45:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3:@0.073089:0.136836:0.148264:0.136836:0.148264:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: identifiquemos el dominio de la función. Determinemos las asíntotas, si las hay, y construyamos la gráfica de :@0.148161:0.136836:0.930292:0.136836:0.930292:0.121124:0.148161:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.073096:0.158138:0.089975:0.158138:0.089975:0.142702:0.073096:0.142702:0.000000:0.000000:0.000000
( )   :@0.077716:0.158138:0.117918:0.158138:0.117918:0.142425:0.077716:0.142425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.098645:0.157583:0.113979:0.157583:0.113979:0.143867:0.098645:0.143867:0.000000
3:@0.120443:0.150169:0.128609:0.150169:0.128609:0.135884:0.120443:0.135884:0.000000
x:@0.128609:0.150169:0.135387:0.150169:0.135387:0.136137:0.128609:0.136137:0.000000
2:@0.135386:0.144656:0.140147:0.144656:0.140147:0.136328:0.135386:0.136328:0.000000
1 2:@0.140147:0.149664:0.182969:0.149664:0.182969:0.137196:0.140147:0.137196:0.000000:0.000000:0.000000
2:@0.154086:0.150169:0.162252:0.150169:0.162252:0.135884:0.154086:0.135884:0.000000
x:@0.162252:0.150169:0.169030:0.150169:0.169030:0.136137:0.162252:0.136137:0.000000
4:@0.182969:0.150169:0.191135:0.150169:0.191135:0.135884:0.182969:0.135884:0.000000
x:@0.128617:0.166558:0.135395:0.166558:0.135395:0.152526:0.128617:0.152526:0.000000
2:@0.135386:0.161046:0.140147:0.161046:0.140147:0.152718:0.135386:0.152718:0.000000
1 2:@0.140147:0.166054:0.174803:0.166054:0.174803:0.153585:0.140147:0.153585:0.000000:0.000000:0.000000
x:@0.154086:0.166558:0.160864:0.166558:0.160864:0.152526:0.154086:0.152526:0.000000
6:@0.174803:0.166558:0.182969:0.166558:0.182969:0.152274:0.174803:0.152274:0.000000
 :@0.182969:0.167031:0.187183:0.167031:0.187183:0.150604:0.182969:0.150604:0.000000
.:@0.193657:0.158137:0.196860:0.158137:0.196860:0.142424:0.193657:0.142424:0.000000
Factoricemos el denominador y determinemos los ceros de   ( )   :@0.073089:0.198465:0.556501:0.198465:0.556501:0.182753:0.073089:0.182753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.511679:0.198465:0.528558:0.198465:0.528558:0.183030:0.511679:0.183030:0.000000:0.000000:0.000000
5:@0.537228:0.197910:0.552561:0.197910:0.552561:0.184195:0.537228:0.184195:0.000000
3:@0.565047:0.189339:0.573213:0.189339:0.573213:0.175054:0.565047:0.175054:0.000000
x:@0.573213:0.189339:0.579990:0.189339:0.579990:0.175307:0.573213:0.175307:0.000000
2:@0.579990:0.183826:0.584751:0.183826:0.584751:0.175498:0.579990:0.175498:0.000000
1 2:@0.584751:0.188834:0.627573:0.188834:0.627573:0.176366:0.584751:0.176366:0.000000:0.000000:0.000000
2:@0.598690:0.189339:0.606856:0.189339:0.606856:0.175054:0.598690:0.175054:0.000000
x:@0.606856:0.189339:0.613633:0.189339:0.613633:0.175307:0.606856:0.175307:0.000000
4:@0.627573:0.189339:0.635739:0.189339:0.635739:0.175054:0.627573:0.175054:0.000000
(x:@0.560554:0.205728:0.571765:0.205728:0.571765:0.191696:0.560554:0.191696:0.000000:0.000000
1 :@0.571765:0.205224:0.589888:0.205224:0.589888:0.192755:0.571765:0.192755:0.000000:0.000000
3)(:@0.589888:0.205728:0.606923:0.205728:0.606923:0.191444:0.589888:0.191444:0.000000:0.000000:0.000000
x:@0.606923:0.205728:0.613700:0.205728:0.613700:0.191696:0.606923:0.191696:0.000000
2:@0.613700:0.205224:0.627640:0.205224:0.627640:0.192755:0.613700:0.192755:0.000000
