85:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, métrico y variacional:@0.541231:0.043660:0.930030:0.043660:0.930030:0.024915:0.541231:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea fijo. Dado con :@0.073089:0.136836:0.311353:0.136836:0.311353:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.103148:0.136836:0.110603:0.136836:0.110603:0.121401:0.103148:0.121401:0.000000 0:@0.110552:0.140009:0.115789:0.140009:0.115789:0.130848:0.110552:0.130848:0.000000 :@0.120111:0.136698:0.135444:0.136698:0.135444:0.122649:0.120111:0.122649:0.000000 :@0.139725:0.135976:0.153015:0.135976:0.153015:0.123079:0.139725:0.123079:0.000000 x:@0.230724:0.136836:0.238179:0.136836:0.238179:0.121401:0.230724:0.121401:0.000000 :@0.242488:0.136698:0.257821:0.136698:0.257821:0.122649:0.242488:0.122649:0.000000 :@0.262103:0.135976:0.275393:0.135976:0.275393:0.123079:0.262103:0.123079:0.000000 x :@0.311684:0.136836:0.322397:0.136836:0.322397:0.121401:0.311684:0.121401:0.000000:0.000000 Þ:@0.322673:0.136281:0.338007:0.136281:0.338007:0.122566:0.322673:0.122566:0.000000 , por la propiedad de tricotoma, se verifica una y :@0.337933:0.136836:0.710281:0.136836:0.710281:0.121124:0.337933:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.342295:0.136836:0.349750:0.136836:0.349750:0.121401:0.342295:0.121401:0.000000 0:@0.349687:0.140009:0.354924:0.140009:0.354924:0.130848:0.349687:0.130848:0.000000 solo una de las dos condiciones siguientes: , x .:@0.073084:0.153478:0.484726:0.153478:0.484726:0.137765:0.073084:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.387793:0.153478:0.395248:0.153478:0.395248:0.138043:0.387793:0.138043:0.000000 ,:@0.399132:0.152923:0.414465:0.152923:0.414465:0.139208:0.399132:0.139208:0.000000 x:@0.418331:0.153478:0.425786:0.153478:0.425786:0.138043:0.418331:0.138043:0.000000 0:@0.425722:0.156650:0.430959:0.156650:0.430959:0.147490:0.425722:0.147490:0.000000 .:@0.449744:0.152923:0.465077:0.152923:0.465077:0.139208:0.449744:0.139208:0.000000 x:@0.468942:0.153478:0.476397:0.153478:0.476397:0.138043:0.468942:0.138043:0.000000 0:@0.476332:0.156650:0.481569:0.156650:0.481569:0.147490:0.476332:0.147490:0.000000 Consideremos el caso . Se tiene ( , ) | | 0.:@0.073084:0.180840:0.568708:0.180841:0.568708:0.165129:0.073084:0.165127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.235123:0.180840:0.242578:0.180840:0.242578:0.165405:0.235123:0.165405:0.000000 .:@0.246462:0.180285:0.261795:0.180285:0.261795:0.166570:0.246462:0.166570:0.000000 x:@0.265661:0.180840:0.273116:0.180840:0.273116:0.165405:0.265661:0.165405:0.000000 0:@0.273047:0.184014:0.278284:0.184014:0.278284:0.174853:0.273047:0.174853:0.000000 d x x:@0.347468:0.180841:0.388556:0.180841:0.388556:0.165406:0.347468:0.165406:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.368842:0.184014:0.374079:0.184014:0.374079:0.174853:0.368842:0.174853:0.000000 5:@0.397226:0.180287:0.412559:0.180287:0.412559:0.166571:0.397226:0.166571:0.000000 x:@0.420235:0.180841:0.427690:0.180841:0.427690:0.165406:0.420235:0.165406:0.000000 0:@0.427645:0.184014:0.432882:0.184014:0.432882:0.174853:0.427645:0.174853:0.000000 2:@0.436792:0.180287:0.452125:0.180287:0.452125:0.166571:0.436792:0.166571:0.000000 x:@0.455990:0.180841:0.463445:0.180841:0.463445:0.165406:0.455990:0.165406:0.000000 5 2:@0.471140:0.180287:0.517010:0.180287:0.517010:0.166571:0.471140:0.166571:0.000000:0.000000:0.000000 x:@0.490338:0.180841:0.497793:0.180841:0.497793:0.165406:0.490338:0.165406:0.000000 x:@0.520876:0.180841:0.528331:0.180841:0.528331:0.165406:0.520876:0.165406:0.000000 0:@0.528249:0.184014:0.533486:0.184014:0.533486:0.174853:0.528249:0.174853:0.000000 .:@0.537397:0.180287:0.552731:0.180287:0.552731:0.166571:0.537397:0.166571:0.000000 Si imaginamos que el punto asociado al número real se mueve en la recta numérica del :@0.073093:0.208203:0.710438:0.208203:0.710438:0.192491:0.073093:0.192491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.451288:0.208203:0.458743:0.208203:0.458743:0.192768:0.451288:0.192768:0.000000 lado derecho hacia , la distancia de a , ( , ) será cada vez mas pequeña. :@0.073093:0.224845:0.641605:0.224846:0.641605:0.209134:0.073093:0.209132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.215326:0.224845:0.222780:0.224845:0.222780:0.209410:0.215326:0.209410:0.000000 0:@0.222707:0.228019:0.227665:0.228019:0.227665:0.219020:0.222707:0.219020:0.000000 x x d x