:0.205019:0.192627:0.188521:0.184131:0.188521:0.000000
x:@0.115964:0.229972:0.123439:0.229972:0.123439:0.213504:0.115964:0.213504:0.000000
1:@0.123660:0.232076:0.128578:0.232076:0.128578:0.222527:0.123660:0.222527:0.000000
+:@0.130884:0.230493:0.141461:0.230493:0.141461:0.214212:0.130884:0.214212:0.000000
1:@0.145333:0.221022:0.153829:0.221022:0.153829:0.204525:0.145333:0.204525:0.000000
2:@0.144697:0.241221:0.153193:0.241221:0.153193:0.224724:0.144697:0.224724:0.000000
2:@0.162871:0.210583:0.167788:0.210583:0.167788:0.201034:0.162871:0.201034:0.000000
+:@0.171247:0.230493:0.181824:0.230493:0.181824:0.214212:0.171247:0.214212:0.000000
3:@0.185484:0.221022:0.193980:0.221022:0.193980:0.204525:0.185484:0.204525:0.000000
4:@0.185484:0.241221:0.193980:0.241221:0.193980:0.224724:0.185484:0.224724:0.000000
>:@0.197736:0.229857:0.208544:0.229857:0.208544:0.213359:0.197736:0.213359:0.000000
x:@0.218677:0.229972:0.226152:0.229972:0.226152:0.213504:0.218677:0.213504:0.000000
2:@0.226843:0.232076:0.231761:0.232076:0.231761:0.222527:0.226843:0.222527:0.000000
+:@0.235220:0.230493:0.245796:0.230493:0.245796:0.214212:0.235220:0.214212:0.000000
1:@0.249669:0.221022:0.258164:0.221022:0.258164:0.204525:0.249669:0.204525:0.000000
2:@0.249033:0.241221:0.257529:0.241221:0.257529:0.224724:0.249033:0.224724:0.000000
2:@0.267207:0.210583:0.272124:0.210583:0.272124:0.201034:0.267207:0.201034:0.000000
+:@0.275583:0.230493:0.286159:0.230493:0.286159:0.214212:0.275583:0.214212:0.000000
3:@0.289820:0.221022:0.298316:0.221022:0.298316:0.204525:0.289820:0.204525:0.000000
4:@0.289820:0.241221:0.298316:0.241221:0.298316:0.224724:0.289820:0.224724:0.000000
3:@0.317935:0.221015:0.326431:0.221015:0.326431:0.204518:0.317935:0.204518:0.000000
4:@0.317935:0.241214:0.326431:0.241214:0.326431:0.224717:0.317935:0.224717:0.000000
,:@0.330341:0.229857:0.333096:0.229857:0.333096:0.213359:0.330341:0.213359:0.000000
 es decir que  ()>( ):@0.340918:0.231736:0.526219:0.230479:0.526219:0.213981:0.340918:0.215239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.545022:0.221167:0.553518:0.221167:0.553518:0.204670:0.545022:0.204670:0.000000
4:@0.545017:0.241480:0.553513:0.241480:0.553513:0.224983:0.545017:0.224983:0.000000
.   :@0.556743:0.230479:0.571563:0.231737:0.571563:0.215239:0.556743:0.213981:0.000000:0.000000:0.000000:0.000000
1:@0.461936:0.232698:0.466854:0.232698:0.466854:0.223149:0.461936:0.223149:0.000000
2:@0.513497:0.232698:0.518415:0.232698:0.518415:0.223149:0.513497:0.223149:0.000000
≥:@0.529469:0.231115:0.540045:0.231115:0.540045:0.214834:0.529469:0.214834:0.000000
fx:@0.440425:0.230595:0.461713:0.230595:0.461713:0.214126:0.440425:0.214126:0.000000:0.000000
fx:@0.491516:0.230595:0.512804:0.230595:0.512804:0.214126:0.491516:0.214126:0.000000:0.000000
De modo similar, se muestra que si :@0.108234:0.266901:0.365780:0.266900:0.365780:0.250403:0.108234:0.250403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.372309:0.265428:0.399213:0.265428:0.399213:0.248959:0.372309:0.248959:0.000000:0.000000:0.000000
1:@0.380006:0.267531:0.384923:0.267531:0.384923:0.257983:0.380006:0.257983:0.000000
,:@0.386864:0.265313:0.389619:0.265313:0.389619:0.248815:0.386864:0.248815:0.000000
2:@0.399899:0.267531:0.404816:0.267531:0.404816:0.257983:0.399899:0.257983:0.000000
1:@0.446544:0.256472:0.455040:0.256472:0.455040:0.239975:0.446544:0.239975:0.000000
