45:@0.921538:0.966074:0.940353:0.966074:0.940353:0.949450:0.921538:0.949450:0.000000:0.000000 Producto de números reales por funciones:@0.108233:0.097328:0.448106:0.097328:0.448106:0.079645:0.108233:0.079645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.108233:0.114498:0.188317:0.114498:0.188317:0.097552:0.108233:0.097552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean :@0.188319:0.114035:0.232530:0.114035:0.232530:0.097538:0.188319:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.232052:0.121109:0.240636:0.121109:0.240636:0.102974:0.232052:0.102974:0.000000 , f F(A).:@0.240632:0.114151:0.331912:0.114151:0.331912:0.097682:0.240632:0.097682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.257948:0.112948:0.271252:0.112948:0.271252:0.100086:0.257948:0.100086:0.000000 El producto de por se designa con :@0.331912:0.114035:0.599903:0.114035:0.599903:0.097538:0.331912:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.444273:0.121109:0.452857:0.121109:0.452857:0.102974:0.444273:0.102974:0.000000 f:@0.485467:0.114151:0.489764:0.114151:0.489764:0.097682:0.485467:0.097682:0.000000 :@0.595761:0.114035:0.599903:0.114035:0.599903:0.097538:0.595761:0.097538:0.000000 λ:@0.108233:0.138460:0.116817:0.138460:0.116817:0.120325:0.108233:0.120325:0.000000 f:@0.116813:0.131502:0.121110:0.131502:0.121110:0.115033:0.116813:0.115033:0.000000 y es la función definida en como::@0.121110:0.131386:0.374465:0.131386:0.374465:0.114888:0.121110:0.114888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.314512:0.131502:0.325782:0.131502:0.325782:0.115033:0.314512:0.115033:0.000000 (:@0.267506:0.155865:0.273459:0.155865:0.273459:0.139367:0.267506:0.139367:0.000000 λ:@0.273452:0.162940:0.282036:0.162940:0.282036:0.144804:0.273452:0.144804:0.000000 f) (x) = f(x), x A.:@0.282032:0.155981:0.436501:0.155981:0.436501:0.139513:0.282032:0.139513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.335126:0.162940:0.343710:0.162940:0.343710:0.144804:0.335126:0.144804:0.000000 :@0.108241:0.173216:0.112383:0.173216:0.112383:0.156719:0.108241:0.156719:0.000000 Intervienen los siguientes elementos: :@0.108241:0.190567:0.374827:0.190567:0.374827:0.174070:0.108241:0.174070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.375985:0.197641:0.384569:0.197641:0.384569:0.179506:0.375985:0.179506:0.000000 , f(x) :@0.384566:0.190683:0.478060:0.190683:0.478060:0.174214:0.384566:0.174214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.389879:0.190049:0.404532:0.190049:0.404532:0.176675:0.389879:0.176675:0.000000 R:@0.409845:0.189480:0.423150:0.189480:0.423150:0.176618:0.409845:0.176618:0.000000 :@0.459264:0.190049:0.473917:0.190049:0.473917:0.176675:0.459264:0.176675:0.000000 R:@0.479232:0.189480:0.492536:0.189480:0.492536:0.176618:0.479232:0.176618:0.000000 y el producto :@0.492536:0.190567:0.599921:0.190567:0.599921:0.174070:0.492536:0.174070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de números reales “ ”, de modo que :@0.108233:0.207918:0.367907:0.207918:0.367907:0.191420:0.108233:0.191420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.249216:0.204607:0.253243:0.204607:0.253243:0.187661:0.249216:0.187661:0.000000 λ:@0.368678:0.214992:0.377261:0.214992:0.377261:0.196856:0.368678:0.196856:0.000000 f(x) ,:@0.377256:0.208034:0.454187:0.208034:0.454187:0.191565:0.377256:0.191565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.382150:0.204607:0.390203:0.204607:0.390203:0.187661:0.382150:0.187661:0.000000:0.000000 :@0.418481:0.207399:0.433133:0.207399:0.433133:0.194026:0.418481:0.194026:0.000000 R:@0.438031:0.206831:0.451336:0.206831:0.451336:0.193969:0.438031:0.193969:0.000000 que se escribe sim-:@0.454187:0.207918:0.595744:0.207918:0.595744:0.191420:0.454187:0.191420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 plemente :@0.108241:0.225269:0.180348:0.225269:0.180348:0.208771:0.108241:0.208771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.180831:0.232343:0.189415:0.232343:0.189415:0.214207:0.180831:0.214207:0.000000 