67:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000 Para > –2::@0.131966:0.096194:0.214768:0.096194:0.214768:0.079697:0.131966:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.166451:0.096310:0.173926:0.096310:0.173926:0.079841:0.166451:0.079841:0.000000 :@0.108231:0.120674:0.112373:0.120674:0.112373:0.104176:0.108231:0.104176:0.000000 f:@0.131966:0.120790:0.136262:0.120790:0.136262:0.104321:0.131966:0.104321:0.000000 (–1,5) = = 6,:@0.136262:0.120674:0.289980:0.120674:0.289980:0.104176:0.136262:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108231:0.152281:0.112373:0.152281:0.112373:0.135783:0.108231:0.135783:0.000000 f:@0.131966:0.152397:0.136262:0.152397:0.136262:0.135928:0.131966:0.135928:0.000000 (–1) = = 3,:@0.136262:0.152281:0.274587:0.152281:0.274587:0.135783:0.136262:0.135783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108231:0.183888:0.112373:0.183888:0.112373:0.167391:0.108231:0.167391:0.000000 f:@0.131966:0.184004:0.136262:0.184004:0.136262:0.167535:0.131966:0.167535:0.000000 (0) = = 1,5,:@0.136262:0.183888:0.258770:0.183888:0.258770:0.167391:0.136262:0.167391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108231:0.215496:0.112373:0.215496:0.112373:0.198998:0.108231:0.198998:0.000000 f:@0.131966:0.215611:0.136262:0.215611:0.136262:0.199143:0.131966:0.199143:0.000000 (1) = = 1,:@0.136262:0.215496:0.247519:0.215496:0.247519:0.198998:0.136262:0.198998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108231:0.247103:0.112373:0.247103:0.112373:0.230605:0.108231:0.230605:0.000000 f:@0.131966:0.247219:0.136262:0.247219:0.136262:0.230750:0.131966:0.230750:0.000000 (2) = = 0,75.:@0.136262:0.247103:0.267266:0.247103:0.267266:0.230605:0.136262:0.230605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108231:0.264454:0.112373:0.264454:0.112373:0.247956:0.108231:0.247956:0.000000 :@0.108231:0.290856:0.112373:0.290856:0.112373:0.274358:0.108231:0.274358:0.000000 En la región (ver Figura 2.8.), en la que > –2, tenemos que la :@0.131966:0.290856:0.599858:0.290856:0.599858:0.274358:0.131966:0.274358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.422754:0.290972:0.430229:0.290972:0.430229:0.274503:0.422754:0.274503:0.000000 función es estrictamente decreciente al igual que en la región :@0.131966:0.308207:0.599948:0.308207:0.599948:0.291709:0.131966:0.291709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.198217:0.308322:0.202514:0.308322:0.202514:0.291854:0.198217:0.291854:0.000000 en que < –2. Así, es decreciente en el conjunto \ {–2}.:@0.131966:0.325557:0.553654:0.325556:0.553654:0.309058:0.131966:0.309060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.185485:0.325673:0.192960:0.325673:0.192960:0.309204:0.185485:0.309204:0.000000 f:@0.268306:0.325673:0.272603:0.325673:0.272603:0.309204:0.268306:0.309204:0.000000 :@0.492287:0.324469:0.505592:0.324469:0.505592:0.311607:0.492287:0.311607:0.000000 Producto de números reales por funciones racionales:@0.108231:0.362409:0.533598:0.362409:0.533598:0.344727:0.108231:0.344727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , polinomios reales de grado ≤ 2, y una función racio-:@0.108231:0.379117:0.595770:0.379117:0.595770:0.362619:0.108231:0.362619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p q:@0.145721:0.379233:0.170747:0.379233:0.170747:0.362764:0.145721:0.362764:0.000000:0.000000:0.000000 c:@0.399269:0.379233:0.406455:0.379233:0.406455:0.362764:0.399269:0.362764:0.000000 :@0.410280:0.378598:0.424933:0.378598:0.424933:0.365225:0.410280:0.365225:0.000000 :@0.428767:0.378030:0.442071:0.378030:0.442071:0.365168:0.428767:0.365168:0.000000 f:@0.457561:0.379233:0.461857:0.379233:0.461857:0.362764:0.457561:0.362764:0.000000 nal definida como::@0.108243:0.396468:0.240228:0.396468:0.240228:0.379970:0.108243:0.379970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.108243:0.426759:0.125967:0.426759:0.125967:0.410291:0.108243:0.410291:0.000000:0.000000:0.000000 ( ) = , :@0.112539:0.426644:0.250071:0.426643:0.250071:0.410145:0.112539:0.410146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.208081:0.434230:0.219653:0.434230:0.219653:0.415230:0.208081:0.415230:0.000000 x:@0.219660:0.426759:0.227135:0.426759:0.227135:0.410290:0.219660:0.410290:0.000000 :@0.231278:0.426124:0.245930:0.426124:0.245930:0.412751:0.231278:0.412751:0.000000 Dom f:@0.250071:0.426759:0.295537:0.426759:0.295537:0.410290:0.250071:0.410290:0.000000:0.000000:0.000000:0.000000:0.000000 ( ).:@0.285288:0.426643:0.304245:0.426643:0.304245:0.410145:0.285288:0.410145:0.000000:0.000000:0.000000:0.000000 Definición:@0.108241:0.472362:0.188324:0.472362:0.188324:0.455416:0.108241:0.455416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Se define la función como sigue::@0.188326:0.471900:0.439618:0.471900:0.439618:0.455402:0.188326:0.455402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cf:@0.339458:0.472015:0.350940:0.472015:0.350940:0.455547:0.339458:0.455547:0.000000:0.000000 ( )( ) = ( ) = , :@0.214065:0.503579:0.435777:0.503590:0.435777:0.487092:0.214065:0.487082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cf x:@0.220018:0.503695:0.250881:0.503695:0.250881:0.487226:0.220018:0.487226:0.000000:0.000000:0.000000:0.000000 cf x:@0.275925:0.503695:0.300835:0.503695:0.300835:0.487226:0.275925:0.487226:0.000000:0.000000:0.000000:0.000000 c:@0.325880:0.503695:0.333066:0.503695:0.333066:0.487226:0.325880:0.487226:0.000000 ∀:@0.393786:0.511176:0.405359:0.511176:0.405359:0.492177:0.393786:0.492177:0.000000 x:@0.405367:0.503706:0.412842:0.503706:0.412842:0.487237:0.405367:0.487237:0.000000 :@0.416983:0.503071:0.431636:0.503071:0.431636:0.489698:0.416983:0.489698:0.000000 Dom f:@0.435777:0.503706:0.481243:0.503706:0.481243:0.487237:0.435777:0.487237:0.000000:0.000000:0.000000:0.000000:0.000000 ( ).:@0.470994:0.503590:0.489951:0.503590:0.489951:0.487092:0.470994:0.487092:0.000000:0.000000:0.000000:0.000000 Si existe peligro de confusión se escribe × en vez de .:@0.108229:0.538291:0.511528:0.538291:0.511528:0.521794:0.108229:0.521794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c f:@0.390326:0.538407:0.420900:0.538407:0.420900:0.521938:0.390326:0.521938:0.000000:0.000000:0.000000 cf:@0.496131:0.538407:0.508769:0.538407:0.508769:0.521938:0.496131:0.521938:0.000000:0.000000 Ejercicios resueltos:@0.108229:0.573369:0.238884:0.573369:0.238884:0.556582:0.108229:0.556582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108229:0.590561:0.120501:0.590561:0.120501:0.573846:0.108229:0.573846:0.000000:0.000000 Sea la función racional definida como ( ) = , \{–2}.:@0.120501:0.590344:0.595765:0.590344:0.595765:0.573846:0.120501:0.573846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.160150:0.590459:0.164446:0.590459:0.164446:0.573991:0.160150:0.573991:0.000000 f x:@0.411388:0.590459:0.429112:0.590459:0.429112:0.573991:0.411388:0.573991:0.000000:0.000000:0.000000 ∀:@0.501599:0.597930:0.513172:0.597930:0.513172:0.578931:0.501599:0.578931:0.000000 