91:@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 1.4 Definición de asíntota horizontal y asíntota vertical:@0.073089:0.136836:0.501111:0.136836:0.501111:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Dada una función ( ), la recta es una asíntota vertical de dicha función si para :@0.073089:0.169202:0.750431:0.169202:0.750431:0.153489:0.073089:0.153489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.238176:0.169202:0.245649:0.169202:0.245649:0.153767:0.238176:0.153767:0.000000 5:@0.249956:0.168647:0.265290:0.168647:0.265290:0.154932:0.249956:0.154932:0.000000 f x:@0.269578:0.169202:0.286476:0.169202:0.286476:0.153767:0.269578:0.153767:0.000000:0.000000:0.000000 x:@0.355872:0.169202:0.363327:0.169202:0.363327:0.153767:0.355872:0.153767:0.000000 5:@0.367634:0.168647:0.382967:0.168647:0.382967:0.154932:0.367634:0.154932:0.000000 a:@0.387256:0.169202:0.396515:0.169202:0.396515:0.153767:0.387256:0.153767:0.000000 valores de cercanos a por la derecha o por la izquierda, el valor de y tiende . :@0.103214:0.185844:0.689816:0.185844:0.689816:0.170131:0.103214:0.170131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.180727:0.185844:0.188182:0.185844:0.188182:0.170409:0.180727:0.170409:0.000000 a :@0.273039:0.185844:0.285538:0.185844:0.285538:0.170409:0.273039:0.170409:0.000000:0.000000 6:@0.667341:0.185289:0.682674:0.185289:0.682674:0.171574:0.667341:0.171574:0.000000 A continuación, se muestran varios ejemplos::@0.073081:0.218212:0.400467:0.218212:0.400467:0.202500:0.073081:0.202500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.178560:0.257640:0.192246:0.257640:0.192246:0.236824:0.178560:0.236824:0.000000:0.000000 → :@0.192245:0.257112:0.221135:0.257112:0.221135:0.235557:0.192245:0.235557:0.000000:0.000000 ` :@0.221131:0.256936:0.242547:0.256936:0.242547:0.239534:0.221131:0.239534:0.000000:0.000000 cuando :@0.242547:0.257640:0.318731:0.257640:0.318731:0.236789:0.242547:0.236789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.318731:0.257640:0.332394:0.257640:0.332394:0.236824:0.318731:0.236824:0.000000:0.000000 → :@0.332392:0.257112:0.361282:0.257112:0.361282:0.235557:0.332392:0.235557:0.000000:0.000000 a:@0.361283:0.257640:0.373031:0.257640:0.373031:0.236824:0.361283:0.236824:0.000000 1:@0.373026:0.249536:0.384368:0.249536:0.384368:0.239391:0.373026:0.239391:0.000000 0:@0.119639:0.509549:0.131036:0.509549:0.131036:0.488698:0.119639:0.488698:0.000000 5:@0.116720:0.398942:0.128117:0.398942:0.128117:0.378091:0.116720:0.378091:0.000000 10:@0.388431:0.511221:0.411226:0.511221:0.411226:0.490370:0.388431:0.490370:0.000000:0.000000 10:@0.106046:0.295197:0.128841:0.295197:0.128841:0.274346:0.106046:0.274346:0.000000:0.000000 x :@0.172795:0.532089:0.186457:0.532089:0.186457:0.511274:0.172795:0.511274:0.000000:0.000000 5 :@0.186457:0.531386:0.211751:0.531386:0.211751:0.513983:0.186457:0.513983:0.000000:0.000000 a:@0.211751:0.532089:0.223498:0.532089:0.223498:0.511274:0.211751:0.511274:0.000000 5:@0.261402:0.510993:0.272800:0.510993:0.272800:0.490142:0.261402:0.490142:0.000000 y :@0.628679:0.257640:0.642365:0.257640:0.642365:0.236824:0.628679:0.236824:0.000000:0.000000 → :@0.642365:0.257112:0.671255:0.257112:0.671255:0.235557:0.642365:0.235557:0.000000:0.000000 ` :@0.671251:0.256936:0.692668:0.256936:0.692668:0.239534:0.671251:0.239534:0.000000:0.000000 cuando :@0.692668:0.257640:0.768852:0.257640:0.768852:0.236789:0.692668:0.236789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.768852:0.257640:0.782514:0.257640:0.782514:0.236824:0.768852:0.236824:0.000000:0.000000 → :@0.782513:0.257112:0.811403:0.257112:0.811403:0.235557:0.782513:0.235557:0.000000:0.000000 a:@0.811403:0.257640:0.823150:0.257640:0.823150:0.236824:0.811403:0.236824:0.000000 2:@0.823146:0.249536:0.834489:0.249536:0.834489:0.239391:0.823146:0.239391:0.000000 0:@0.703652:0.509866:0.715049:0.509866:0.715049:0.489015:0.703652:0.489015:0.000000 5:@0.702998:0.398185:0.714395:0.398185:0.714395:0.377334:0.702998:0.377334:0.000000 10:@0.838526:0.510446:0.861321:0.510446:0.861321:0.489595:0.838526:0.489595:0.000000:0.000000 