x:@0.341750:0.224846:0.426064:0.224846:0.426064:0.209411:0.341750:0.209411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.372708:0.228019:0.377944:0.228019:0.377944:0.218858:0.372708:0.218858:0.000000 0:@0.406349:0.228019:0.411586:0.228019:0.411586:0.218858:0.406349:0.218858:0.000000 En la Figura 1.1. se muestran los puntos , , , que se aproximan a . La flecha :@0.073086:0.252208:0.662993:0.252210:0.662993:0.236497:0.073086:0.236496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x x x:@0.357736:0.252208:0.422978:0.252210:0.422978:0.236774:0.357736:0.236773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.365127:0.255382:0.370364:0.255382:0.370364:0.246221:0.365127:0.246221:0.000000 2:@0.384389:0.255382:0.389626:0.255382:0.389626:0.246221:0.384389:0.246221:0.000000 3:@0.403650:0.255382:0.408887:0.255382:0.408887:0.246221:0.403650:0.246221:0.000000 4:@0.422913:0.255382:0.428149:0.255382:0.428149:0.246221:0.422913:0.246221:0.000000 x:@0.575967:0.252210:0.583422:0.252210:0.583422:0.236774:0.575967:0.236774:0.000000 0:@0.583348:0.255382:0.588585:0.255382:0.588585:0.246221:0.583348:0.246221:0.000000 indica ese movimiento. :@0.073098:0.268851:0.245388:0.268851:0.245388:0.253139:0.073098:0.253139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Diremos que tiende a x por el lado derecho, que escribiremos :@0.073098:0.296213:0.573517:0.296215:0.573517:0.280502:0.073098:0.280501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.170693:0.296213:0.178148:0.296213:0.178148:0.280778:0.170693:0.280778:0.000000 0:@0.253049:0.299387:0.258286:0.299387:0.258286:0.290226:0.253049:0.290226:0.000000 x:@0.539998:0.296215:0.547453:0.296215:0.547453:0.280779:0.539998:0.280779:0.000000 →:@0.551410:0.295799:0.569578:0.295799:0.569578:0.278810:0.551410:0.278810:0.000000 x:@0.573517:0.296215:0.580972:0.296215:0.580972:0.280779:0.573517:0.280779:0.000000 0:@0.580922:0.299387:0.586159:0.299387:0.586159:0.290226:0.580922:0.290226:0.000000 1:@0.586116:0.289830:0.595055:0.289830:0.595055:0.281834:0.586116:0.281834:0.000000 , si y solo :@0.594997:0.296215:0.662975:0.296215:0.662975:0.280502:0.594997:0.280502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si se verifica y para cada :@0.073096:0.312856:0.296006:0.312856:0.296006:0.297144:0.073096:0.297144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.162242:0.312856:0.169697:0.312856:0.169697:0.297421:0.162242:0.297421:0.000000 .:@0.173581:0.312302:0.188914:0.312302:0.188914:0.298586:0.173581:0.298586:0.000000 x:@0.192780:0.312856:0.200235:0.312856:0.200235:0.297421:0.192780:0.297421:0.000000 0:@0.200160:0.316029:0.205397:0.316029:0.205397:0.306868:0.200160:0.306868:0.000000 d .:@0.268119:0.339664:0.296522:0.339664:0.296522:0.325948:0.268119:0.325948:0.000000:0.000000:0.000000 0, ( , ) .:@0.277231:0.340218:0.463880:0.340220:0.463880:0.324507:0.277231:0.324506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d x x:@0.316346:0.340218:0.357436:0.340220:0.357436:0.324784:0.316346:0.324783:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.337722:0.343392:0.342959:0.343392:0.342959:0.334231:0.337722:0.334231:0.000000 5 2:@0.366106:0.339665:0.411977:0.339665:0.411977:0.325949:0.366106:0.325949:0.000000:0.000000:0.000000 x:@0.385305:0.340220:0.392760:0.340220:0.392760:0.324784:0.385305:0.324784:0.000000 x:@0.415842:0.340220:0.423297:0.340220:0.423297:0.324784:0.415842:0.324784:0.000000 0:@0.423234:0.343392:0.428471:0.343392:0.428471:0.334231:0.423234:0.334231:0.000000 , d:@0.432381:0.339665:0.460770:0.339665:0.460770:0.325949:0.432381:0.325949:0.000000:0.000000:0.000000 Sean 0 y 0 . Si , se tiene , ( , ) , lo :@0.073094:0.367582:0.710359:0.367583:0.710359:0.351870:0.073094:0.351869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d .:@0.112504:0.367027:0.140888:0.367027:0.140888:0.353311:0.112504:0.353311:0.000000:0.000000:0.000000 , , d:@0.182397:0.367027:0.243325:0.367027:0.243325:0.353311:0.182397:0.353311:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.201577:0.367582:0.211075:0.367582:0.211075:0.352146:0.201577:0.352146:0.000000 x:@0.266463:0.367582:0.273918:0.367582:0.273918:0.352146:0.266463:0.352146:0.000000 5:@0.277783:0.367027:0.293116:0.367027:0.293116:0.353311:0.277783:0.353311:0.000000 x:@0.296963:0.367582:0.304418:0.367582:0.304418:0.352146:0.296963:0.352146:0.000000 0:@0.304378:0.370755:0.309615:0.370755:0.309615:0.361595:0.304378:0.361595:0.000000 