2:@0.445909:0.276672:0.454405:0.276672:0.454405:0.260174:0.445909:0.260174:0.000000
,:@0.458323:0.265313:0.461078:0.265313:0.461078:0.248815:0.458323:0.248815:0.000000
, tal que  <  , :@0.487420:0.266902:0.599909:0.266902:0.599909:0.250404:0.487420:0.250404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.550724:0.267017:0.558199:0.267017:0.558199:0.250549:0.550724:0.250549:0.000000
1 :@0.558197:0.269636:0.564699:0.269636:0.564699:0.260869:0.558197:0.260869:0.000000:0.000000
x:@0.581242:0.267017:0.588717:0.267017:0.588717:0.250549:0.581242:0.250549:0.000000
2:@0.588715:0.269636:0.593012:0.269636:0.593012:0.260869:0.588715:0.260869:0.000000
 :@0.595767:0.266902:0.599909:0.266902:0.599909:0.250404:0.595767:0.250404:0.000000
entonces :@0.108241:0.293680:0.177093:0.293680:0.177093:0.277182:0.108241:0.277182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.183751:0.282535:0.192247:0.282535:0.192247:0.266037:0.183751:0.266037:0.000000
4:@0.183751:0.302835:0.192247:0.302835:0.192247:0.286338:0.183751:0.286338:0.000000
()<( ).:@0.221588:0.291838:0.302676:0.291838:0.302676:0.275340:0.221588:0.275340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.235985:0.294057:0.240903:0.294057:0.240903:0.284508:0.235985:0.284508:0.000000
2:@0.287546:0.294057:0.292464:0.294057:0.292464:0.284508:0.287546:0.284508:0.000000
<:@0.197297:0.291838:0.208105:0.291838:0.208105:0.275340:0.197297:0.275340:0.000000
fx:@0.214482:0.291953:0.235770:0.291953:0.235770:0.275485:0.214482:0.275485:0.000000:0.000000
fx:@0.265573:0.291953:0.286861:0.291953:0.286861:0.275485:0.265573:0.275485:0.000000:0.000000
 La prueba se propone como ejercicio. :@0.304412:0.293689:0.578900:0.293689:0.578900:0.277191:0.304412:0.277191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la gráfica se interpretan estos dos resultados (figura 3.4.).:@0.108234:0.318168:0.527916:0.318162:0.527916:0.301664:0.108234:0.301670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.108226:0.353080:0.120498:0.353080:0.120498:0.336366:0.108226:0.336366:0.000000:0.000000
  Consideremos la función  , definida como :@0.120499:0.352863:0.435001:0.352863:0.435001:0.336366:0.120499:0.336366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.312572:0.352979:0.320008:0.352979:0.320008:0.336510:0.312572:0.336510:0.000000
 :@0.108226:0.372094:0.112368:0.372094:0.112368:0.355596:0.108226:0.355596:0.000000
−+:@0.180897:0.372735:0.220313:0.372735:0.220313:0.356454:0.180897:0.356454:0.000000:0.000000
−:@0.243046:0.372735:0.253623:0.372735:0.253623:0.356454:0.243046:0.356454:0.000000
∀ ∈:@0.277550:0.372735:0.316563:0.372735:0.316563:0.356454:0.277550:0.356454:0.000000:0.000000:0.000000
() =:@0.144158:0.372099:0.178411:0.372099:0.178411:0.355601:0.144158:0.355601:0.000000:0.000000:0.000000:0.000000
4:@0.222683:0.372099:0.231179:0.372099:0.231179:0.355601:0.222683:0.355601:0.000000
4,:@0.255973:0.372099:0.268631:0.372099:0.268631:0.355601:0.255973:0.355601:0.000000:0.000000
.:@0.334922:0.372099:0.337677:0.372099:0.337677:0.355601:0.334922:0.355601:0.000000
2:@0.201105:0.364063:0.206022:0.364063:0.206022:0.354514:0.201105:0.354514:0.000000
gx:@0.135823:0.372215:0.158324:0.372215:0.158324:0.355746:0.135823:0.355746:0.000000:0.000000
x:@0.192424:0.372215:0.199899:0.372215:0.199899:0.355746:0.192424:0.355746:0.000000
x:@0.232573:0.372215:0.240048:0.372215:0.240048:0.355746:0.232573:0.355746:0.000000
x:@0.291158:0.372215:0.298633:0.372215:0.298633:0.355746:0.291158:0.355746:0.000000