2):@0.627640:0.205728:0.640240:0.205728:0.640240:0.191444:0.627640:0.191444:0.000000:0.000000
 :@0.640235:0.206201:0.644450:0.206201:0.644450:0.189774:0.640235:0.189774:0.000000
.:@0.644275:0.198465:0.647478:0.198465:0.647478:0.182753:0.644275:0.182753:0.000000
Los ceros del polinomio del denominador serán :@0.073079:0.232969:0.537102:0.232969:0.537102:0.217257:0.073079:0.217257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.546017:0.232415:0.561350:0.232415:0.561350:0.218699:0.546017:0.218699:0.000000
3 y 2. El dominio de la función será :@0.562988:0.232969:0.930986:0.232969:0.930986:0.217257:0.562988:0.217257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.926900:0.232969:0.930931:0.232969:0.930931:0.217257:0.926900:0.217257:0.000000
D:@0.073079:0.249611:0.084602:0.249611:0.084602:0.234176:0.073079:0.234176:0.000000
     :@0.084529:0.249611:0.124914:0.249611:0.124914:0.233898:0.084529:0.233898:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.088486:0.249056:0.103819:0.249056:0.103819:0.235341:0.088486:0.235341:0.000000
R:@0.107685:0.248751:0.120975:0.248751:0.120975:0.235854:0.107685:0.235854:0.000000
2 2:@0.124841:0.249056:0.159409:0.249056:0.159409:0.235341:0.124841:0.235341:0.000000:0.000000:0.000000
H:@0.140082:0.250194:0.144168:0.250194:0.144168:0.232539:0.140082:0.232539:0.000000
3, 2 . :@0.159317:0.249611:0.195414:0.249611:0.195414:0.233898:0.159317:0.233898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
J:@0.184185:0.250194:0.188272:0.250194:0.188272:0.232539:0.184185:0.232539:0.000000
Como son dos ceros, debemos tomar valores cercanos a cada uno de ellos por derecha e izquierda.:@0.073079:0.284115:0.791045:0.284115:0.791045:0.268403:0.073079:0.268403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.175891:0.328144:0.184579:0.328144:0.184579:0.312445:0.175891:0.312445:0.000000
f x:@0.334101:0.329087:0.353852:0.329087:0.353852:0.313388:0.334101:0.313388:0.000000:0.000000:0.000000
( ) :@0.339697:0.329087:0.363055:0.329087:0.363055:0.312140:0.339697:0.312140:0.000000:0.000000:0.000000:0.000000
5 :@0.362982:0.328533:0.382825:0.328533:0.382825:0.314817:0.362982:0.314817:0.000000:0.000000
3:@0.384982:0.318494:0.392708:0.318494:0.392708:0.304856:0.384982:0.304856:0.000000
x:@0.392708:0.318494:0.399350:0.318494:0.399350:0.304844:0.392708:0.304844:0.000000
2:@0.399348:0.313533:0.403852:0.313533:0.403852:0.305582:0.399348:0.305582:0.000000
1 2:@0.403853:0.318041:0.443311:0.318041:0.443311:0.306819:0.403853:0.306819:0.000000:0.000000:0.000000
2:@0.416398:0.318494:0.424124:0.318494:0.424124:0.304856:0.416398:0.304856:0.000000
x:@0.424124:0.318494:0.430766:0.318494:0.430766:0.304844:0.424124:0.304844:0.000000
4:@0.443311:0.318494:0.451037:0.318494:0.451037:0.304856:0.443311:0.304856:0.000000
x:@0.392708:0.334879:0.399350:0.334879:0.399350:0.321229:0.392708:0.321229:0.000000
2:@0.399348:0.329923:0.403852:0.329923:0.403852:0.321971:0.399348:0.321971:0.000000
1 2:@0.403853:0.334430:0.435585:0.334430:0.435585:0.323208:0.403853:0.323208:0.000000:0.000000:0.000000
x:@0.416398:0.334884:0.423040:0.334884:0.423040:0.321234:0.416398:0.321234:0.000000
6:@0.435585:0.334884:0.443311:0.334884:0.443311:0.321245:0.435585:0.321245:0.000000
 :@0.443311:0.334884:0.446609:0.334884:0.446609:0.322028:0.443311:0.322028:0.000000
x:@0.602802:0.328144:0.611490:0.328144:0.611490:0.312445:0.602802:0.312445:0.000000