f (x). :@0.189412:0.225384:0.223665:0.225384:0.223665:0.208916:0.189412:0.208916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Este elemento :@0.224147:0.225269:0.329256:0.225269:0.329256:0.208771:0.224147:0.208771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.329768:0.232343:0.338352:0.232343:0.338352:0.214207:0.329768:0.214207:0.000000 f (x):@0.338349:0.225384:0.365609:0.225384:0.365609:0.208916:0.338349:0.208916:0.000000:0.000000:0.000000:0.000000:0.000000 es la imagen de la función en :@0.365609:0.225269:0.599902:0.225269:0.599902:0.208771:0.365609:0.208771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.560709:0.232343:0.569293:0.232343:0.569293:0.214207:0.560709:0.214207:0.000000 f:@0.569289:0.225384:0.573585:0.225384:0.573585:0.208916:0.569289:0.208916:0.000000 :@0.595760:0.225269:0.599902:0.225269:0.599902:0.208771:0.595760:0.208771:0.000000 x A:@0.108233:0.242735:0.147998:0.242735:0.147998:0.226266:0.108233:0.226266:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.118880:0.242101:0.133532:0.242101:0.133532:0.228728:0.118880:0.228728:0.000000 , así, (:@0.147806:0.242619:0.183100:0.242619:0.183100:0.226122:0.147806:0.226122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.182885:0.249694:0.191469:0.249694:0.191469:0.231558:0.182885:0.231558:0.000000 f)(x) = f(x) . :@0.191290:0.242735:0.304250:0.242735:0.304250:0.226266:0.191290:0.226266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.237531:0.249694:0.246115:0.249694:0.246115:0.231558:0.237531:0.231558:0.000000 R:@0.284329:0.241533:0.297634:0.241533:0.297634:0.228670:0.284329:0.228670:0.000000 Se tiene, entonces, la siguiente implicación::@0.303480:0.242619:0.595807:0.242619:0.595807:0.226122:0.303480:0.226122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.250251:0.274172:0.258835:0.274172:0.258835:0.256036:0.250251:0.256036:0.000000 , f F(A) :@0.258830:0.267214:0.363127:0.267214:0.363127:0.250745:0.258830:0.250745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.262973:0.266579:0.277626:0.266579:0.277626:0.253206:0.262973:0.253206:0.000000 R:@0.281768:0.266011:0.295073:0.266011:0.295073:0.253149:0.281768:0.253149:0.000000 :@0.310503:0.266579:0.325156:0.266579:0.325156:0.253206:0.310503:0.253206:0.000000 ⇒ :@0.363126:0.266454:0.385921:0.266454:0.385921:0.249511:0.363126:0.249511:0.000000:0.000000 λ:@0.385917:0.274172:0.394501:0.274172:0.394501:0.256036:0.385917:0.256036:0.000000 f F(A).:@0.394498:0.267214:0.453750:0.267214:0.453750:0.250745:0.394498:0.250745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicios resueltos:@0.108227:0.300252:0.238882:0.300252:0.238882:0.283465:0.108227:0.283465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.238882:0.299876:0.243024:0.299876:0.243024:0.283379:0.238882:0.283379:0.000000 1.:@0.108227:0.324457:0.120499:0.324457:0.120499:0.307742:0.108227:0.307742:0.000000:0.000000 Sea la función real definida como :@0.120499:0.324240:0.380847:0.324240:0.380847:0.307742:0.120499:0.307742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.160225:0.324355:0.164521:0.324355:0.164521:0.307887:0.160225:0.307887:0.000000 f(x) = x +:@0.380847:0.324355:0.449873:0.324353:0.449873:0.307884:0.380847:0.307887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.430140:0.317953:0.434846:0.317953:0.434846:0.308352:0.430140:0.308352:0.000000 :@0.449873:0.315547:0.454015:0.315547:0.454015:0.299079:0.449873:0.299079:0.000000 1:@0.456154:0.314044:0.464650:0.314044:0.464650:0.297546:0.456154:0.297546:0.000000 2:@0.456154:0.330382:0.464650:0.330382:0.464650:0.313885:0.456154:0.313885:0.000000 , x .:@0.470872:0.324353:0.524433:0.324353:0.524433:0.307884:0.470872:0.307884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.489482:0.323719:0.504135:0.323719:0.504135:0.310345:0.489482:0.310345:0.000000 R:@0.508277:0.323150:0.521582:0.323150:0.521582:0.310288:0.508277:0.310288:0.000000 :@0.108226:0.341704:0.112368:0.341704:0.112368:0.325235:0.108226:0.325235:0.000000 