 :@0.108233:0.395780:0.112375:0.395780:0.112375:0.379282:0.108233:0.379282:0.000000
  Puesto que :@0.131687:0.395780:0.215084:0.395780:0.215084:0.379282:0.131687:0.379282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−+:@0.180897:0.416533:0.220313:0.416533:0.220313:0.400252:0.180897:0.400252:0.000000:0.000000
−:@0.243046:0.416533:0.253623:0.416533:0.253623:0.400252:0.243046:0.400252:0.000000
−:@0.280941:0.416533:0.291518:0.416533:0.291518:0.400252:0.280941:0.400252:0.000000
−:@0.315753:0.416533:0.326330:0.416533:0.326330:0.400252:0.315753:0.400252:0.000000
+:@0.348639:0.416533:0.359216:0.416533:0.359216:0.400252:0.348639:0.400252:0.000000
−−:@0.401503:0.416533:0.439610:0.416533:0.439610:0.400252:0.401503:0.400252:0.000000:0.000000
∀∈:@0.476002:0.416533:0.515033:0.416533:0.515033:0.400252:0.476002:0.400252:0.000000:0.000000
()=:@0.144138:0.415897:0.178392:0.415897:0.178392:0.399399:0.144138:0.399399:0.000000:0.000000:0.000000
4:@0.222664:0.415897:0.231160:0.415897:0.231160:0.399399:0.222664:0.399399:0.000000
4= (:@0.255954:0.415897:0.297239:0.415897:0.297239:0.399399:0.255954:0.399399:0.000000:0.000000:0.000000:0.000000
4:@0.328661:0.415897:0.337157:0.415897:0.337157:0.399399:0.328661:0.399399:0.000000
4)=(:@0.361547:0.415897:0.417801:0.415897:0.417801:0.399399:0.361547:0.399399:0.000000:0.000000:0.000000:0.000000
2) ,:@0.441536:0.415897:0.467082:0.415897:0.467082:0.399399:0.441536:0.399399:0.000000:0.000000:0.000000:0.000000
,  y :@0.534106:0.415897:0.556557:0.415897:0.556557:0.399399:0.534106:0.399399:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.201105:0.407861:0.206022:0.407861:0.206022:0.398312:0.201105:0.398312:0.000000
2:@0.306702:0.407861:0.311620:0.407861:0.311620:0.398312:0.306702:0.398312:0.000000
2:@0.456267:0.407861:0.461185:0.407861:0.461185:0.398312:0.456267:0.398312:0.000000
gx:@0.135823:0.416013:0.158324:0.416013:0.158324:0.399544:0.135823:0.399544:0.000000:0.000000
x:@0.192424:0.416013:0.199899:0.416013:0.199899:0.399544:0.192424:0.399544:0.000000
x:@0.232573:0.416013:0.240048:0.416013:0.240048:0.399544:0.232573:0.399544:0.000000
x:@0.298017:0.416013:0.305492:0.416013:0.305492:0.399544:0.298017:0.399544:0.000000
x:@0.338589:0.416013:0.346064:0.416013:0.346064:0.399544:0.338589:0.399544:0.000000
x:@0.371475:0.416013:0.378950:0.416013:0.378950:0.399544:0.371475:0.399544:0.000000
x:@0.418598:0.416013:0.426073:0.416013:0.426073:0.399544:0.418598:0.399544:0.000000
x:@0.489629:0.416013:0.497104:0.416013:0.497104:0.399544:0.489629:0.399544:0.000000
tomando en consideración que :@0.131700:0.436009:0.359080:0.436009:0.359080:0.419512:0.131700:0.419512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.361528:0.433904:0.367227:0.433904:0.367227:0.418109:0.361528:0.418109:0.000000
2):@0.389546:0.433904:0.403325:0.433904:0.403325:0.418109:0.389546:0.418109:0.000000:0.000000
0,:@0.426640:0.433904:0.438749:0.433904:0.438749:0.418109:0.426640:0.418109:0.000000:0.000000
,:@0.504230:0.433904:0.506868:0.433904:0.506868:0.418109:0.504230:0.418109:0.000000
2:@0.403631:0.426210:0.408340:0.426210:0.408340:0.417067:0.403631:0.417067:0.000000
x:@0.367944:0.434015:0.375101:0.434015:0.375101:0.418247:0.367944:0.418247:0.000000
x:@0.461333:0.434015:0.468490:0.434015:0.468490:0.418247:0.461333:0.418247:0.000000
−:@0.377767:0.434513:0.387894:0.434513:0.387894:0.418925:0.377767:0.418925:0.000000