f:@0.760809:0.328477:0.766479:0.328477:0.766479:0.312778:0.760809:0.312778:0.000000
(x) :@0.766405:0.328477:0.790169:0.328477:0.790169:0.311530:0.766405:0.311530:0.000000:0.000000:0.000000:0.000000
5 :@0.790077:0.327922:0.809920:0.327922:0.809920:0.314207:0.790077:0.314207:0.000000:0.000000
3:@0.812090:0.318494:0.819816:0.318494:0.819816:0.304856:0.812090:0.304856:0.000000
x:@0.819816:0.318494:0.826458:0.318494:0.826458:0.304844:0.819816:0.304844:0.000000
2:@0.826458:0.313533:0.830962:0.313533:0.830962:0.305582:0.826458:0.305582:0.000000
1 2:@0.830963:0.318041:0.870421:0.318041:0.870421:0.306819:0.830963:0.306819:0.000000:0.000000:0.000000
2:@0.843508:0.318494:0.851234:0.318494:0.851234:0.304856:0.843508:0.304856:0.000000
x:@0.851234:0.318494:0.857876:0.318494:0.857876:0.304844:0.851234:0.304844:0.000000
4:@0.870421:0.318494:0.878147:0.318494:0.878147:0.304856:0.870421:0.304856:0.000000
x:@0.819818:0.334879:0.826460:0.334879:0.826460:0.321229:0.819818:0.321229:0.000000
2:@0.826458:0.329923:0.830962:0.329923:0.830962:0.321971:0.826458:0.321971:0.000000
1 2:@0.830963:0.334430:0.862695:0.334430:0.862695:0.323208:0.830963:0.323208:0.000000:0.000000:0.000000
x:@0.843508:0.334884:0.850150:0.334884:0.850150:0.321234:0.843508:0.321234:0.000000
6:@0.862695:0.334884:0.870421:0.334884:0.870421:0.321245:0.862695:0.321245:0.000000
 :@0.870421:0.334884:0.873720:0.334884:0.873720:0.322028:0.870421:0.322028:0.000000
2:@0.232327:0.359397:0.247660:0.359397:0.247660:0.345681:0.232327:0.345681:0.000000
3,01:@0.247568:0.359952:0.277499:0.359952:0.277499:0.344239:0.247568:0.344239:0.000000:0.000000:0.000000:0.000000
342,521:@0.434310:0.359952:0.490967:0.359952:0.490967:0.344239:0.434310:0.344239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.668137:0.359397:0.683471:0.359397:0.683471:0.345681:0.668137:0.345681:0.000000
2,9:@0.683379:0.359952:0.704400:0.359952:0.704400:0.344239:0.683379:0.344239:0.000000:0.000000:0.000000
2:@0.854879:0.359397:0.870212:0.359397:0.870212:0.345681:0.854879:0.345681:0.000000
31,490:@0.870120:0.359952:0.917869:0.359952:0.917869:0.344239:0.870120:0.344239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.223418:0.391197:0.238751:0.391197:0.238751:0.377481:0.223418:0.377481:0.000000
3,001:@0.238659:0.391751:0.277499:0.391751:0.277499:0.376039:0.238659:0.376039:0.000000:0.000000:0.000000:0.000000:0.000000
3402,520:@0.425401:0.391751:0.490967:0.391751:0.490967:0.376039:0.425401:0.376039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.659228:0.391197:0.674561:0.391197:0.674561:0.377481:0.659228:0.377481:0.000000
2,99:@0.674469:0.391751:0.704400:0.391751:0.704400:0.376039:0.674469:0.376039:0.000000:0.000000:0.000000:0.000000
2:@0.845970:0.391197:0.861303:0.391197:0.861303:0.377481:0.845970:0.377481:0.000000
337,481:@0.861211:0.391751:0.917869:0.391751:0.917869:0.376039:0.861211:0.376039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.214509:0.422996:0.229842:0.422996:0.229842:0.409281:0.214509:0.409281:0.000000
3,0001:@0.229750:0.423551:0.277499:0.423551:0.277499:0.407838:0.229750:0.407838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
34002,520:@0.416492:0.423551:0.490967:0.423551:0.490967:0.407838:0.416492:0.407838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.650319:0.422996:0.665652:0.422996:0.665652:0.409281:0.650319:0.409281:0.000000