x:@0.513180:0.590459:0.520655:0.590459:0.520655:0.573991:0.513180:0.573991:0.000000 :@0.524726:0.589825:0.539379:0.589825:0.539379:0.576452:0.524726:0.576452:0.000000 :@0.543450:0.589257:0.556755:0.589257:0.556755:0.576395:0.543450:0.576395:0.000000 :@0.108240:0.625045:0.112382:0.625045:0.112382:0.608548:0.108240:0.608548:0.000000 Entonces, las funciones –3 , –1 × , 0 × , 10 están definidas como :@0.131975:0.625045:0.599862:0.625045:0.599862:0.608548:0.131975:0.608548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.318786:0.625161:0.323082:0.625161:0.323082:0.608692:0.318786:0.608692:0.000000 f:@0.368009:0.625161:0.372305:0.625161:0.372305:0.608692:0.368009:0.608692:0.000000 f:@0.406732:0.625161:0.411028:0.625161:0.411028:0.608692:0.406732:0.608692:0.000000 f:@0.434898:0.625161:0.439194:0.625161:0.439194:0.608692:0.434898:0.608692:0.000000 sigue::@0.131975:0.642396:0.170582:0.642396:0.170582:0.625898:0.131975:0.625898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (–3 ) = –3 ( ) = –3 = , \ {–2}.:@0.131975:0.672572:0.488170:0.672571:0.488170:0.656073:0.131975:0.656075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.156923:0.672688:0.161219:0.672688:0.161219:0.656219:0.156923:0.656219:0.000000 f x:@0.205260:0.672688:0.222984:0.672688:0.222984:0.656219:0.205260:0.656219:0.000000:0.000000:0.000000 ∀:@0.385577:0.680158:0.397150:0.680158:0.397150:0.661159:0.385577:0.661159:0.000000 x:@0.397158:0.672687:0.404633:0.672687:0.404633:0.656218:0.397158:0.656218:0.000000 :@0.408774:0.672053:0.423427:0.672053:0.423427:0.658679:0.408774:0.658679:0.000000 :@0.427569:0.671484:0.440874:0.671484:0.440874:0.658622:0.427569:0.658622:0.000000 :@0.108239:0.712898:0.112381:0.712898:0.112381:0.696400:0.108239:0.696400:0.000000 (–1 × )( ) = –1 × ( ) = – ( ) = – , \ {–2}.:@0.131975:0.712898:0.532689:0.712892:0.532689:0.696394:0.131975:0.696400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.176015:0.713014:0.199692:0.713014:0.199692:0.696545:0.176015:0.696545:0.000000:0.000000:0.000000 f x:@0.262824:0.713014:0.280548:0.713014:0.280548:0.696545:0.262824:0.696545:0.000000:0.000000:0.000000 f x:@0.316093:0.713014:0.333817:0.713014:0.333817:0.696545:0.316093:0.696545:0.000000:0.000000:0.000000 ∀:@0.430099:0.720478:0.441671:0.720478:0.441671:0.701479:0.430099:0.701479:0.000000 x:@0.441678:0.713007:0.449153:0.713007:0.449153:0.696538:0.441678:0.696538:0.000000 :@0.453296:0.712373:0.467948:0.712373:0.467948:0.699000:0.453296:0.699000:0.000000 :@0.472088:0.711805:0.485393:0.711805:0.485393:0.698942:0.472088:0.698942:0.000000 :@0.108238:0.751150:0.112380:0.751150:0.112380:0.734652:0.108238:0.734652:0.000000 (0 × )( ) = 0 × ( ) = 0, \ {–2}.:@0.131973:0.751150:0.410858:0.751158:0.410858:0.734660:0.131973:0.734652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.165514:0.751266:0.189191:0.751266:0.189191:0.734797:0.165514:0.734797:0.000000:0.000000:0.000000 f x:@0.241823:0.751266:0.259547:0.751266:0.259547:0.734797:0.241823:0.734797:0.000000:0.000000:0.000000 ∀:@0.308267:0.758744:0.319839:0.758744:0.319839:0.739745:0.308267:0.739745:0.000000 x:@0.319846:0.751273:0.327321:0.751273:0.327321:0.734804:0.319846:0.734804:0.000000 :@0.331464:0.750639:0.346116:0.750639:0.346116:0.737266:0.331464:0.737266:0.000000 :@0.350258:0.750071:0.363563:0.750071:0.363563:0.737208:0.350258:0.737208:0.000000 :@0.108239:0.768508:0.112381:0.768508:0.112381:0.752011:0.108239:0.752011:0.000000 (10 )( ) = 10 ( ) = 10 = , \ {–2}. :@0.131975:0.792987:0.510594:0.792987:0.510594:0.776489:0.131975:0.776489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.154919:0.793102:0.178596:0.793102:0.178596:0.776634:0.154919:0.776634:0.000000:0.000000:0.000000 f x:@0.220633:0.793102:0.238357:0.793102:0.238357:0.776634:0.220633:0.776634:0.000000:0.000000:0.000000 ∀:@0.403859:0.800573:0.415432:0.800573:0.415432:0.781574:0.403859:0.781574:0.000000 x:@0.415440:0.793102:0.422915:0.793102:0.422915:0.776634:0.415440:0.776634:0.000000 :@0.427056:0.792468:0.441709:0.792468:0.441709:0.779095:0.427056:0.779095:0.000000 :@0.445851:0.791900:0.459156:0.791900:0.459156:0.779038:0.445851:0.779038:0.000000 :@0.108239:0.810337:0.112381:0.810337:0.112381:0.793840:0.108239:0.793840:0.000000 2.:@0.108239:0.835033:0.120511:0.835033:0.120511:0.818319:0.108239:0.818319:0.000000:0.000000 Sea la función racional definida como ( ) = , \ {–1}.:@0.120511:0.834817:0.595771:0.834817:0.595771:0.818319:0.120511:0.818319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.159599:0.834933:0.163895:0.834933:0.163895:0.818464:0.159599:0.818464:0.000000 f x:@0.407483:0.834933:0.425207:0.834933:0.425207:0.818464:0.407483:0.818464:0.000000:0.000000:0.000000 ∀:@0.495726:0.842403:0.507299:0.842403:0.507299:0.823404:0.495726:0.823404:0.000000 x:@0.507307:0.834933:0.514782:0.834933:0.514782:0.818464:0.507307:0.818464:0.000000 :@0.518285:0.834298:0.532937:0.834298:0.532937:0.820925:0.518285:0.820925:0.000000 :@0.536441:0.833730:0.549746:0.833730:0.549746:0.820868:0.536441:0.820868:0.000000 :@0.108225:0.859295:0.112367:0.859295:0.112367:0.842798:0.108225:0.842798:0.000000 Entonces, las funciones –2 , están definidas como sigue::@0.131959:0.859295:0.558508:0.859295:0.558508:0.842798:0.131959:0.842798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.318831:0.859411:0.323127:0.859411:0.323127:0.842942:0.318831:0.842942:0.000000 f:@0.350734:0.859411:0.355030:0.859411:0.355030:0.842942:0.350734:0.842942:0.000000 (–2 ) = –2 ( ) = –2 = .:@0.131959:0.896050:0.370442:0.896050:0.370442:0.879552:0.131959:0.879552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.156908:0.896166:0.161204:0.896166:0.161204:0.879697:0.156908:0.879697:0.000000 f x:@0.205245:0.896166:0.222969:0.896166:0.222969:0.879697:0.205245:0.879697:0.000000:0.000000:0.000000 :@0.108225:0.937880:0.112367:0.937880:0.112367:0.921382:0.108225:0.921382:0.000000 = ( ) = = .:@0.131959:0.937880:0.409722:0.937880:0.409722:0.921382:0.131959:0.921382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.156812:0.937996:0.161108:0.937996:0.161108:0.921527:0.156812:0.921527:0.000000 f x:@0.211022:0.937996:0.228746:0.937996:0.228746:0.921527:0.211022:0.921527:0.000000:0.000000:0.000000 p:@0.532977:0.248771:0.544457:0.248771:0.544457:0.238746:0.532977:0.238746:0.000000 :@0.544459:0.249479:0.547340:0.249479:0.547340:0.238002:0.544459:0.238002:0.000000 Figura 2.8.:@0.547340:0.249479:0.595909:0.249479:0.595909:0.238002:0.547340:0.238002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.154203:0.419119:0.176898:0.419119:0.176898:0.402651:0.154203:0.402651:0.000000:0.000000:0.000000 ( ):@0.163470:0.419004:0.182851:0.419004:0.182851:0.402506:0.163470:0.402506:0.000000:0.000000:0.000000 q x:@0.154261:0.435458:0.176859:0.435458:0.176859:0.418989:0.154261:0.418989:0.000000:0.000000:0.000000 ( ):@0.163431:0.435342:0.182812:0.435342:0.182812:0.418845:0.163431:0.418845:0.000000:0.000000:0.000000 p x:@0.339165:0.496109:0.361859:0.496109:0.361859:0.479640:0.339165:0.479640:0.000000:0.000000:0.000000 ( ):@0.348431:0.495993:0.367812:0.495993:0.367812:0.479496:0.348431:0.479496:0.000000:0.000000:0.000000 q x:@0.339223:0.512448:0.361821:0.512448:0.361821:0.495979:0.339223:0.495979:0.000000:0.000000:0.000000 ( ):@0.348393:0.512332:0.367774:0.512332:0.367774:0.495834:0.348393:0.495834:0.000000:0.000000:0.000000 3:@0.469818:0.582919:0.478314:0.582919:0.478314:0.566422:0.469818:0.566422:0.000000 x:@0.456545:0.599374:0.464020:0.599374:0.464020:0.582905:0.456545:0.582905:0.000000 + 2:@0.464020:0.599258:0.491607:0.599258:0.491607:0.582760:0.464020:0.582760:0.000000:0.000000:0.000000:0.000000 3:@0.284302:0.664851:0.292798:0.664851:0.292798:0.648354:0.284302:0.648354:0.000000 x:@0.271029:0.681306:0.278504:0.681306:0.278504:0.664837:0.271029:0.664837:0.000000 + 2:@0.278504:0.681190:0.306091:0.681190:0.306091:0.664692:0.278504:0.664692:0.000000:0.000000:0.000000:0.000000 3:@0.387956:0.705302:0.396452:0.705302:0.396452:0.688805:0.387956:0.688805:0.000000 x:@0.374682:0.721757:0.382157:0.721757:0.382157:0.705288:0.374682:0.705288:0.000000 + 2:@0.382157:0.721641:0.409745:0.721641:0.409745:0.705143:0.382157:0.705143:0.000000:0.000000:0.000000:0.000000 3:@0.298904:0.785483:0.307400:0.785483:0.307400:0.768985:0.298904:0.768985:0.000000 x:@0.285630:0.801937:0.293105:0.801937:0.293105:0.785469:0.285630:0.785469:0.000000 + 2:@0.293105:0.801822:0.320693:0.801822:0.320693:0.785324:0.293105:0.785324:0.000000:0.000000:0.000000:0.000000 30:@0.356073:0.785483:0.373065:0.785483:0.373065:0.768985:0.356073:0.768985:0.000000:0.000000 x:@0.347038:0.801937:0.354513:0.801937:0.354513:0.785469:0.347038:0.785469:0.000000 + 2:@0.354513:0.801822:0.382100:0.801822:0.382100:0.785324:0.354513:0.785324:0.000000:0.000000:0.000000:0.000000 –9:@0.339493:0.664851:0.358489:0.664851:0.358489:0.648354:0.339493:0.648354:0.000000:0.000000 x:@0.331460:0.681306:0.338934:0.681306:0.338934:0.664837:0.331460:0.664837:0.000000 + 2:@0.338934:0.681190:0.366522:0.681190:0.366522:0.664692:0.338934:0.664692:0.000000:0.000000:0.000000:0.000000 x:@0.463206:0.828010:0.470681:0.828010:0.470681:0.811541:0.463206:0.811541:0.000000 x:@0.449412:0.844349:0.456887:0.844349:0.456887:0.827880:0.449412:0.827880:0.000000 + 1:@0.456887:0.844233:0.484475:0.844233:0.484475:0.827735:0.456887:0.827735:0.000000:0.000000:0.000000:0.000000 x:@0.284457:0.888767:0.291931:0.888767:0.291931:0.872298:0.284457:0.872298:0.000000 x:@0.270663:0.905105:0.278138:0.905105:0.278138:0.888636:0.270663:0.888636:0.000000 + 1:@0.278138:0.904990:0.305725:0.904990:0.305725:0.888492:0.278138:0.888492:0.000000:0.000000:0.000000:0.000000 x:@0.293493:0.930644:0.300968:0.930644:0.300968:0.914175:0.293493:0.914175:0.000000 x:@0.279699:0.946982:0.287174:0.946982:0.287174:0.930513:0.279699:0.930513:0.000000 + 1:@0.287174:0.946866:0.314762:0.946866:0.314762:0.930369:0.287174:0.930369:0.000000:0.000000:0.000000:0.000000 4:@0.367202:0.930528:0.375698:0.930528:0.375698:0.914030:0.367202:0.914030:0.000000 x:@0.375698:0.930644:0.383173:0.930644:0.383173:0.914175:0.375698:0.914175:0.000000 5( + 1):@0.347455:0.946866:0.402919:0.946866:0.402919:0.930369:0.347455:0.930369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.361904:0.946982:0.369379:0.946982:0.369379:0.930513:0.361904:0.930513:0.000000 4:@0.140245:0.930528:0.148741:0.930528:0.148741:0.914030:0.140245:0.914030:0.000000 5:@0.140245:0.946866:0.148741:0.946866:0.148741:0.930369:0.140245:0.930369:0.000000 4:@0.192168:0.930528:0.200664:0.930528:0.200664:0.914030:0.192168:0.914030:0.000000 