≥:@0.413348:0.434513:0.423475:0.434513:0.423475:0.418925:0.413348:0.418925:0.000000
∀∈:@0.448284:0.434513:0.485802:0.434513:0.485802:0.418925:0.448284:0.418925:0.000000:0.000000
 resulta  :@0.509843:0.436014:0.569489:0.436014:0.569489:0.419516:0.509843:0.419516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
() 0,:@0.141014:0.455062:0.188104:0.455062:0.188104:0.439570:0.141014:0.439570:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.252325:0.455062:0.254912:0.455062:0.254912:0.439570:0.252325:0.439570:0.000000
gx:@0.133197:0.455171:0.154327:0.455171:0.154327:0.439706:0.133197:0.439706:0.000000:0.000000
x:@0.210227:0.455171:0.217246:0.455171:0.217246:0.439706:0.210227:0.439706:0.000000
≤:@0.163174:0.455659:0.173105:0.455659:0.173105:0.440371:0.163174:0.440371:0.000000
∀ ∈:@0.197437:0.455659:0.234233:0.455659:0.234233:0.440371:0.197437:0.440371:0.000000:0.000000:0.000000
 es decir que el recorrido de   es el conjunto :@0.258308:0.456131:0.574599:0.456131:0.574599:0.439633:0.258308:0.439633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.459163:0.456246:0.466600:0.456246:0.466600:0.439777:0.459163:0.439777:0.000000
Recg:@0.131348:0.476363:0.169884:0.476363:0.169884:0.459894:0.131348:0.459894:0.000000:0.000000:0.000000:0.000000
−∞:@0.197260:0.476884:0.224713:0.476884:0.224713:0.460603:0.197260:0.460603:0.000000:0.000000
()=]:@0.155326:0.476247:0.195417:0.476247:0.195417:0.459750:0.155326:0.459750:0.000000:0.000000:0.000000:0.000000
,0]. El dominio de   es obviamente el conjunto  .:@0.226106:0.476247:0.581109:0.476247:0.581109:0.459750:0.226106:0.459750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.359927:0.476363:0.367363:0.476363:0.367363:0.459894:0.359927:0.459894:0.000000
R:@0.564444:0.475279:0.578354:0.475279:0.578354:0.461832:0.564444:0.461832:0.000000
 :@0.108228:0.503488:0.112370:0.503488:0.112370:0.486990:0.108228:0.486990:0.000000
Calculemos algunos valores de la función  .:@0.131675:0.503488:0.438065:0.503488:0.438065:0.486990:0.131675:0.486990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.427874:0.503604:0.435311:0.503604:0.435311:0.487135:0.427874:0.487135:0.000000
 :@0.108228:0.529008:0.112370:0.529008:0.112370:0.512510:0.108228:0.512510:0.000000
(2)= (2 2) =0,:@0.144147:0.522729:0.271606:0.522729:0.271606:0.506231:0.144147:0.506231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(1)=(12)= 1, (3)= (3 2) =1.:@0.301929:0.522729:0.591834:0.522729:0.591834:0.506231:0.301929:0.506231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.236704:0.514693:0.241621:0.514693:0.241621:0.505144:0.236704:0.505144:0.000000
2:@0.392502:0.514693:0.397419:0.514693:0.397419:0.505144:0.392502:0.505144:0.000000
−−:@0.180635:0.523365:0.219281:0.523365:0.219281:0.507084:0.180635:0.507084:0.000000:0.000000
−−:@0.338418:0.523365:0.375060:0.523365:0.375060:0.507084:0.338418:0.507084:0.000000:0.000000
−:@0.416211:0.523365:0.426787:0.523365:0.426787:0.507084:0.416211:0.507084:0.000000
g:@0.135823:0.522844:0.143259:0.522844:0.143259:0.506375:0.135823:0.506375:0.000000
g:@0.293605:0.522844:0.301041:0.522844:0.301041:0.506375:0.293605:0.506375:0.000000
−−:@0.490973:0.523365:0.528984:0.523365:0.528984:0.507084:0.490973:0.507084:0.000000:0.000000
−:@0.570231:0.523365:0.580807:0.523365:0.580807:0.507084:0.570231:0.507084:0.000000
g:@0.445739:0.522844:0.453175:0.522844:0.453175:0.506375:0.445739:0.506375:0.000000