Entonces, es la función definida como sigue: :@0.131961:0.341588:0.464898:0.341588:0.464898:0.325090:0.131961:0.325090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2f:@0.204108:0.341704:0.216476:0.341704:0.216476:0.325235:0.204108:0.325235:0.000000:0.000000 2:@0.190234:0.369786:0.199100:0.369786:0.199100:0.352571:0.190234:0.352571:0.000000 f x:@0.203120:0.369907:0.233896:0.369907:0.233896:0.352722:0.203120:0.352722:0.000000:0.000000:0.000000 ( )( ):@0.182383:0.371267:0.242597:0.371267:0.242597:0.349668:0.182383:0.349668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =2:@0.244314:0.369786:0.266890:0.369786:0.266890:0.352571:0.244314:0.352571:0.000000:0.000000 f x:@0.270911:0.369907:0.295094:0.369907:0.295094:0.352722:0.270911:0.352722:0.000000:0.000000:0.000000 ( ):@0.278184:0.371267:0.303796:0.371267:0.303796:0.349668:0.278184:0.349668:0.000000:0.000000:0.000000 =2:@0.305513:0.369786:0.328088:0.369786:0.328088:0.352571:0.305513:0.352571:0.000000:0.000000 x:@0.335607:0.369907:0.343407:0.369907:0.343407:0.352722:0.335607:0.352722:0.000000 2:@0.344671:0.361405:0.349797:0.361405:0.349797:0.351453:0.344671:0.351453:0.000000 +:@0.353466:0.369756:0.369106:0.369756:0.369106:0.351605:0.353466:0.351605:0.000000 1:@0.373147:0.360402:0.382012:0.360402:0.382012:0.343187:0.373147:0.343187:0.000000 2:@0.372524:0.381494:0.381389:0.381494:0.381389:0.364279:0.372524:0.364279:0.000000 =2:@0.391054:0.369786:0.413629:0.369786:0.413629:0.352571:0.391054:0.352571:0.000000:0.000000 x:@0.415137:0.369907:0.422937:0.369907:0.422937:0.352722:0.415137:0.352722:0.000000 2:@0.424193:0.361405:0.429319:0.361405:0.429319:0.351453:0.424193:0.351453:0.000000 +:@0.432988:0.369756:0.448628:0.369756:0.448628:0.351605:0.432988:0.351605:0.000000 1 ,:@0.449633:0.369786:0.465696:0.369786:0.465696:0.352571:0.449633:0.352571:0.000000:0.000000:0.000000 x:@0.474340:0.369907:0.482140:0.369907:0.482140:0.352722:0.474340:0.352722:0.000000 .:@0.516331:0.370391:0.519206:0.370391:0.519206:0.353176:0.516331:0.353176:0.000000 :@0.108233:0.404579:0.112375:0.404579:0.112375:0.388081:0.108233:0.388081:0.000000 Calculemos algunos valores de las funciones y .:@0.131968:0.404579:0.484497:0.404579:0.484497:0.388081:0.131968:0.388081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f 2f:@0.448972:0.404694:0.481742:0.404694:0.481742:0.388226:0.448972:0.388226:0.000000:0.000000:0.000000:0.000000 :@0.108233:0.548214:0.112375:0.548214:0.112375:0.531716:0.108233:0.531716:0.000000 x:@0.193434:0.441131:0.201525:0.441131:0.201525:0.423968:0.193434:0.423968:0.000000 f(x) = x +:@0.293247:0.441131:0.369936:0.441131:0.369936:0.423968:0.293247:0.423968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.348109:0.434490:0.358667:0.434490:0.358667:0.424484:0.348109:0.424484:0.000000:0.000000:0.000000 :@0.369936:0.436099:0.374464:0.436099:0.374464:0.418936:0.369936:0.418936:0.000000 1:@0.374464:0.435868:0.383846:0.435868:0.383846:0.418922:0.374464:0.418922:0.000000 :@0.383846:0.440900:0.387872:0.440900:0.387872:0.423954:0.383846:0.423954:0.000000 2:@0.291585:0.448187:0.385522:0.448187:0.385522:0.431241:0.291585:0.431241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2f(x) = 2x + 1:@0.451602:0.441131:0.559229:0.441131:0.559229:0.423968:0.451602:0.423968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.524570:0.434490:0.529849:0.434490:0.529849:0.424484:0.524570:0.424484:0.000000 –2:@0.187794:0.474155:0.207175:0.474155:0.207175:0.457600:0.187794:0.457600:0.000000:0.000000 9/2:@0.326658:0.474155:0.350451:0.474155:0.350451:0.457600:0.326658:0.457600:0.000000:0.000000:0.000000 9:@0.501086:0.474155:0.509755:0.474155:0.509755:0.457600:0.501086:0.457600:0.000000 –1/ 2:@0.171149:0.495497:0.223840:0.495497:0.223840:0.478941:0.171149:0.478941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.334230:0.495497:0.342899:0.495497:0.342899:0.478941:0.334230:0.478941:0.000000 