5:@0.192168:0.946866:0.200664:0.946866:0.200664:0.930369:0.192168:0.930369:0.000000 4:@0.256133:0.930528:0.264629:0.930528:0.264629:0.914030:0.256133:0.914030:0.000000 5:@0.256133:0.946866:0.264629:0.946866:0.264629:0.930369:0.256133:0.930369:0.000000 –2:@0.334318:0.888651:0.353314:0.888651:0.353314:0.872153:0.334318:0.872153:0.000000:0.000000 x:@0.353314:0.888767:0.360789:0.888767:0.360789:0.872298:0.353314:0.872298:0.000000 x:@0.330022:0.905105:0.337497:0.905105:0.337497:0.888636:0.330022:0.888636:0.000000 + 1:@0.337497:0.904990:0.365085:0.904990:0.365085:0.888492:0.337497:0.888492:0.000000:0.000000:0.000000:0.000000 4:@0.334072:0.852674:0.342568:0.852674:0.342568:0.836177:0.334072:0.836177:0.000000 5:@0.334072:0.869013:0.342568:0.869013:0.342568:0.852515:0.334072:0.852515:0.000000 3:@0.208768:0.145028:0.217264:0.145028:0.217264:0.128530:0.208768:0.128530:0.000000 –1 + 2:@0.189733:0.161366:0.236317:0.161366:0.236317:0.144869:0.189733:0.144869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.190801:0.176760:0.199297:0.176760:0.199297:0.160262:0.190801:0.160262:0.000000 0 + 2:@0.177007:0.193098:0.213090:0.193098:0.213090:0.176600:0.177007:0.176600:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.190801:0.208490:0.199297:0.208490:0.199297:0.191992:0.190801:0.191992:0.000000 1 + 2:@0.177007:0.224829:0.213090:0.224829:0.213090:0.208331:0.177007:0.208331:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.190326:0.240222:0.198822:0.240222:0.198822:0.223724:0.190326:0.223724:0.000000 2 + 2:@0.176533:0.256560:0.212616:0.256560:0.212616:0.240063:0.176533:0.240063:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.222381:0.113486:0.230877:0.113486:0.230877:0.096988:0.222381:0.096988:0.000000 –1,5 + 2:@0.197721:0.129824:0.255555:0.129824:0.255555:0.113327:0.197721:0.113327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.466558:0.175314:0.470252:0.175314:0.470252:0.168141:0.466558:0.168141:0.000000 y:@0.462519:0.091477:0.466600:0.091477:0.466600:0.082870:0.462519:0.082870:0.000000 asíntota V:@0.405608:0.122935:0.443442:0.122935:0.443442:0.114328:0.405608:0.114328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 asíntota H:@0.394431:0.165927:0.432878:0.165927:0.432878:0.157320:0.394431:0.157320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.582051:0.178216:0.586222:0.178216:0.586222:0.169609:0.582051:0.169609:0.000000 1:@0.465007:0.161405:0.468701:0.161405:0.468701:0.154232:0.465007:0.154232:0.000000 1:@0.484323:0.175908:0.488017:0.175908:0.488017:0.168735:0.484323:0.168735:0.000000 –1:@0.455751:0.175908:0.463592:0.175908:0.463592:0.168735:0.455751:0.168735:0.000000:0.000000 –2:@0.442601:0.175908:0.450441:0.175908:0.450441:0.168735:0.442601:0.168735:0.000000:0.000000 –3:@0.429450:0.175908:0.437290:0.175908:0.437290:0.168735:0.429450:0.168735:0.000000:0.000000 –4:@0.416300:0.175908:0.424140:0.175908:0.424140:0.168735:0.416300:0.168735:0.000000:0.000000 –5:@0.403149:0.175908:0.410989:0.175908:0.410989:0.168735:0.403149:0.168735:0.000000:0.000000 –6:@0.389998:0.175908:0.397838:0.175908:0.397838:0.168735:0.389998:0.168735:0.000000:0.000000 –7:@0.376848:0.175908:0.384688:0.175908:0.384688:0.168735:0.376848:0.168735:0.000000:0.000000 2:@0.497498:0.175908:0.501192:0.175908:0.501192:0.168735:0.497498:0.168735:0.000000 3:@0.510649:0.175908:0.514343:0.175908:0.514343:0.168735:0.510649:0.168735:0.000000 4:@0.523800:0.175908:0.527494:0.175908:0.527494:0.168735:0.523800:0.168735:0.000000 5:@0.536950:0.175908:0.540644:0.175908:0.540644:0.168735:0.536950:0.168735:0.000000 