2:@0.546204:0.514693:0.551122:0.514693:0.551122:0.505144:0.546204:0.505144:0.000000
En la figura 3.5. se muestra la gráfica de la función  . :@0.108233:0.553493:0.476408:0.553493:0.476408:0.536996:0.108233:0.536996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.462074:0.553609:0.469511:0.553609:0.469511:0.537140:0.462074:0.537140:0.000000
Esta es una parábola que se abre hacia abajo,:@0.108233:0.577972:0.432699:0.577972:0.432699:0.561475:0.108233:0.561475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−−:@0.155716:0.604974:0.193823:0.604974:0.193823:0.588693:0.155716:0.588693:0.000000:0.000000
∀∈:@0.230215:0.604974:0.269246:0.604974:0.269246:0.588693:0.230215:0.588693:0.000000:0.000000
() =(:@0.118977:0.604337:0.172034:0.604337:0.172034:0.587840:0.118977:0.587840:0.000000:0.000000:0.000000:0.000000:0.000000
2) ,:@0.195769:0.604337:0.221295:0.604337:0.221295:0.587840:0.195769:0.587840:0.000000:0.000000:0.000000:0.000000
2:@0.210476:0.596302:0.215394:0.596302:0.215394:0.586753:0.210476:0.586753:0.000000
gx:@0.110642:0.604453:0.133144:0.604453:0.133144:0.587984:0.110642:0.587984:0.000000:0.000000
x:@0.172783:0.604453:0.180258:0.604453:0.180258:0.587984:0.172783:0.587984:0.000000
x:@0.243834:0.604453:0.251309:0.604453:0.251309:0.587984:0.243834:0.587984:0.000000
, y su vértice es el punto (2, 0).:@0.287956:0.604337:0.499737:0.604337:0.499737:0.587840:0.287956:0.587840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.244492:0.644007:0.250472:0.644007:0.250472:0.630832:0.244492:0.630832:0.000000
:@0.250472:0.643741:0.263310:0.643741:0.263310:0.632023:0.250472:0.632023:0.000000
R:@0.263312:0.643139:0.274439:0.643139:0.274439:0.632382:0.263312:0.632382:0.000000
Se tiene 0 =  (2) = :@0.108233:0.632764:0.242936:0.632764:0.242936:0.616266:0.108233:0.616266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.196006:0.632879:0.203442:0.632879:0.203442:0.616411:0.196006:0.616411:0.000000
máx g(x).:@0.242936:0.632879:0.306933:0.632879:0.306933:0.616411:0.242936:0.616411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta función es estrictamente creciente en el intervalo ]–∞, 2] y estric-:@0.108233:0.676256:0.595760:0.676256:0.595760:0.659759:0.108233:0.659759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tamente decreciente sobre el intervalo [2, ∞[ .:@0.108233:0.693607:0.433043:0.693607:0.433043:0.677109:0.108233:0.677109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Probemos que es estrictamente creciente en el intervalo ]–∞, 2].:@0.108233:0.725214:0.563773:0.725214:0.563773:0.708717:0.108233:0.708717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,    ]–∞, 2], tal que :@0.108233:0.756822:0.318148:0.756823:0.318148:0.740325:0.108233:0.740324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.147688:0.756937:0.175712:0.756939:0.175712:0.740470:0.147688:0.740469:0.000000:0.000000:0.000000
1:@0.155160:0.759494:0.159682:0.759494:0.159682:0.750712:0.155160:0.750712:0.000000
2:@0.175708:0.759494:0.180231:0.759494:0.180231:0.750712:0.175708:0.750712:0.000000
:@0.186029:0.756606:0.202077:0.756606:0.202077:0.741959:0.186029:0.741959:0.000000
x x:@0.319805:0.756939:0.352215:0.756939:0.352215:0.740470:0.319805:0.740470:0.000000:0.000000:0.000000
1   2 :@0.327264:0.759494:0.358942:0.759494:0.358942:0.750712:0.327264:0.750712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
<:@0.331787:0.756502:0.341655:0.756502:0.341655:0.741439:0.331787:0.741439:0.000000