10:@0.690129:0.294440:0.712923:0.294440:0.712923:0.273589:0.690129:0.273589:0.000000:0.000000 x :@0.732098:0.529925:0.745761:0.529925:0.745761:0.509109:0.732098:0.509109:0.000000:0.000000 5 :@0.745761:0.529221:0.788640:0.529221:0.788640:0.511819:0.745761:0.511819:0.000000:0.000000:0.000000:0.000000 a:@0.771054:0.529925:0.782802:0.529925:0.782802:0.509109:0.771054:0.509109:0.000000 5:@0.551127:0.509708:0.562525:0.509708:0.562525:0.488857:0.551127:0.488857:0.000000 y :@0.165621:0.571148:0.179099:0.571148:0.179099:0.550648:0.165621:0.550648:0.000000:0.000000 → :@0.179099:0.570628:0.207551:0.570628:0.207551:0.549400:0.179099:0.549400:0.000000:0.000000 2` :@0.207548:0.570455:0.247799:0.570455:0.247799:0.553317:0.207548:0.553317:0.000000:0.000000:0.000000 cuando :@0.247798:0.571148:0.322825:0.571148:0.322825:0.550613:0.247798:0.550613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.322825:0.571148:0.336281:0.571148:0.336281:0.550648:0.322825:0.550648:0.000000:0.000000 → :@0.336281:0.570628:0.364732:0.570628:0.364732:0.549400:0.336281:0.549400:0.000000:0.000000 a:@0.364732:0.571148:0.376302:0.571148:0.376302:0.550648:0.364732:0.550648:0.000000 1:@0.376295:0.563167:0.387465:0.563167:0.387465:0.553175:0.376295:0.553175:0.000000 0:@0.127974:0.616328:0.139198:0.616328:0.139198:0.595793:0.127974:0.595793:0.000000 2:@0.104721:0.709609:0.123880:0.709609:0.123880:0.692471:0.104721:0.692471:0.000000 5:@0.123880:0.710302:0.135104:0.710302:0.135104:0.689768:0.123880:0.689768:0.000000 2:@0.093491:0.810366:0.112650:0.810366:0.112650:0.793228:0.093491:0.793228:0.000000 10:@0.112650:0.811059:0.135099:0.811059:0.135099:0.790524:0.112650:0.790524:0.000000:0.000000 10:@0.391463:0.618172:0.413911:0.618172:0.413911:0.597637:0.391463:0.597637:0.000000:0.000000 x :@0.174128:0.841424:0.187584:0.841424:0.187584:0.820924:0.174128:0.820924:0.000000:0.000000 5 :@0.187584:0.840731:0.212493:0.840731:0.212493:0.823593:0.187584:0.823593:0.000000:0.000000 a:@0.212493:0.841424:0.224063:0.841424:0.224063:0.820924:0.212493:0.820924:0.000000 5:@0.266367:0.617985:0.277591:0.617985:0.277591:0.597450:0.266367:0.597450:0.000000 y :@0.608911:0.571148:0.622389:0.571148:0.622389:0.550648:0.608911:0.550648:0.000000:0.000000 → :@0.622389:0.570628:0.650841:0.570628:0.650841:0.549400:0.622389:0.549400:0.000000:0.000000 2` :@0.650836:0.570455:0.691087:0.570455:0.691087:0.553317:0.650836:0.553317:0.000000:0.000000:0.000000 cuando :@0.691088:0.571148:0.766116:0.571148:0.766116:0.550613:0.691088:0.550613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.766116:0.571148:0.779571:0.571148:0.779571:0.550648:0.766116:0.550648:0.000000:0.000000 → :@0.779571:0.570628:0.808023:0.570628:0.808023:0.549400:0.779571:0.549400:0.000000:0.000000 a:@0.808023:0.571148:0.819592:0.571148:0.819592:0.550648:0.808023:0.550648:0.000000 2:@0.819585:0.563167:0.830756:0.563167:0.830756:0.553175:0.819585:0.553175:0.000000 0:@0.702453:0.615759:0.713678:0.615759:0.713678:0.595225:0.702453:0.595225:0.000000 2:@0.682098:0.708867:0.701257:0.708867:0.701257:0.691729:0.682098:0.691729:0.000000 5:@0.701257:0.709560:0.712482:0.709560:0.712482:0.689026:0.701257:0.689026:0.000000 5:@0.843884:0.618186:0.855108:0.618186:0.855108:0.597651:0.843884:0.597651:0.000000 2:@0.669103:0.829008:0.688262:0.829008:0.688262:0.811870:0.669103:0.811870:0.000000 10:@0.688262:0.829701:0.710711:0.829701:0.710711:0.809166:0.688262:0.809166:0.000000:0.000000 x :@0.748236:0.840680:0.761691:0.840680:0.761691:0.820180:0.748236:0.820180:0.000000:0.000000 5 :@0.761691:0.839987:0.786601:0.839987:0.786601:0.822849:0.761691:0.822849:0.000000:0.000000 a:@0.786601:0.840680:0.798170:0.840680:0.798170:0.820180:0.786601:0.820180:0.000000 2:@0.560231:0.617672:0.579390:0.617672:0.579390:0.600534:0.560231:0.600534:0.000000 5:@0.579390:0.618365:0.590614:0.618365:0.590614:0.597831:0.579390:0.597831:0.000000 DBA 7 (Ev. 4) Relaciona características algebraicas de las funciones, sus gráficas y procesos de aproximación sucesiva.:@0.085573:0.971366:0.696663:0.971366:0.696663:0.959939:0.085573:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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