6:@0.550101:0.175908:0.553795:0.175908:0.553795:0.168735:0.550101:0.168735:0.000000 7:@0.563252:0.175908:0.566946:0.175908:0.566946:0.168735:0.563252:0.168735:0.000000 –2:@0.460442:0.191668:0.468701:0.191668:0.468701:0.184495:0.460442:0.184495:0.000000:0.000000 –3:@0.460442:0.201431:0.468701:0.201431:0.468701:0.194258:0.460442:0.194258:0.000000:0.000000 –4:@0.460442:0.211194:0.468701:0.211194:0.468701:0.204021:0.460442:0.204021:0.000000:0.000000 –5:@0.460442:0.220957:0.468701:0.220957:0.468701:0.213784:0.460442:0.213784:0.000000:0.000000 –6:@0.460442:0.230720:0.468701:0.230720:0.468701:0.223547:0.460442:0.223547:0.000000:0.000000 –7:@0.460442:0.240483:0.468701:0.240483:0.468701:0.233310:0.460442:0.233310:0.000000:0.000000 2:@0.465007:0.151516:0.468701:0.151516:0.468701:0.144343:0.465007:0.144343:0.000000 3:@0.465007:0.141646:0.468701:0.141646:0.468701:0.134473:0.465007:0.134473:0.000000 4:@0.465007:0.131776:0.468701:0.131776:0.468701:0.124604:0.465007:0.124604:0.000000 5:@0.465007:0.121907:0.468701:0.121907:0.468701:0.114734:0.465007:0.114734:0.000000 6:@0.465007:0.112037:0.468701:0.112037:0.468701:0.104864:0.465007:0.104864:0.000000 7:@0.465007:0.102167:0.468701:0.102167:0.468701:0.094994:0.465007:0.094994:0.000000 –1:@0.460442:0.181908:0.468701:0.181908:0.468701:0.174735:0.460442:0.174735:0.000000:0.000000 Interdisciplinariedad:@0.684804:0.106800:0.831589:0.106800:0.831589:0.091327:0.684804:0.091327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Física:@0.685042:0.135849:0.823260:0.135849:0.823260:0.120377:0.685042:0.120377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las mayores aplicaciones de la :@0.638498:0.151269:0.838370:0.151269:0.838370:0.136206:0.638498:0.136206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática se dan en la física.:@0.638498:0.167111:0.833851:0.167111:0.833851:0.152048:0.638498:0.152048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La matriz energética está :@0.638498:0.190082:0.801646:0.190082:0.801646:0.175019:0.638498:0.175019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vinculada con la producción y :@0.638498:0.205924:0.837651:0.205924:0.837651:0.190861:0.638498:0.190861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 consumo de energía que puede :@0.638498:0.221766:0.847378:0.221766:0.847378:0.206703:0.638498:0.206703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ser de índole eólica, térmica, :@0.638498:0.237608:0.826372:0.237608:0.826372:0.222545:0.638498:0.222545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hidráulica, química y nuclear. :@0.638498:0.253450:0.829276:0.253450:0.829276:0.238387:0.638498:0.238387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Esta matriz se analiza y estudia :@0.638498:0.269292:0.839075:0.269292:0.839075:0.254229:0.638498:0.254229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en mayor profundidad con mé-:@0.638498:0.285134:0.843809:0.285134:0.843809:0.270071:0.638498:0.270071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 todos matemáticos de modelos :@0.638498:0.300976:0.848539:0.300976:0.848539:0.285913:0.638498:0.285913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 previamente elaborados, en los :@0.638498:0.316818:0.843067:0.316818:0.843067:0.301755:0.638498:0.301755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuales intervienen, por ejemplo, :@0.638498:0.332660:0.847255:0.332660:0.847255:0.317597:0.638498:0.317597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones racionales.:@0.638498:0.348502:0.772814:0.348502:0.772814:0.333439:0.638498:0.333439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Medioambiente:@0.678232:0.432818:0.790261:0.432818:0.790261:0.417345:0.678232:0.417345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La matemática contribuye con :@0.638496:0.448237:0.840533:0.448237:0.840533:0.433174:0.638496:0.433174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los estudios que se realizan :@0.638496:0.464079:0.815993:0.464079:0.815993:0.449016:0.638496:0.449016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para optimizar los recursos de :@0.638496:0.479921:0.836573:0.479921:0.836573:0.464858:0.638496:0.464858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 energía renovables. Estos no son :@0.638496:0.495763:0.850419:0.495763:0.850419:0.480700:0.638496:0.480700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 más que recursos abundantes :@0.638496:0.511605:0.835131:0.511605:0.835131:0.496542:0.638496:0.496542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y limpios que no producen :@0.638496:0.527447:0.817682:0.527447:0.817682:0.512384:0.638496:0.512384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gases de efecto invernadero ni :@0.638496:0.543289:0.838280:0.543289:0.838280:0.528226:0.638496:0.528226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 otras emisiones dañinas para el :@0.638496:0.559131:0.843011:0.559131:0.843011:0.544068:0.638496:0.544068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 medioambiente.:@0.638496:0.574973:0.745107:0.574973:0.745107:0.559910:0.638496:0.559910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.684804:0.395353:0.782426:0.395353:0.782426:0.379880:0.684804:0.379880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 comunicacional:@0.684804:0.407921:0.796762:0.407921:0.796762:0.392448:0.684804:0.392448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Shutterstock, 150408947:@0.871305:0.690337:0.871305:0.622164:0.859836:0.622164:0.859836:0.690337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.638108:0.703582:0.649588:0.703582:0.649588:0.693557:0.638108:0.693557:0.000000 :@0.649588:0.704290:0.652470:0.704290:0.652470:0.692813:0.649588:0.692813:0.000000 Fuente de energía renovable:@0.652470:0.704290:0.791579:0.704290:0.791579:0.692813:0.652470:0.692813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia digital:@0.684804:0.761289:0.827156:0.761289:0.827156:0.745816:0.684804:0.745816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para conocer más sobre :@0.685042:0.789916:0.843262:0.789916:0.843262:0.774853:0.685042:0.774853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones racionales, :@0.638498:0.805758:0.776596:0.805758:0.776596:0.790695:0.638498:0.790695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 visita:@0.776596:0.806181:0.813779:0.806181:0.813779:0.790708:0.776596:0.790708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 esta :@0.813783:0.805758:0.847290:0.805758:0.847290:0.790695:0.813783:0.790695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 página: :@0.638498:0.821600:0.688014:0.821600:0.688014:0.806537:0.638498:0.806537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lynk.ec/12m04:@0.688014:0.821930:0.784847:0.821930:0.784847:0.806616:0.688014:0.806616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@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 :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000