≤:@0.359822:0.756502:0.369690:0.756502:0.369690:0.741439:0.359822:0.741439:0.000000
 2. Sumando –2 en la desigual-:@0.369689:0.756823:0.595786:0.756823:0.595786:0.740325:0.369689:0.740325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dad, obtenemos   –2 < :@0.108241:0.774795:0.295563:0.774802:0.295563:0.758305:0.108241:0.758298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.234600:0.774911:0.242074:0.774911:0.242074:0.758442:0.234600:0.758442:0.000000
1:@0.242068:0.777473:0.246590:0.777473:0.246590:0.768692:0.242068:0.768692:0.000000
x:@0.298935:0.774918:0.306410:0.774918:0.306410:0.758449:0.298935:0.758449:0.000000
2 :@0.306411:0.777473:0.313138:0.777473:0.313138:0.768692:0.306411:0.768692:0.000000:0.000000
–2 ≤ 0, de donde  (:@0.314934:0.774802:0.466826:0.776060:0.466826:0.759562:0.314934:0.758305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.467574:0.776175:0.475049:0.776175:0.475049:0.759707:0.467574:0.759707:0.000000
x:@0.540242:0.776175:0.547717:0.776175:0.547717:0.759707:0.540242:0.759707:0.000000
−:@0.483853:0.776696:0.420143:0.776696:0.420143:0.760415:0.483853:0.760415:0.000000
−:@0.558140:0.776696:0.494429:0.776696:0.494429:0.760415:0.558140:0.760415:0.000000
2)>(:@0.497149:0.776060:0.539489:0.776060:0.539489:0.759562:0.497149:0.759562:0.000000:0.000000:0.000000:0.000000
2) , :@0.571431:0.776060:0.599909:0.774802:0.599909:0.758305:0.571431:0.759562:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.475270:0.778278:0.480187:0.778278:0.480187:0.768730:0.475270:0.768730:0.000000
2:@0.511864:0.768023:0.516781:0.768023:0.516781:0.758474:0.511864:0.758474:0.000000
2:@0.548404:0.778278:0.553321:0.778278:0.553321:0.768730:0.548404:0.768730:0.000000
2:@0.586149:0.768023:0.591066:0.768023:0.591066:0.758474:0.586149:0.758474:0.000000
 :@0.595767:0.774802:0.599909:0.774802:0.599909:0.758305:0.595767:0.758305:0.000000
y multiplicando por –1, en esta última desigualdad, se deduce :@0.108241:0.792153:0.599944:0.792153:0.599944:0.775655:0.108241:0.775655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.129068:0.811505:0.136543:0.811505:0.136543:0.795037:0.129068:0.795037:0.000000
x:@0.213296:0.811505:0.220771:0.811505:0.220771:0.795037:0.213296:0.795037:0.000000
−:@0.111217:0.812026:0.087656:0.812026:0.087656:0.795745:0.111217:0.795745:0.000000
−:@0.145355:0.812026:0.121794:0.812026:0.121794:0.795745:0.145355:0.795745:0.000000
−:@0.195445:0.812026:0.170265:0.812026:0.170265:0.795745:0.195445:0.795745:0.000000
−:@0.231201:0.812026:0.206021:0.812026:0.206021:0.795745:0.231201:0.795745:0.000000
(:@0.122372:0.811390:0.128325:0.811390:0.128325:0.794892:0.122372:0.794892:0.000000
2)< (:@0.158648:0.811390:0.212554:0.811390:0.212554:0.794892:0.158648:0.794892:0.000000:0.000000:0.000000:0.000000:0.000000
2), es decir que  ()<( ).:@0.244496:0.811390:0.456073:0.810132:0.456073:0.793635:0.244496:0.794892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.136764:0.813609:0.141682:0.813609:0.141682:0.804060:0.136764:0.804060:0.000000
2:@0.173358:0.803353:0.178275:0.803353:0.178275:0.793804:0.173358:0.793804:0.000000
2:@0.221469:0.813609:0.226387:0.813609:0.226387:0.804060:0.221469:0.804060:0.000000
2:@0.259214:0.803353:0.264132:0.803353:0.264132:0.793804:0.259214:0.793804:0.000000
1:@0.390173:0.812351:0.395090:0.812351:0.395090:0.802803:0.390173:0.802803:0.000000
2:@0.440953:0.812351:0.445870:0.812351:0.445870:0.802803:0.440953:0.802803:0.000000