2,999:@0.665560:0.423551:0.704400:0.423551:0.704400:0.407838:0.665560:0.407838:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.837061:0.422996:0.852394:0.422996:0.852394:0.409281:0.837061:0.409281:0.000000
3397,480:@0.852302:0.423551:0.917869:0.423551:0.917869:0.407838:0.852302:0.407838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.205600:0.454796:0.220933:0.454796:0.220933:0.441080:0.205600:0.441080:0.000000
3,00001:@0.220841:0.455351:0.277499:0.455351:0.277499:0.439638:0.220841:0.439638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
340002,520:@0.407583:0.455351:0.490967:0.455351:0.490967:0.439638:0.407583:0.439638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.641410:0.454796:0.656743:0.454796:0.656743:0.441080:0.641410:0.441080:0.000000
2,9999:@0.656651:0.455351:0.704400:0.455351:0.704400:0.439638:0.656651:0.439638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.828152:0.454796:0.843485:0.454796:0.843485:0.441080:0.828152:0.441080:0.000000
33997,480:@0.843393:0.455351:0.917869:0.455351:0.917869:0.439638:0.843393:0.439638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.196691:0.486610:0.212024:0.486610:0.212024:0.472894:0.196691:0.472894:0.000000
3,000001:@0.211932:0.487164:0.277499:0.487164:0.277499:0.471452:0.211932:0.471452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3400002,519:@0.398674:0.487164:0.490967:0.487164:0.490967:0.471452:0.398674:0.471452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.632501:0.486610:0.647834:0.486610:0.647834:0.472894:0.632501:0.472894:0.000000
2,99999:@0.647742:0.487164:0.704400:0.487164:0.704400:0.471452:0.647742:0.471452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.819242:0.486610:0.834576:0.486610:0.834576:0.472894:0.819242:0.472894:0.000000
339997,480:@0.834484:0.487164:0.917869:0.487164:0.917869:0.471452:0.834484:0.471452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.187782:0.518410:0.203115:0.518410:0.203115:0.504694:0.187782:0.504694:0.000000
3,0000001:@0.203023:0.518964:0.277499:0.518964:0.277499:0.503252:0.203023:0.503252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
34000002,561:@0.389764:0.518964:0.490967:0.518964:0.490967:0.503252:0.389764:0.503252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.623592:0.518410:0.638925:0.518410:0.638925:0.504694:0.623592:0.504694:0.000000
2,999999:@0.638833:0.518964:0.704400:0.518964:0.704400:0.503252:0.638833:0.503252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.810333:0.518410:0.825667:0.518410:0.825667:0.504694:0.810333:0.504694:0.000000
3399997,480:@0.825575:0.518964:0.917869:0.518964:0.917869:0.503252:0.825575:0.503252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.101528:0.559469:0.108983:0.559469:0.108983:0.544034:0.101528:0.544034:0.000000
    3:@0.108925:0.559469:0.152974:0.559469:0.152974:0.543757:0.108925:0.543757:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.112883:0.560995:0.124884:0.560995:0.124884:0.542287:0.112883:0.542287:0.000000
2:@0.128750:0.558915:0.144083:0.558915:0.144083:0.545199:0.128750:0.545199:0.000000
2 :@0.152888:0.553082:0.164457:0.553082:0.164457:0.545086:0.152888:0.545086:0.000000:0.000000
entonces  ( )     :@0.201940:0.559469:0.330925:0.559469:0.330925:0.543757:0.201940:0.543757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.273287:0.559469:0.290166:0.559469:0.290166:0.544034:0.273287:0.544034:0.000000:0.000000:0.000000