1:@0.313506:0.367028:0.328840:0.367028:0.328840:0.353312:0.313506:0.353312:0.000000 h:@0.332687:0.367583:0.342185:0.367583:0.342185:0.352148:0.332687:0.352148:0.000000 x:@0.409556:0.367583:0.417010:0.367583:0.417010:0.352148:0.409556:0.352148:0.000000 .:@0.420876:0.367028:0.436209:0.367028:0.436209:0.353312:0.420876:0.353312:0.000000 x y d x x:@0.440056:0.367583:0.506958:0.367583:0.506958:0.352148:0.440056:0.352148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.447468:0.370755:0.452705:0.370755:0.452705:0.361595:0.447468:0.361595:0.000000 0:@0.506905:0.370755:0.512142:0.370755:0.512142:0.361595:0.506905:0.361595:0.000000 5:@0.520839:0.367028:0.536172:0.367028:0.536172:0.353312:0.520839:0.353312:0.000000 x:@0.540019:0.367583:0.547474:0.367583:0.547474:0.352148:0.540019:0.352148:0.000000 0:@0.547409:0.370755:0.552646:0.370755:0.552646:0.361595:0.547409:0.361595:0.000000 1 2:@0.556537:0.367028:0.604415:0.367028:0.604415:0.353312:0.556537:0.353312:0.000000:0.000000:0.000000 h:@0.575718:0.367583:0.585216:0.367583:0.585216:0.352148:0.575718:0.352148:0.000000 x:@0.608262:0.367583:0.615717:0.367583:0.615717:0.352148:0.608262:0.352148:0.000000 0:@0.615673:0.370755:0.620910:0.370755:0.620910:0.361595:0.615673:0.361595:0.000000 5 , d:@0.624802:0.367028:0.685730:0.367028:0.685730:0.353312:0.624802:0.353312:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.643982:0.367583:0.653480:0.367583:0.653480:0.352148:0.643982:0.352148:0.000000 que da lugar a la siguiente interpretación: tiende a , conforme 0 tiende :@0.073063:0.384225:0.710405:0.384225:0.710405:0.368512:0.073063:0.368512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.377261:0.384225:0.384716:0.384225:0.384716:0.368789:0.377261:0.368789:0.000000 5:@0.388544:0.383670:0.403878:0.383670:0.403878:0.369954:0.388544:0.369954:0.000000 x:@0.407688:0.384225:0.415143:0.384225:0.415143:0.368789:0.407688:0.368789:0.000000 0:@0.415106:0.387397:0.420343:0.387397:0.420343:0.378236:0.415106:0.378236:0.000000 1:@0.424199:0.383670:0.439533:0.383670:0.439533:0.369954:0.424199:0.369954:0.000000 h:@0.443343:0.384225:0.452841:0.384225:0.452841:0.368789:0.443343:0.368789:0.000000 x:@0.519549:0.384225:0.527004:0.384225:0.527004:0.368789:0.519549:0.368789:0.000000 0:@0.526940:0.387397:0.532177:0.387397:0.532177:0.378236:0.526940:0.378236:0.000000 h:@0.614191:0.384225:0.623689:0.384225:0.623689:0.368789:0.614191:0.368789:0.000000 .:@0.627518:0.383670:0.642851:0.383670:0.642851:0.369954:0.627518:0.369954:0.000000 a cero. En tal caso, escribimos::@0.073091:0.400866:0.289165:0.400866:0.289165:0.385154:0.073091:0.385154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.245033:0.428228:0.252488:0.428228:0.252488:0.412793:0.245033:0.412793:0.000000 0:@0.252418:0.431402:0.257655:0.431402:0.257655:0.422242:0.252418:0.422242:0.000000 , o también :@0.257607:0.428230:0.414935:0.428230:0.414935:0.412517:0.257607:0.412517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.261565:0.427675:0.276898:0.427675:0.276898:0.413959:0.261565:0.413959:0.000000 h:@0.280763:0.428230:0.290261:0.428230:0.290261:0.412794:0.280763:0.412794:0.000000 →:@0.294145:0.427814:0.312313:0.427814:0.312313:0.410825:0.294145:0.410825:0.000000 x:@0.316179:0.428230:0.323634:0.428230:0.323634:0.412794:0.316179:0.412794:0.000000 0:@0.323545:0.431402:0.328782:0.431402:0.328782:0.422242:0.323545:0.422242:0.000000 lím x:@0.414770:0.428230:0.452965:0.428230:0.452965:0.412794:0.414770:0.412794:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) , :@0.436766:0.428230:0.538431:0.428230:0.538431:0.412517:0.436766:0.412517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.452915:0.431402:0.458152:0.431402:0.458152:0.422242:0.452915:0.422242:0.000000 1:@0.462063:0.427675:0.477396:0.427675:0.477396:0.413959:0.462063:0.413959:0.000000 h:@0.481262:0.428230:0.490760:0.428230:0.490760:0.412794:0.481262:0.412794:0.000000 5:@0.499430:0.427675:0.514763:0.427675:0.514763:0.413959:0.499430:0.413959:0.000000 x:@0.518629:0.428230:0.526083:0.428230:0.526083:0.412794:0.518629:0.412794:0.000000 0:@0.526007:0.431402:0.531243:0.431402:0.531243:0.422242:0.526007:0.422242:0.000000 que se lee: “límite de cuando tiende a cero por la derecha es igual a ”. Estas dos :@0.073096:0.455592:0.710428:0.455592:0.710428:0.439879:0.073096:0.439879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.223060:0.455592:0.230515:0.455592:0.230515:0.440156:0.223060:0.440156:0.000000 