2:@0.501105:0.495497:0.509775:0.495497:0.509775:0.478941:0.501105:0.478941:0.000000 0:@0.193169:0.516838:0.201839:0.516838:0.201839:0.500283:0.193169:0.500283:0.000000 1/2:@0.326678:0.516838:0.350470:0.516838:0.350470:0.500283:0.326678:0.500283:0.000000:0.000000:0.000000 1:@0.501105:0.516838:0.509775:0.516838:0.509775:0.500283:0.501105:0.500283:0.000000 1:@0.193169:0.538180:0.201839:0.538180:0.201839:0.521624:0.193169:0.521624:0.000000 3/2:@0.326678:0.538180:0.350470:0.538180:0.350470:0.521624:0.326678:0.521624:0.000000:0.000000:0.000000 3:@0.501105:0.538180:0.509775:0.538180:0.509775:0.521624:0.501105:0.521624:0.000000 :@0.108233:0.565566:0.112375:0.565566:0.112375:0.549068:0.108233:0.549068:0.000000 En la Figura 2.5., se representan gráficamente las funciones y:@0.131968:0.565566:0.570753:0.565566:0.570753:0.549068:0.131968:0.549068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f 2f :@0.553625:0.565682:0.592196:0.565682:0.592196:0.549213:0.553625:0.549213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.592985:0.565566:0.599882:0.565566:0.599882:0.549068:0.592985:0.549068:0.000000:0.000000 Identifica estas funciones.:@0.131968:0.582917:0.313616:0.582917:0.313616:0.566419:0.131968:0.566419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.108233:0.617835:0.120505:0.617835:0.120505:0.601121:0.108233:0.601121:0.000000:0.000000 Considera la función real definida como :@0.120506:0.617618:0.428167:0.617618:0.428167:0.601121:0.120506:0.601121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.311634:0.617734:0.315930:0.617734:0.315930:0.601265:0.311634:0.601265:0.000000 f(x) =:@0.428167:0.617734:0.465831:0.617734:0.465831:0.601265:0.428167:0.601265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.450804:0.617618:0.454946:0.617618:0.454946:0.601121:0.450804:0.601121:0.000000 :@0.465835:0.607555:0.478261:0.607555:0.478261:0.591057:0.465835:0.591057:0.000000:0.000000:0.000000 –1, x ≤ 0,:@0.478261:0.607671:0.555129:0.607671:0.555129:0.591202:0.478261:0.591202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si:@0.503363:0.607555:0.513420:0.607555:0.513420:0.591057:0.503363:0.591057:0.000000:0.000000 :@0.108233:0.625021:0.112375:0.625021:0.112375:0.608553:0.108233:0.608553:0.000000 :@0.131987:0.625021:0.136129:0.625021:0.136129:0.608553:0.131987:0.608553:0.000000 :@0.168551:0.625021:0.172693:0.625021:0.172693:0.608553:0.168551:0.608553:0.000000 :@0.228861:0.625021:0.233003:0.625021:0.233003:0.608553:0.228861:0.608553:0.000000 :@0.289168:0.625021:0.293311:0.625021:0.293311:0.608553:0.289168:0.608553:0.000000 :@0.349476:0.625021:0.353618:0.625021:0.353618:0.608553:0.349476:0.608553:0.000000 :@0.409786:0.625021:0.413928:0.625021:0.413928:0.608553:0.409786:0.608553:0.000000 x +2, si x > 0.:@0.470093:0.625021:0.575937:0.625021:0.575937:0.608553:0.470093:0.608553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para:@0.131968:0.652320:0.162311:0.652320:0.162311:0.635822:0.131968:0.635822:0.000000:0.000000:0.000000:0.000000 λ:@0.166461:0.659394:0.175045:0.659394:0.175045:0.641258:0.166461:0.641258:0.000000 ,:@0.175042:0.652435:0.214133:0.652435:0.214133:0.635967:0.175042:0.635967:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.179184:0.651801:0.193837:0.651801:0.193837:0.638428:0.179184:0.638428:0.000000 R:@0.197977:0.651233:0.211282:0.651233:0.211282:0.638371:0.197977:0.638371:0.000000 la función real está definida como::@0.214133:0.652320:0.478647:0.652320:0.478647:0.635822:0.214133:0.635822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.322366:0.659394:0.330949:0.659394:0.330949:0.641258:0.322366:0.641258:0.000000 f:@0.330944:0.652435:0.335241:0.652435:0.335241:0.635967:0.330944:0.635967:0.000000 (:@0.131973:0.687021:0.137926:0.687021:0.137926:0.670524:0.131973:0.670524:0.000000 λ:@0.137930:0.694095:0.146514:0.694095:0.146514:0.675960:0.137930:0.675960:0.000000 f)(x) = f(x) = :@0.146511:0.687137:0.249989:0.687137:0.249989:0.670668:0.146511:0.670668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.195461:0.694095:0.204045:0.694095:0.204045:0.675960:0.195461:0.675960:0.000000 :@0.249989:0.676958:0.262415:0.676958:0.262415:0.660460:0.249989:0.660460:0.000000:0.000000:0.000000 – , x ≤ 0,:@0.262415:0.677074:0.339791:0.677079:0.339791:0.660610:0.262415:0.660605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.272452:0.684037:0.281036:0.684037:0.281036:0.665901:0.272452:0.665901:0.000000 si:@0.288026:0.676963:0.298082:0.676963:0.298082:0.660465:0.288026:0.660465:0.000000:0.000000 :@0.108242:0.704377:0.116526:0.704377:0.116526:0.687879:0.108242:0.687879:0.000000:0.000000 :@0.168550:0.704377:0.172692:0.704377:0.172692:0.687879:0.168550:0.687879:0.000000 :@0.228862:0.704377:0.270282:0.704377:0.270282:0.687879:0.228862:0.687879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.270271:0.705160:0.278855:0.705160:0.278855:0.687024:0.270271:0.687024:0.000000 x + 2 , si x > 0 .:@0.278851:0.698201:0.384989:0.698201:0.384989:0.681732:0.278851:0.681732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.313566:0.705160:0.322149:0.705160:0.322149:0.687024:0.313566:0.687024:0.000000 :@0.108224:0.727901:0.112309:0.727901:0.112309:0.711186:0.108224:0.711186:0.000000 Particularmente, para – :@0.131959:0.727684:0.330165:0.727681:0.330165:0.711184:0.131959:0.711186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 λ:@0.287774:0.734755:0.296357:0.734755:0.296357:0.716620:0.287774:0.716620:0.000000 =:@0.300496:0.727797:0.311381:0.727797:0.311381:0.711328:0.300496:0.711328:0.000000 1:@0.330165:0.718991:0.344517:0.718659:0.344517:0.702190:0.330165:0.702523:0.000000:0.000000 4:@0.336445:0.734997:0.344517:0.734997:0.344517:0.718529:0.336445:0.718529:0.000000 :@0.351163:0.727797:0.355305:0.727797:0.355305:0.711328:0.351163:0.711328:0.000000 tenemos: :@0.355305:0.727681:0.424716:0.727681:0.424716:0.711184:0.355305:0.711184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108229:0.768340:0.112371:0.768340:0.112371:0.751842:0.108229:0.751842:0.000000 –:@0.131963:0.774629:0.150746:0.774629:0.150746:0.758131:0.131963:0.758131:0.000000:0.000000:0.000000 f (x) =:@0.150746:0.774744:0.227045:0.774743:0.227045:0.758274:0.150746:0.758276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.158087:0.766633:0.166582:0.766633:0.166582:0.750135:0.158087:0.750135:0.000000 4:@0.158087:0.782972:0.166582:0.782972:0.166582:0.766474:0.158087:0.766474:0.000000 :@0.227045:0.768454:0.231187:0.768454:0.231187:0.751985:0.227045:0.751985:0.000000 , x 0,:@0.231187:0.758390:0.319152:0.758398:0.319152:0.741930:0.231187:0.741921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.241610:0.749136:0.250106:0.749136:0.250106:0.732639:0.241610:0.732639:0.000000 4:@0.241610:0.765475:0.250106:0.765475:0.250106:0.748977:0.241610:0.748977:0.000000 si ≤:@0.267463:0.758283:0.304086:0.758283:0.304086:0.741785:0.267463:0.741785:0.000000:0.000000:0.000000:0.000000 :@0.108236:0.782574:0.112378:0.782574:0.112378:0.766105:0.108236:0.766105:0.000000 :@0.131971:0.782574:0.136113:0.782574:0.136113:0.766105:0.131971:0.766105:0.000000 :@0.168534:0.782574:0.172676:0.782574:0.172676:0.766105:0.168534:0.766105:0.000000 :@0.228855:0.782574:0.241281:0.782574:0.241281:0.766105:0.228855:0.766105:0.000000:0.000000:0.000000 – x – , x > 0.:@0.241281:0.791379:0.377868:0.791371:0.377868:0.774902:0.241281:0.774910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.261741:0.781403:0.270237:0.781403:0.270237:0.764905:0.261741:0.764905:0.000000 4:@0.261741:0.797741:0.270237:0.797741:0.270237:0.781243:0.261741:0.781243:0.000000 1:@0.304390:0.781365:0.312462:0.781365:0.312462:0.764897:0.304390:0.764897:0.000000 2:@0.304390:0.797704:0.312462:0.797704:0.312462:0.781235:0.304390:0.781235:0.000000 si:@0.326102:0.791255:0.336159:0.791255:0.336159:0.774758:0.326102:0.774758:0.000000:0.000000 :@0.108231:0.832883:0.112373:0.832883:0.112373:0.816415:0.108231:0.816415:0.000000 Para:@0.131966:0.832768:0.162309:0.832768:0.162309:0.816270:0.131966:0.816270:0.000000:0.000000:0.000000:0.000000 