→:@0.298836:0.560995:0.310837:0.560995:0.310837:0.542287:0.298836:0.542287:0.000000
`:@0.314703:0.558915:0.326981:0.558915:0.326981:0.545199:0.314703:0.545199:0.000000
x:@0.424501:0.559469:0.431955:0.559469:0.431955:0.544034:0.424501:0.544034:0.000000
    3:@0.431882:0.559469:0.475930:0.559469:0.475930:0.543757:0.431882:0.543757:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.435839:0.560995:0.447841:0.560995:0.447841:0.542287:0.435839:0.542287:0.000000
2:@0.451706:0.558915:0.467040:0.558915:0.467040:0.545199:0.451706:0.545199:0.000000
1 :@0.475852:0.553082:0.487420:0.553082:0.487420:0.545086:0.475852:0.545086:0.000000:0.000000
entonces  ( )   :@0.546658:0.559469:0.659494:0.559469:0.659494:0.543757:0.546658:0.543757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.618004:0.559469:0.634884:0.559469:0.634884:0.544034:0.618004:0.544034:0.000000:0.000000:0.000000
→:@0.643554:0.560995:0.655555:0.560995:0.655555:0.542287:0.643554:0.542287:0.000000
2`:@0.659421:0.558915:0.686939:0.558915:0.686939:0.545199:0.659421:0.545199:0.000000:0.000000
x:@0.175891:0.603664:0.184579:0.603664:0.184579:0.587965:0.175891:0.587965:0.000000
f x:@0.334101:0.604440:0.353852:0.604440:0.353852:0.588741:0.334101:0.588741:0.000000:0.000000:0.000000
( ) :@0.339697:0.604440:0.363055:0.604440:0.363055:0.587493:0.339697:0.587493:0.000000:0.000000:0.000000:0.000000
5 :@0.362982:0.603886:0.382825:0.603886:0.382825:0.590170:0.362982:0.590170:0.000000:0.000000
3:@0.384982:0.593835:0.392708:0.593835:0.392708:0.580196:0.384982:0.580196:0.000000
x:@0.392708:0.593835:0.399350:0.593835:0.399350:0.580185:0.392708:0.580185:0.000000
2:@0.399348:0.588873:0.403852:0.588873:0.403852:0.580922:0.399348:0.580922:0.000000
1 2:@0.403853:0.593381:0.443311:0.593381:0.443311:0.582159:0.403853:0.582159:0.000000:0.000000:0.000000
2:@0.416398:0.593835:0.424124:0.593835:0.424124:0.580196:0.416398:0.580196:0.000000
x:@0.424124:0.593835:0.430766:0.593835:0.430766:0.580185:0.424124:0.580185:0.000000
4:@0.443311:0.593835:0.451037:0.593835:0.451037:0.580196:0.443311:0.580196:0.000000
x:@0.392708:0.610219:0.399350:0.610219:0.399350:0.596569:0.392708:0.596569:0.000000
2:@0.399348:0.605263:0.403852:0.605263:0.403852:0.597312:0.399348:0.597312:0.000000
1 2:@0.403853:0.609771:0.435585:0.609771:0.435585:0.598549:0.403853:0.598549:0.000000:0.000000:0.000000
x:@0.416398:0.610225:0.423040:0.610225:0.423040:0.596574:0.416398:0.596574:0.000000
6:@0.435585:0.610225:0.443311:0.610225:0.443311:0.596586:0.435585:0.596586:0.000000
 :@0.443311:0.610225:0.446609:0.610225:0.446609:0.597369:0.443311:0.597369:0.000000
x:@0.602803:0.603664:0.611491:0.603664:0.611491:0.587965:0.602803:0.587965:0.000000
f:@0.760811:0.603830:0.766481:0.603830:0.766481:0.588131:0.760811:0.588131:0.000000
(x) :@0.766407:0.603830:0.790171:0.603830:0.790171:0.586883:0.766407:0.586883:0.000000:0.000000:0.000000:0.000000
5 :@0.790079:0.603275:0.809922:0.603275:0.809922:0.589560:0.790079:0.589560:0.000000:0.000000
3:@0.812090:0.593835:0.819816:0.593835:0.819816:0.580196:0.812090:0.580196:0.000000
x:@0.819816:0.593835:0.826458:0.593835:0.826458:0.580185:0.819816:0.580185:0.000000
2:@0.826458:0.588873:0.830962:0.588873:0.830962:0.580922:0.826458:0.580922:0.000000
1 2:@0.830963:0.593381:0.870421:0.593381:0.870421:0.582159:0.830963:0.582159:0.000000:0.000000:0.000000
2:@0.843508:0.593835:0.851234:0.593835:0.851234:0.580196:0.843508:0.580196:0.000000