0:@0.230441:0.458764:0.235678:0.458764:0.235678:0.449603:0.230441:0.449603:0.000000 1:@0.239220:0.455037:0.254553:0.455037:0.254553:0.441321:0.239220:0.441321:0.000000 h:@0.258050:0.455592:0.267549:0.455592:0.267549:0.440156:0.258050:0.440156:0.000000 h:@0.330188:0.455592:0.339687:0.455592:0.339687:0.440156:0.330188:0.440156:0.000000 x:@0.618004:0.455592:0.625459:0.455592:0.625459:0.440156:0.618004:0.440156:0.000000 0:@0.625396:0.458764:0.630633:0.458764:0.630633:0.449603:0.625396:0.449603:0.000000 últimas notaciones significan lo mismo que :@0.073084:0.472233:0.424405:0.472233:0.424405:0.456521:0.073084:0.456521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.390959:0.472233:0.398414:0.472233:0.398414:0.456798:0.390959:0.456798:0.000000 →:@0.402298:0.471817:0.420466:0.471817:0.420466:0.454829:0.402298:0.454829:0.000000 x:@0.424332:0.472233:0.431786:0.472233:0.431786:0.456798:0.424332:0.456798:0.000000 0:@0.431710:0.475406:0.436946:0.475406:0.436946:0.466245:0.431710:0.466245:0.000000 1:@0.436904:0.465849:0.445843:0.465849:0.445843:0.457853:0.436904:0.457853:0.000000 Ejercicios resueltos:@0.073089:0.499597:0.216098:0.499597:0.216098:0.482927:0.073089:0.482927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Sea x = –2,5. Entonces,:@0.073089:0.526960:0.271898:0.526960:0.271898:0.511247:0.073089:0.511247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.140652:0.530132:0.145889:0.530132:0.145889:0.520972:0.140652:0.520972:0.000000 :@0.073089:0.554323:0.077120:0.554323:0.077120:0.538610:0.073089:0.538610:0.000000 d(:@0.103210:0.554323:0.117273:0.554323:0.117273:0.538888:0.103210:0.538888:0.000000:0.000000 2:@0.117218:0.553768:0.132551:0.553768:0.132551:0.540053:0.117218:0.540053:0.000000 2,5, 2,49) :@0.132459:0.554323:0.218346:0.554323:0.218346:0.538610:0.132459:0.538610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.160456:0.553768:0.175790:0.553768:0.175790:0.540053:0.160456:0.540053:0.000000 5:@0.253815:0.553768:0.269148:0.553768:0.269148:0.540053:0.253815:0.540053:0.000000 :@0.269056:0.554323:0.277045:0.554323:0.277045:0.538610:0.269056:0.538610:0.000000:0.000000 2,5 2,49 :@0.314062:0.554323:0.395978:0.554323:0.395978:0.538610:0.314062:0.538610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.338934:0.553768:0.354267:0.553768:0.354267:0.540053:0.338934:0.540053:0.000000 5:@0.434541:0.553768:0.449874:0.553768:0.449874:0.540053:0.434541:0.540053:0.000000 :@0.449782:0.554323:0.457771:0.554323:0.457771:0.538610:0.449782:0.538610:0.000000:0.000000 0,01,:@0.494788:0.554323:0.527838:0.554323:0.527838:0.538610:0.494788:0.538610:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.581686:0.077120:0.581686:0.077120:0.565974:0.073089:0.565974:0.000000 d:@0.103210:0.581686:0.112469:0.581686:0.112469:0.566251:0.103210:0.566251:0.000000 ( 2,5, 2,495) :@0.112395:0.581686:0.227240:0.581686:0.227240:0.565974:0.112395:0.565974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.117199:0.581132:0.132533:0.581132:0.132533:0.567416:0.117199:0.567416:0.000000 2:@0.160438:0.581132:0.175771:0.581132:0.175771:0.567416:0.160438:0.567416:0.000000 5:@0.253815:0.581132:0.269148:0.581132:0.269148:0.567416:0.253815:0.567416:0.000000 :@0.269056:0.581686:0.277045:0.581686:0.277045:0.565974:0.269056:0.565974:0.000000:0.000000 2,5 2,495 :@0.314062:0.581686:0.404887:0.581686:0.404887:0.565974:0.314062:0.565974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.338934:0.581132:0.354267:0.581132:0.354267:0.567416:0.338934:0.567416:0.000000 5:@0.434541:0.581132:0.449874:0.581132:0.449874:0.567416:0.434541:0.567416:0.000000 :@0.449782:0.581686:0.457771:0.581686:0.457771:0.565974:0.449782:0.565974:0.000000:0.000000 0,005, :@0.494788:0.581686:0.540788:0.581686:0.540788:0.565974:0.494788:0.565974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.609050:0.077120:0.609050:0.077120:0.593337:0.073089:0.593337:0.000000 d:@0.103210:0.609050:0.112469:0.609050:0.112469:0.593614:0.103210:0.593614:0.000000 ( 2,5, 2,499 9) :@0.112395:0.609050:0.240107:0.609050:0.240107:0.593337:0.112395:0.593337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.117199:0.608495:0.132533:0.608495:0.132533:0.594779:0.117199:0.594779:0.000000 2:@0.160438:0.608495:0.175771:0.608495:0.175771:0.594779:0.160438:0.594779:0.000000 5:@0.253815:0.608495:0.269148:0.608495:0.269148:0.594779:0.253815:0.594779:0.000000 :@0.269056:0.609050:0.277045:0.609050:0.277045:0.593337:0.269056:0.593337:0.000000:0.000000 2,5 2,499 9 :@0.314062:0.609050:0.417753:0.609050:0.417753:0.593337:0.314062:0.593337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.338934:0.608495:0.354267:0.608495:0.354267:0.594779:0.338934:0.594779:0.000000 5:@0.434541:0.608495:0.449874:0.608495:0.449874:0.594779:0.434541:0.594779:0.000000 :@0.449782:0.609050:0.457771:0.609050:0.457771:0.593337:0.449782:0.593337:0.000000:0.000000 0,000 1.:@0.494788:0.609050:0.549623:0.609050:0.549623:0.593337:0.494788:0.593337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.636413:0.077120:0.636413:0.077120:0.620700:0.073089:0.620700:0.000000 Se observa que los números reales :@0.103203:0.636413:0.357948:0.636413:0.357948:0.620700:0.103203:0.620700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.663776:0.077120:0.663776:0.077120:0.648063:0.073089:0.648063:0.000000 2:@0.103210:0.663221:0.118543:0.663221:0.118543:0.649506:0.103210:0.649506:0.000000 2,49, 2,495, 2,499 9 se aproximan cada vez más a 2,5. :@0.118451:0.663776:0.544873:0.663776:0.544873:0.648063:0.118451:0.648063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.155358:0.663221:0.170691:0.663221:0.170691:0.649506:0.155358:0.649506:0.000000 2:@0.216396:0.663221:0.231729:0.663221:0.231729:0.649506:0.216396:0.649506:0.000000 2:@0.501451:0.663221:0.516784:0.663221:0.516784:0.649506:0.501451:0.649506:0.000000 Para 0 y 2,5 , se tiene :@0.103203:0.691139:0.362018:0.691139:0.362018:0.675426:0.103203:0.675426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.137670:0.691139:0.147169:0.691139:0.147169:0.675704:0.137670:0.675704:0.000000 .:@0.151052:0.690584:0.166386:0.690584:0.166386:0.676869:0.151052:0.676869:0.000000 x:@0.195064:0.691139:0.202519:0.691139:0.202519:0.675704:0.195064:0.675704:0.000000 5 2:@0.206403:0.690584:0.240935:0.690584:0.240935:0.676869:0.206403:0.676869:0.000000:0.000000:0.000000 1:@0.265711:0.690584:0.281044:0.690584:0.281044:0.676869:0.265711:0.676869:0.000000 h:@0.284910:0.691139:0.294408:0.691139:0.294408:0.675704:0.284910:0.675704:0.000000 :@0.073089:0.718502:0.077120:0.718502:0.077120:0.702790:0.073089:0.702790:0.000000 d:@0.103210:0.718502:0.112469:0.718502:0.112469:0.703067:0.103210:0.703067:0.000000 ( 2,5; 2,5 ) 2,5 (2,5) :@0.112395:0.718502:0.383589:0.718502:0.383589:0.702790:0.112395:0.702790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.117199:0.717948:0.132533:0.717948:0.132533:0.704232:0.117199:0.704232:0.000000 2:@0.160438:0.717948:0.175771:0.717948:0.175771:0.704232:0.160438:0.704232:0.000000 1:@0.200547:0.717948:0.215881:0.717948:0.215881:0.704232:0.200547:0.704232:0.000000 h:@0.219746:0.718502:0.229244:0.718502:0.229244:0.703067:0.219746:0.703067:0.000000 5 2:@0.237914:0.717948:0.272446:0.717948:0.272446:0.704232:0.237914:0.704232:0.000000:0.000000:0.000000 1 2:@0.297222:0.717948:0.345136:0.717948:0.345136:0.704232:0.297222:0.704232:0.000000:0.000000:0.000000 h:@0.316421:0.718502:0.325919:0.718502:0.325919:0.703067:0.316421:0.703067:0.000000 5 :@0.383460:0.717948:0.403303:0.717948:0.403303:0.704232:0.383460:0.704232:0.000000:0.000000 h:@0.403211:0.718502:0.412709:0.718502:0.412709:0.703067:0.403211:0.703067:0.000000 .:@0.412636:0.718502:0.415839:0.718502:0.415839:0.702790:0.412636:0.702790:0.000000 :@0.073089:0.745866:0.077120:0.745866:0.077120:0.730153:0.073089:0.730153:0.000000 Si asignamos valores a 0 cada vez mas próximos a cero, tendremos que :@0.103203:0.745866:0.710445:0.745866:0.710445:0.730153:0.103203:0.730153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.285884:0.745866:0.295382:0.745866:0.295382:0.730430:0.285884:0.730430:0.000000 .:@0.302009:0.745311:0.317342:0.745311:0.317342:0.731595:0.302009:0.731595:0.000000 :@0.706324:0.745866:0.710355:0.745866:0.710355:0.730153:0.706324:0.730153:0.000000 x:@0.103192:0.762507:0.110647:0.762507:0.110647:0.747072:0.103192:0.747072:0.000000 2,5 se aproxima cada vez más a 2,5. En la Tabla 1 se muestran :@0.110757:0.762507:0.710387:0.762507:0.710387:0.746795:0.110757:0.746795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.115948:0.761953:0.151953:0.761953:0.151953:0.748237:0.115948:0.748237:0.000000:0.000000:0.000000 1:@0.178846:0.761953:0.194179:0.761953:0.194179:0.748237:0.178846:0.748237:0.000000 h:@0.199517:0.762507:0.209015:0.762507:0.209015:0.747072:0.199517:0.747072:0.000000 x:@0.430694:0.762507:0.438149:0.762507:0.438149:0.747072:0.430694:0.747072:0.000000 0:@0.438284:0.765680:0.443521:0.765680:0.443521:0.756519:0.438284:0.756519:0.000000 