gx:@0.367453:0.810248:0.389955:0.810248:0.389955:0.793779:0.367453:0.793779:0.000000:0.000000
gx:@0.417755:0.810248:0.440256:0.810248:0.440256:0.793779:0.417755:0.793779:0.000000:0.000000
Así,  ,,:@0.108239:0.843619:0.162224:0.842367:0.162224:0.825869:0.108239:0.827122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈−∞∞:@0.179744:0.843003:0.229961:0.843003:0.229961:0.826723:0.179744:0.826723:0.000000:0.000000:0.000000:0.000000
]]:@0.193711:0.842367:0.202701:0.842367:0.202701:0.825869:0.193711:0.825869:0.000000:0.000000
,2],],:@0.227792:0.842367:0.252212:0.842367:0.252212:0.825869:0.227792:0.825869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
<  :@0.269527:0.842367:0.301337:0.843624:0.301337:0.827127:0.269527:0.825869:0.000000:0.000000:0.000000
( )< (),(),  lo que muestra que   es :@0.333141:0.842367:0.599890:0.843624:0.599890:0.827127:0.333141:0.825869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
11:@0.149432:0.844586:0.157482:0.844586:0.157482:0.835037:0.149432:0.835037:0.000000:0.000000
22:@0.169481:0.844586:0.177531:0.844586:0.177531:0.835037:0.169481:0.835037:0.000000:0.000000
11:@0.261620:0.844586:0.269670:0.844586:0.269670:0.835037:0.261620:0.835037:0.000000:0.000000
22:@0.291303:0.844586:0.299353:0.844586:0.299353:0.835037:0.291303:0.835037:0.000000:0.000000
11:@0.347525:0.844586:0.355575:0.844586:0.355575:0.835037:0.347525:0.835037:0.000000:0.000000
22:@0.398149:0.844586:0.406199:0.844586:0.406199:0.835037:0.398149:0.835037:0.000000:0.000000
xxxx:@0.141736:0.842483:0.171917:0.842483:0.171917:0.826014:0.141736:0.826014:0.000000:0.000000:0.000000:0.000000
xx:@0.253925:0.842483:0.264525:0.842483:0.264525:0.826014:0.253925:0.826014:0.000000:0.000000
xx:@0.283131:0.842483:0.293732:0.842483:0.293732:0.826014:0.283131:0.826014:0.000000:0.000000
gxgx:@0.324802:0.842483:0.350443:0.842483:0.350443:0.826014:0.324802:0.826014:0.000000:0.000000:0.000000:0.000000
gxgx:@0.374950:0.842483:0.400590:0.842483:0.400590:0.826014:0.374950:0.826014:0.000000:0.000000:0.000000:0.000000
⇒:@0.302011:0.844174:0.321026:0.844174:0.321026:0.825334:0.302011:0.825334:0.000000
 :@0.321026:0.843624:0.325168:0.843624:0.325168:0.827127:0.321026:0.827127:0.000000
∈−:@0.182877:0.843003:0.214703:0.843003:0.214703:0.826723:0.182877:0.826723:0.000000:0.000000
,2:@0.230924:0.842367:0.243235:0.842367:0.243235:0.825869:0.230924:0.825869:0.000000:0.000000
<:@0.272653:0.842367:0.283461:0.842367:0.283461:0.825869:0.272653:0.825869:0.000000
(:@0.336267:0.842367:0.342220:0.842367:0.342220:0.825869:0.336267:0.825869:0.000000
)<:@0.356001:0.842367:0.374881:0.842367:0.374881:0.825869:0.356001:0.825869:0.000000:0.000000
g:@0.569123:0.843740:0.576559:0.843740:0.576559:0.827271:0.569123:0.827271:0.000000
creciente en el conjunto   = ]–∞, 2]. En forma similar, se prueba que   :@0.108223:0.860975:0.599811:0.860975:0.599811:0.844478:0.108223:0.844478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I:@0.283689:0.861091:0.287696:0.861091:0.287696:0.844622:0.283689:0.844622:0.000000
g:@0.588232:0.861091:0.595669:0.861091:0.595669:0.844622:0.588232:0.844622:0.000000
es decreciente en el conjunto   = [2, ∞[.:@0.108223:0.878326:0.386953:0.878326:0.386953:0.861828:0.108223:0.861828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I:@0.320680:0.878442:0.324687:0.878442:0.324687:0.861973:0.320680:0.861973:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000