x:@0.851234:0.593835:0.857876:0.593835:0.857876:0.580185:0.851234:0.580185:0.000000
4:@0.870421:0.593835:0.878147:0.593835:0.878147:0.580196:0.870421:0.580196:0.000000
x:@0.819818:0.610219:0.826460:0.610219:0.826460:0.596569:0.819818:0.596569:0.000000
2:@0.826458:0.605263:0.830962:0.605263:0.830962:0.597312:0.826458:0.597312:0.000000
1 2:@0.830963:0.609771:0.862695:0.609771:0.862695:0.598549:0.830963:0.598549:0.000000:0.000000:0.000000
x:@0.843508:0.610225:0.850150:0.610225:0.850150:0.596574:0.843508:0.596574:0.000000
6:@0.862695:0.610225:0.870421:0.610225:0.870421:0.596586:0.862695:0.596586:0.000000
 :@0.870421:0.610225:0.873720:0.610225:0.873720:0.597369:0.870421:0.597369:0.000000
1,9:@0.256469:0.635828:0.277490:0.635828:0.277490:0.620115:0.256469:0.620115:0.000000:0.000000:0.000000
21,694:@0.443211:0.635828:0.490959:0.635828:0.490959:0.620115:0.443211:0.620115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,1:@0.683370:0.635828:0.704391:0.635828:0.704391:0.620115:0.683370:0.620115:0.000000:0.000000:0.000000
26,333:@0.870112:0.635828:0.917860:0.635828:0.917860:0.620115:0.870112:0.620115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1,99:@0.247542:0.667988:0.277472:0.667988:0.277472:0.652275:0.247542:0.652275:0.000000:0.000000:0.000000:0.000000
237,681:@0.434283:0.667988:0.490941:0.667988:0.490941:0.652275:0.434283:0.652275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,01:@0.674443:0.667988:0.704373:0.667988:0.704373:0.652275:0.674443:0.652275:0.000000:0.000000:0.000000:0.000000
242,321:@0.861184:0.667988:0.917842:0.667988:0.917842:0.652275:0.861184:0.652275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1,999:@0.238614:0.700148:0.277453:0.700148:0.277453:0.684436:0.238614:0.684436:0.000000:0.000000:0.000000:0.000000:0.000000
2397,680:@0.425356:0.700148:0.490922:0.700148:0.490922:0.684436:0.425356:0.684436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,001:@0.665515:0.700148:0.704354:0.700148:0.704354:0.684436:0.665515:0.684436:0.000000:0.000000:0.000000:0.000000:0.000000
2402,320:@0.852257:0.700148:0.917823:0.700148:0.917823:0.684436:0.852257:0.684436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1,9999:@0.229687:0.732309:0.277435:0.732309:0.277435:0.716596:0.229687:0.716596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
23997,680:@0.416428:0.732309:0.490904:0.732309:0.490904:0.716596:0.416428:0.716596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,0001:@0.656588:0.732309:0.704336:0.732309:0.704336:0.716596:0.656588:0.716596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
24002,320:@0.843329:0.732309:0.917805:0.732309:0.917805:0.716596:0.843329:0.716596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1,99999:@0.220759:0.764469:0.277417:0.764469:0.277417:0.748756:0.220759:0.748756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
239997,680:@0.407501:0.764469:0.490885:0.764469:0.490885:0.748756:0.407501:0.748756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,00001:@0.647660:0.764469:0.704318:0.764469:0.704318:0.748756:0.647660:0.748756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