5 2:@0.448786:0.761953:0.484791:0.761953:0.484791:0.748237:0.448786:0.748237:0.000000:0.000000:0.000000 algunos de estos valores y ( 2,5; 2,5 ).:@0.103190:0.779149:0.430177:0.779149:0.430177:0.763437:0.103190:0.763437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.296209:0.779149:0.305468:0.779149:0.305468:0.763714:0.296209:0.763714:0.000000 2:@0.310198:0.778595:0.325531:0.778595:0.325531:0.764879:0.310198:0.764879:0.000000 2:@0.353437:0.778595:0.368770:0.778595:0.368770:0.764879:0.353437:0.764879:0.000000 1:@0.393546:0.778595:0.408879:0.778595:0.408879:0.764879:0.393546:0.764879:0.000000 h:@0.412745:0.779149:0.422243:0.779149:0.422243:0.763714:0.412745:0.763714:0.000000 Tabla 1:@0.362990:0.806511:0.416423:0.806511:0.416423:0.789842:0.362990:0.789842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.156479:0.865617:0.160382:0.865617:0.160382:0.848948:0.156479:0.848948:0.000000 h:@0.233147:0.837225:0.242083:0.837225:0.242083:0.822059:0.233147:0.822059:0.000000 x:@0.346536:0.837225:0.353915:0.837225:0.353915:0.822059:0.346536:0.822059:0.000000 2,5 :@0.353614:0.837225:0.427544:0.837225:0.427544:0.822071:0.353614:0.822071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.356861:0.836721:0.387684:0.836721:0.387684:0.824252:0.356861:0.824252:0.000000:0.000000:0.000000 1:@0.410359:0.836721:0.424298:0.836721:0.424298:0.824252:0.410359:0.824252:0.000000 h:@0.427243:0.837225:0.436179:0.837225:0.436179:0.822059:0.427243:0.822059:0.000000 d:@0.485310:0.837225:0.494095:0.837225:0.494095:0.822059:0.485310:0.822059:0.000000 ( 2,5, 2,5 ):@0.493794:0.837225:0.604907:0.837225:0.604907:0.822071:0.493794:0.822071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.498245:0.836721:0.512184:0.836721:0.512184:0.824252:0.498245:0.824252:0.000000 2:@0.538021:0.836721:0.551961:0.836721:0.551961:0.824252:0.538021:0.824252:0.000000 1:@0.574635:0.836721:0.588574:0.836721:0.588574:0.824252:0.574635:0.824252:0.000000 h:@0.591520:0.837225:0.600455:0.837225:0.600455:0.822059:0.591520:0.822059:0.000000 0,1:@0.208180:0.858671:0.227424:0.858671:0.227424:0.844386:0.208180:0.844386:0.000000:0.000000:0.000000 2:@0.354802:0.858166:0.368742:0.858166:0.368742:0.845698:0.354802:0.845698:0.000000 0,4:@0.368742:0.858671:0.387986:0.858671:0.387986:0.844386:0.368742:0.844386:0.000000:0.000000:0.000000 0,1:@0.513289:0.858671:0.532533:0.858671:0.532533:0.844386:0.513289:0.844386:0.000000:0.000000:0.000000 0,01:@0.208180:0.876535:0.235590:0.876535:0.235590:0.862251:0.208180:0.862251:0.000000:0.000000:0.000000:0.000000 2:@0.354802:0.876031:0.368742:0.876031:0.368742:0.863562:0.354802:0.863562:0.000000 0,49:@0.368742:0.876535:0.396152:0.876535:0.396152:0.862251:0.368742:0.862251:0.000000:0.000000:0.000000:0.000000 0,01:@0.513289:0.876535:0.540699:0.876535:0.540699:0.862251:0.513289:0.862251:0.000000:0.000000:0.000000:0.000000 0,001:@0.208180:0.894400:0.243756:0.894400:0.243756:0.880116:0.208180:0.880116:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.354802:0.893896:0.368742:0.893896:0.368742:0.881427:0.354802:0.881427:0.000000 0,499:@0.368742:0.894400:0.404318:0.894400:0.404318:0.880116:0.368742:0.880116:0.000000:0.000000:0.000000:0.000000:0.000000 0,001:@0.513289:0.894400:0.548865:0.894400:0.548865:0.880116:0.513289:0.880116:0.000000:0.000000:0.000000:0.000000:0.000000 0,000 1:@0.208180:0.912265:0.255587:0.912265:0.255587:0.897981:0.208180:0.897981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.354802:0.911761:0.368742:0.911761:0.368742:0.899292:0.354802:0.899292:0.000000 0,499 9:@0.368742:0.912265:0.416149:0.912265:0.416149:0.897981:0.368742:0.897981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,000 1:@0.513289:0.912265:0.560696:0.912265:0.560696:0.897981:0.513289:0.897981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,000 01:@0.208180:0.930130:0.263753:0.930130:0.263753:0.915846:0.208180:0.915846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.354802:0.929625:0.368742:0.929625:0.368742:0.917157:0.354802:0.917157:0.000000 0,499 99:@0.368742:0.930130:0.424315:0.930130:0.424315:0.915846:0.368742:0.915846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,000 01:@0.513289:0.930130:0.568862:0.930130:0.568862:0.915846:0.513289:0.915846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.289969:0.438863:0.312377:0.438863:0.312377:0.428864:0.289969:0.428864:0.000000:0.000000:0.000000:0.000000 →:@0.292534:0.438598:0.304095:0.438598:0.304095:0.427787:0.292534:0.427787:0.000000 +:@0.312374:0.433113:0.316444:0.433113:0.316444:0.427284:0.312374:0.427284:0.000000 0:@0.418694:0.437588:0.441102:0.437588:0.441102:0.427589:0.418694:0.427589:0.000000:0.000000:0.000000:0.000000 →:@0.421259:0.437323:0.432821:0.437323:0.432821:0.426513:0.421259:0.426513:0.000000 +:@0.441099:0.431838:0.445169:0.431838:0.445169:0.426009:0.441099:0.426009:0.000000 0:@0.745031:0.258100:0.752381:0.258100:0.752381:0.245244:0.745031:0.245244:0.000000 x x x x x:@0.784960:0.258100:0.865828:0.258100:0.865828:0.245471:0.784960:0.245471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.791059:0.260695:0.795344:0.260695:0.795344:0.253200:0.791059:0.253200:0.000000 4:@0.810034:0.260695:0.814319:0.260695:0.814319:0.253200:0.810034:0.253200:0.000000 3:@0.829007:0.260695:0.833291:0.260695:0.833291:0.253200:0.829007:0.253200:0.000000 2:@0.847506:0.260695:0.851791:0.260695:0.851791:0.253200:0.847506:0.253200:0.000000 1:@0.865828:0.260695:0.870113:0.260695:0.870113:0.253200:0.865828:0.253200:0.000000 Figura 2.1.:@0.872466:0.282650:0.926122:0.282650:0.926122:0.271223:0.872466:0.271223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Simbología :@0.743632:0.346396:0.828921:0.346396:0.828921:0.330990:0.743632:0.330990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.743632:0.361525:0.827891:0.361525:0.827891:0.346119:0.743632:0.346119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Escribimos 0 :@0.744288:0.385633:0.875182:0.385633:0.875182:0.371349:0.744288:0.371349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.833013:0.385633:0.839790:0.385633:0.839790:0.371601:0.833013:0.371601:0.000000 →:@0.843321:0.385255:0.859837:0.385255:0.859837:0.369811:0.843321:0.369811:0.000000 (que se lee: \ tiende :@0.758514:0.399501:0.897621:0.399501:0.897621:0.385217:0.758514:0.385217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.841012:0.399501:0.847789:0.399501:0.847789:0.385469:0.841012:0.385469:0.000000 a cero\) para indicar :@0.758514:0.413369:0.892473:0.413369:0.892473:0.399085:0.758514:0.399085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que se puede hacer :@0.758514:0.427237:0.903270:0.427237:0.903270:0.412953:0.758514:0.412953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.787948:0.427237:0.794726:0.427237:0.794726:0.413205:0.787948:0.413205:0.000000 tan pequeño como se :@0.758497:0.441106:0.908315:0.441106:0.908315:0.426821:0.758497:0.426821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 quiera. Es decir, que :@0.758497:0.454974:0.892210:0.454974:0.892210:0.440690:0.758497:0.440690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para cada :@0.758497:0.468842:0.826420:0.468842:0.826420:0.454558:0.758497:0.454558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.482710:0.747953:0.482710:0.747953:0.468426:0.744288:0.468426:0.000000 d .:@0.758519:0.482206:0.784339:0.482206:0.784339:0.469737:0.758519:0.469737:0.000000:0.000000:0.000000 0, | | δ. También :@0.766802:0.482710:0.912691:0.482710:0.912691:0.468426:0.766802:0.468426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.805842:0.482710:0.812619:0.482710:0.812619:0.468678:0.805842:0.468678:0.000000 ,:@0.819614:0.482206:0.833553:0.482206:0.833553:0.469737:0.819614:0.469737:0.000000 se dice::@0.758519:0.496578:0.807164:0.496578:0.807164:0.482294:0.758519:0.482294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | | es suficientemente :@0.744288:0.510447:0.904431:0.510447:0.904431:0.496162:0.744288:0.496162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.761993:0.510447:0.768770:0.510447:0.768770:0.496415:0.761993:0.496415:0.000000 pequeño.:@0.758512:0.524315:0.821945:0.524315:0.821945:0.510031:0.758512:0.510031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Escribimos :@0.744288:0.538183:0.863418:0.538183:0.863418:0.523899:0.744288:0.523899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.833013:0.538183:0.839790:0.538183:0.839790:0.524151:0.833013:0.524151:0.000000 →:@0.843321:0.537805:0.859837:0.537805:0.859837:0.522361:0.843321:0.522361:0.000000 x:@0.863351:0.538183:0.870128:0.538183:0.870128:0.524151:0.863351:0.524151:0.000000 0:@0.870060:0.541067:0.874567:0.541067:0.874567:0.532886:0.870060:0.532886:0.000000 +:@0.874528:0.532673:0.880342:0.532673:0.880342:0.524345:0.874528:0.524345:0.000000 , que :@0.880303:0.538183:0.916346:0.538183:0.916346:0.523899:0.880303:0.523899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se