x :@0.162309:0.832883:0.182210:0.832883:0.182210:0.816415:0.162309:0.816415:0.000000:0.000000:0.000000:0.000000 = – 1:@0.182210:0.832768:0.220297:0.832768:0.220297:0.816270:0.182210:0.816270:0.000000:0.000000:0.000000:0.000000:0.000000 , – f :@0.220297:0.832883:0.283343:0.832890:0.283343:0.816421:0.220297:0.816415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.251892:0.822892:0.259965:0.822892:0.259965:0.806423:0.251892:0.806423:0.000000 4:@0.251892:0.839231:0.259965:0.839231:0.259965:0.822762:0.251892:0.822762:0.000000 (–1) = :@0.283343:0.832774:0.333336:0.832774:0.333336:0.816276:0.283343:0.816276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.335474:0.823752:0.343546:0.823752:0.343546:0.807283:0.335474:0.807283:0.000000 4:@0.335474:0.840090:0.343546:0.840090:0.343546:0.823621:0.335474:0.823621:0.000000 , :@0.350193:0.832890:0.357186:0.832890:0.357186:0.816421:0.350193:0.816421:0.000000:0.000000 para:@0.357186:0.832774:0.388415:0.832774:0.388415:0.816276:0.357186:0.816276:0.000000:0.000000:0.000000:0.000000 x 2, :@0.131976:0.874285:0.182817:0.874285:0.182817:0.857787:0.131976:0.857787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.144113:0.874401:0.154998:0.874401:0.154998:0.857932:0.144113:0.857932:0.000000 – f :@0.182817:0.874401:0.234718:0.874408:0.234718:0.857939:0.182817:0.857932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.199135:0.864410:0.207207:0.864410:0.207207:0.847941:0.199135:0.847941:0.000000 4:@0.199135:0.880748:0.207207:0.880748:0.207207:0.864279:0.199135:0.864279:0.000000 (2) = –1 mientras que:@0.234718:0.874293:0.393500:0.874293:0.393500:0.857795:0.234718:0.857795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.293207:0.874408:0.300200:0.874408:0.300200:0.857939:0.293207:0.857939:0.000000:0.000000 f:@0.131976:0.909110:0.136272:0.909110:0.136272:0.892641:0.131976:0.892641:0.000000 (1) = –1 (2) = 4.:@0.136272:0.908994:0.256796:0.908994:0.256796:0.892496:0.136272:0.892496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , f:@0.194762:0.909110:0.206051:0.909110:0.206051:0.892641:0.194762:0.892641:0.000000:0.000000:0.000000 En la Figura 2.6., se muestran las gráficas de y de – :@0.108241:0.932634:0.490234:0.932635:0.490234:0.916137:0.108241:0.916137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f :@0.414806:0.932750:0.427386:0.932750:0.427386:0.916281:0.414806:0.916281:0.000000:0.000000:0.000000 1 :@0.471854:0.926345:0.486092:0.926345:0.486092:0.909847:0.471854:0.909847:0.000000:0.000000:0.000000 f.:@0.490234:0.932750:0.496803:0.932750:0.496803:0.916281:0.490234:0.916281:0.000000:0.000000 4:@0.473454:0.939922:0.481950:0.939922:0.481950:0.923424:0.473454:0.923424:0.000000 Recuerda que…:@0.683897:0.677971:0.793657:0.677971:0.793657:0.662499:0.683897:0.662499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las propiedades del :@0.684135:0.706599:0.816426:0.706599:0.816426:0.691536:0.684135:0.691536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 producto de escalares por :@0.637592:0.722441:0.810463:0.722441:0.810463:0.707378:0.637592:0.707378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones son las cuatro que se :@0.637592:0.738283:0.843409:0.738283:0.843409:0.723220:0.637592:0.723220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 detallan a continuación.:@0.637592:0.754125:0.792892:0.754125:0.792892:0.739062:0.637592:0.739062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean :@0.637592:0.769967:0.675886:0.769967:0.675886:0.754904:0.637592:0.754904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α, β :@0.675886:0.769505:0.723027:0.769505:0.723027:0.753333:0.675886:0.753333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.723027:0.769769:0.737679:0.769769:0.737679:0.756395:0.723027:0.756395:0.000000 , f, g F A.:@0.737679:0.770072:0.827034:0.770072:0.827034:0.755036:0.737679:0.755036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.741460:0.769082:0.754160:0.769082:0.754160:0.756805:0.741460:0.756805:0.000000 :@0.784677:0.769769:0.799330:0.769769:0.799330:0.756395:0.784677:0.756395:0.000000 Se verifican las siguientes pro-:@0.637591:0.801651:0.829831:0.801651:0.829831:0.786588:0.637591:0.786588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 piedades::@0.637591:0.817493:0.698486:0.817493:0.698486:0.802430:0.637591:0.802430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i.:@0.637591:0.833533:0.644539:0.833533:0.644539:0.818272:0.637591:0.818272:0.000000:0.000000 :@0.644539:0.833335:0.659667:0.833335:0.659667:0.818272:0.644539:0.818272:0.000000:0.000000:0.000000:0.000000 α β :@0.659667:0.832873:0.702973:0.832873:0.702973:0.816701:0.659667:0.816701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.679561:0.833440:0.684521:0.833440:0.684521:0.818404:0.679561:0.818404:0.000000 f) = ( )f .:@0.702973:0.833440:0.775690:0.833440:0.775690:0.818404:0.702973:0.818404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.735884:0.832873:0.760422:0.832873:0.760422:0.816701:0.735884:0.816701:0.000000:0.000000:0.000000 ii.:@0.637591:0.849375:0.648427:0.849375:0.648427:0.834114:0.637591:0.834114:0.000000:0.000000:0.000000 :@0.648427:0.849177:0.659772:0.849177:0.659772:0.834114:0.648427:0.834114:0.000000:0.000000:0.000000 α :@0.659772:0.848715:0.689024:0.848715:0.689024:0.832543:0.659772:0.832543:0.000000:0.000000:0.000000:0.000000:0.000000 ( f + g) = f + g.:@0.679667:0.849282:0.795778:0.849282:0.795778:0.834246:0.679667:0.834246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α :@0.739701:0.848715:0.755198:0.848715:0.755198:0.832543:0.739701:0.832543:0.000000:0.000000 β:@0.776623:0.848715:0.786280:0.848715:0.786280:0.832543:0.776623:0.832543:0.000000 iii.:@0.637591:0.865217:0.652314:0.865217:0.652314:0.849956:0.637591:0.849956:0.000000:0.000000:0.000000:0.000000 :@0.652314:0.865019:0.659878:0.865019:0.659878:0.849956:0.652314:0.849956:0.000000:0.000000 α β:@0.659878:0.864557:0.711891:0.864557:0.711891:0.848385:0.659878:0.848385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + )f = f + f.:@0.664275:0.865124:0.790853:0.865124:0.790853:0.850088:0.664275:0.850088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α :@0.738276:0.864557:0.753773:0.864557:0.753773:0.848385:0.738276:0.848385:0.000000:0.000000 β:@0.775198:0.864557:0.784855:0.864557:0.784855:0.848385:0.775198:0.848385:0.000000 iv.:@0.637591:0.881059:0.651470:0.881059:0.651470:0.865798:0.637591:0.865798:0.000000:0.000000:0.000000 :@0.651470:0.880861:0.662815:0.880861:0.662815:0.865798:0.651470:0.865798:0.000000:0.000000:0.000000 1 :@0.662815:0.880399:0.689200:0.880399:0.689200:0.864227:0.662815:0.864227:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.676008:0.876623:0.680405:0.876623:0.680405:0.860451:0.676008:0.860451:0.000000 f = f .:@0.689200:0.880966:0.720933:0.880966:0.720933:0.865930:0.689200:0.865930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La demostración se deja como :@0.637591:0.912545:0.839767:0.912545:0.839767:0.897482:0.637591:0.897482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 investigación para el estudiante.:@0.637591:0.928387:0.843057:0.928387:0.843057:0.913324:0.637591:0.913324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.731729:0.201135:0.735433:0.201135:0.735433:0.193848:0.731729:0.193848:0.000000 2:@0.731729:0.178403:0.735433:0.178403:0.735433:0.171116:0.731729:0.171116:0.000000 3:@0.731729:0.158984:0.735433:0.158984:0.735433:0.151698:0.731729:0.151698:0.000000 4:@0.731729:0.139214:0.735433:0.139214:0.735433:0.131927:0.731729:0.131927:0.000000 y = f (x) :@0.655995:0.171761:0.682370:0.171761:0.682370:0.164474:0.655995:0.164474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = 2 f (x) :@0.776790:0.120321:0.808743:0.120321:0.808743:0.113034:0.776790:0.113034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.844359:0.222880:0.847729:0.222880:0.847729:0.215594:0.844359:0.215594:0.000000 y:@0.732193:0.103808:0.735672:0.103808:0.735672:0.096522:0.732193:0.096522:0.000000 