240002,320:@0.834402:0.764469:0.917787:0.764469:0.917787:0.748756:0.834402:0.748756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1,999999:@0.211832:0.796629:0.277398:0.796629:0.277398:0.780917:0.211832:0.780917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2399997,680:@0.398573:0.796629:0.490867:0.796629:0.490867:0.780917:0.398573:0.780917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,000001:@0.638733:0.796629:0.704299:0.796629:0.704299:0.780917:0.638733:0.780917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2400002,320:@0.825474:0.796629:0.917768:0.796629:0.917768:0.780917:0.825474:0.780917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.101528:0.837311:0.108983:0.837311:0.108983:0.821876:0.101528:0.821876:0.000000
   2:@0.108925:0.837311:0.137733:0.837311:0.137733:0.821599:0.108925:0.821599:0.000000:0.000000:0.000000:0.000000
→:@0.112883:0.838837:0.124885:0.838837:0.124885:0.820129:0.112883:0.820129:0.000000
2 :@0.137647:0.830924:0.149216:0.830924:0.149216:0.822928:0.137647:0.822928:0.000000:0.000000
entonces  ( )   :@0.201940:0.837311:0.314777:0.837311:0.314777:0.821599:0.201940:0.821599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.273287:0.837311:0.290166:0.837311:0.290166:0.821876:0.273287:0.821876:0.000000:0.000000:0.000000
→:@0.298836:0.838837:0.310837:0.838837:0.310837:0.820129:0.298836:0.820129:0.000000
2`:@0.314703:0.836756:0.342222:0.836756:0.342222:0.823041:0.314703:0.823041:0.000000:0.000000
 :@0.342135:0.837311:0.346166:0.837311:0.346166:0.821599:0.342135:0.821599:0.000000
x:@0.424501:0.837311:0.431955:0.837311:0.431955:0.821876:0.424501:0.821876:0.000000
   2:@0.431882:0.837311:0.460689:0.837311:0.460689:0.821599:0.431882:0.821599:0.000000:0.000000:0.000000:0.000000
→:@0.435839:0.838837:0.447841:0.838837:0.447841:0.820129:0.435839:0.820129:0.000000
1 :@0.460611:0.830924:0.472179:0.830924:0.472179:0.822928:0.460611:0.822928:0.000000:0.000000
entonces  ( )   :@0.546658:0.837311:0.659494:0.837311:0.659494:0.821599:0.546658:0.821599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.618004:0.837311:0.634884:0.837311:0.634884:0.821876:0.618004:0.821876:0.000000:0.000000:0.000000
→:@0.643554:0.838837:0.655555:0.838837:0.655555:0.820129:0.643554:0.820129:0.000000
`:@0.659421:0.836756:0.671698:0.836756:0.671698:0.823041:0.659421:0.823041:0.000000
Además de las tablas anteriores, haremos tabulaciones entre  3 y 2, valores mayores que 2 y menores que  3, y :@0.073076:0.871815:0.930926:0.871815:0.930926:0.856103:0.073076:0.856103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.533570:0.871261:0.548903:0.871261:0.548903:0.857545:0.533570:0.857545:0.000000
2:@0.885811:0.871261:0.901145:0.871261:0.901145:0.857545:0.885811:0.857545:0.000000
observamos que también se genera una asíntota horizontal en     3.:@0.073076:0.888457:0.574324:0.888457:0.574324:0.872744:0.073076:0.872744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.531656:0.888457:0.539129:0.888457:0.539129:0.873022:0.531656:0.873022:0.000000
5:@0.543013:0.887902:0.558346:0.887902:0.558346:0.874187:0.543013:0.874187:0.000000
Como ya se mencionó, en el apartado sobre límites de funciones el tema de asíntotas horizontales y verticales se tratará :@0.073076:0.922961:0.931241:0.922961:0.931241:0.907249:0.073076:0.907249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con mayor precisión, puesto que se maneja como una aplicación a la teoría de límites de funciones.:@0.073076:0.939603:0.793792:0.939603:0.793792:0.923890:0.073076:0.923890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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