lee: \ tiende a por :@0.758514:0.552051:0.916458:0.552051:0.916458:0.537767:0.758514:0.537767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.807259:0.552051:0.814037:0.552051:0.814037:0.538019:0.807259:0.538019:0.000000 x:@0.874797:0.552051:0.881574:0.552051:0.881574:0.538019:0.874797:0.538019:0.000000 0:@0.881536:0.554935:0.886297:0.554935:0.886297:0.546607:0.881536:0.546607:0.000000 el lado derecho\.:@0.758524:0.565919:0.867106:0.565919:0.867106:0.551635:0.758524:0.551635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • La notación :@0.744288:0.579788:0.843199:0.579788:0.843199:0.565503:0.744288:0.565503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím x:@0.758525:0.593656:0.793265:0.593656:0.793265:0.579624:0.758525:0.579624:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.778522:0.593656:0.849061:0.593656:0.849061:0.579372:0.778522:0.579372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.793188:0.596540:0.797949:0.596540:0.797949:0.588212:0.793188:0.588212:0.000000 1:@0.801503:0.593152:0.815442:0.593152:0.815442:0.580683:0.801503:0.580683:0.000000 h:@0.818956:0.593656:0.827591:0.593656:0.827591:0.579624:0.818956:0.579624:0.000000 x:@0.848960:0.593656:0.855737:0.593656:0.855737:0.579624:0.848960:0.579624:0.000000 0:@0.855679:0.596540:0.860440:0.596540:0.860440:0.588212:0.855679:0.588212:0.000000 se lee: \límite de :@0.744288:0.621392:0.913305:0.621392:0.913305:0.607108:0.744288:0.607108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.868520:0.621392:0.875298:0.621392:0.875298:0.607360:0.868520:0.607360:0.000000 0:@0.875237:0.624276:0.879998:0.624276:0.879998:0.615948:0.875237:0.615948:0.000000 1:@0.883552:0.620888:0.897492:0.620888:0.897492:0.608419:0.883552:0.608419:0.000000 h:@0.901006:0.621392:0.909640:0.621392:0.909640:0.607360:0.901006:0.607360:0.000000 cuando tiende a cero :@0.758534:0.635260:0.914754:0.635260:0.914754:0.620976:0.758534:0.620976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.812601:0.635260:0.821235:0.635260:0.821235:0.621228:0.812601:0.621228:0.000000 por la derecha es igual :@0.758517:0.649129:0.910686:0.649129:0.910686:0.634844:0.758517:0.634844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a \. Estas dos últimas :@0.758517:0.662997:0.906582:0.662997:0.906582:0.648713:0.758517:0.648713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.769628:0.662997:0.776405:0.662997:0.776405:0.648965:0.769628:0.648965:0.000000 0:@0.776350:0.665881:0.781111:0.665881:0.781111:0.657553:0.776350:0.657553:0.000000 notaciones significan lo :@0.758510:0.676865:0.917326:0.676865:0.917326:0.662581:0.758510:0.662581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mismo que :@0.758510:0.690733:0.837427:0.690733:0.837427:0.676449:0.758510:0.676449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.804478:0.704601:0.811255:0.704601:0.811255:0.690569:0.804478:0.690569:0.000000 :@0.811188:0.704601:0.834884:0.704601:0.834884:0.690317:0.811188:0.690317:0.000000:0.000000:0.000000 →:@0.814786:0.704223:0.831303:0.704223:0.831303:0.688779:0.814786:0.688779:0.000000 x:@0.834817:0.704601:0.841594:0.704601:0.841594:0.690569:0.834817:0.690569:0.000000 0:@0.841525:0.707485:0.846286:0.707485:0.846286:0.699158:0.841525:0.699158:0.000000 1:@0.846247:0.698797:0.854374:0.698797:0.854374:0.691528:0.846247:0.691528:0.000000 .:@0.854322:0.704601:0.857233:0.704601:0.857233:0.690317:0.854322:0.690317:0.000000 Indaga y responde:@0.744296:0.718470:0.872704:0.718470:0.872704:0.703315:0.744296:0.703315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : :@0.872578:0.718470:0.879155:0.718470:0.879155:0.704185:0.872578:0.704185:0.000000:0.000000 desde el punto de vista :@0.758537:0.732338:0.916080:0.732338:0.916080:0.718054:0.758537:0.718054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemático, ¿qué es el :@0.758537:0.746206:0.913680:0.746206:0.913680:0.731922:0.758537:0.731922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 límite?:@0.758537:0.760074:0.801940:0.760074:0.801940:0.745790:0.758537:0.745790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.765025:0.608265:0.787433:0.608265:0.787433:0.598266:0.765025:0.598266:0.000000:0.000000:0.000000:0.000000 →:@0.767590:0.608001:0.779151:0.608001:0.779151:0.597190:0.767590:0.597190:0.000000 +:@0.787431:0.602515:0.791502:0.602515:0.791502:0.596686:0.787431:0.596686:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000