0:@0.733364:0.221286:0.737069:0.221286:0.737069:0.214000:0.733364:0.214000:0.000000 –3:@0.655919:0.224801:0.664073:0.224801:0.664073:0.217514:0.655919:0.217514:0.000000:0.000000 –2:@0.682261:0.224801:0.690414:0.224801:0.690414:0.217514:0.682261:0.217514:0.000000:0.000000 –1:@0.708603:0.224801:0.716756:0.224801:0.716756:0.217514:0.708603:0.217514:0.000000:0.000000 1:@0.763502:0.224801:0.767207:0.224801:0.767207:0.217514:0.763502:0.217514:0.000000 2:@0.789844:0.224801:0.793549:0.224801:0.793549:0.217514:0.789844:0.217514:0.000000 3:@0.816186:0.224801:0.819890:0.224801:0.819890:0.217514:0.816186:0.217514:0.000000 1:@0.721517:0.433030:0.724856:0.433030:0.724856:0.426461:0.721517:0.426461:0.000000 –1:@0.718252:0.472426:0.725602:0.472426:0.725602:0.465857:0.718252:0.465857:0.000000:0.000000 –2:@0.717137:0.485846:0.724487:0.485846:0.724487:0.479277:0.717137:0.479277:0.000000:0.000000 –3:@0.717137:0.503668:0.724487:0.503668:0.724487:0.497100:0.717137:0.497100:0.000000:0.000000 –4:@0.717137:0.521491:0.724487:0.521491:0.724487:0.514922:0.717137:0.514922:0.000000:0.000000 2:@0.721517:0.414851:0.724856:0.414851:0.724856:0.408283:0.721517:0.408283:0.000000 3:@0.721517:0.397346:0.724856:0.397346:0.724856:0.390777:0.721517:0.390777:0.000000 4:@0.721517:0.379524:0.724856:0.379524:0.724856:0.372955:0.721517:0.372955:0.000000 x:@0.845243:0.454936:0.848281:0.454936:0.848281:0.448367:0.845243:0.448367:0.000000 y:@0.721927:0.354351:0.725063:0.354351:0.725063:0.347782:0.721927:0.347782:0.000000 0:@0.722982:0.453493:0.726322:0.453493:0.726322:0.446924:0.722982:0.446924:0.000000 –3:@0.653168:0.456661:0.660518:0.456661:0.660518:0.450092:0.653168:0.450092:0.000000:0.000000 –2:@0.676914:0.456661:0.684264:0.456661:0.684264:0.450092:0.676914:0.450092:0.000000:0.000000 –1:@0.700661:0.456661:0.708011:0.456661:0.708011:0.450092:0.700661:0.450092:0.000000:0.000000 1:@0.750151:0.456661:0.753491:0.456661:0.753491:0.450092:0.750151:0.450092:0.000000 2:@0.773898:0.456661:0.777238:0.456661:0.777238:0.450092:0.773898:0.450092:0.000000 3:@0.797644:0.456661:0.800984:0.456661:0.800984:0.450092:0.797644:0.450092:0.000000 4:@0.821391:0.456661:0.824731:0.456661:0.824731:0.450092:0.821391:0.450092:0.000000 y = :@0.666845:0.434612:0.694699:0.434612:0.694699:0.425124:0.666845:0.425124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.682395:0.431980:0.687219:0.431980:0.687219:0.422492:0.682395:0.422492:0.000000 4:@0.682395:0.439270:0.687219:0.439270:0.687219:0.429782:0.682395:0.429782:0.000000 y = – x – :@0.773560:0.491502:0.822266:0.491502:0.822266:0.482014:0.773560:0.482014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.798746:0.488609:0.803570:0.488609:0.803570:0.479121:0.798746:0.479121:0.000000 4:@0.798746:0.496504:0.803570:0.496504:0.803570:0.487016:0.798746:0.487016:0.000000 1:@0.822721:0.488962:0.827545:0.488962:0.827545:0.479474:0.822721:0.479474:0.000000 2:@0.822721:0.496497:0.827545:0.496497:0.827545:0.487009:0.822721:0.487009:0.000000 y = x + 2:@0.783162:0.384155:0.819161:0.384155:0.819161:0.374667:0.783162:0.374667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = –1:@0.667444:0.476504:0.693719:0.476504:0.693719:0.467016:0.667444:0.467016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.794059:0.278042:0.805540:0.278042:0.805540:0.268018:0.794059:0.268018:0.000000 :@0.805540:0.278750:0.808421:0.278750:0.808421:0.267273:0.805540:0.267273:0.000000 Figura 2.5.:@0.808421:0.278750:0.856990:0.278750:0.856990:0.267273:0.808421:0.267273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.794059:0.549312:0.805540:0.549312:0.805540:0.539288:0.794059:0.539288:0.000000 :@0.805540:0.550020:0.808421:0.550020:0.808421:0.538544:0.805540:0.538544:0.000000 Figura 2.6.:@0.808421:0.550020:0.856990:0.550020:0.856990:0.538544:0.808421:0.538544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@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 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