148:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000 Cociente incremental:@0.404236:0.097328:0.576918:0.097328:0.576918:0.079645:0.404236:0.079645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea la función polinomial definida como ( ) = 2 – 1 con . :@0.404236:0.114035:0.895912:0.114035:0.895912:0.097538:0.404236:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.432787:0.114151:0.442054:0.114151:0.442054:0.097682:0.432787:0.097682:0.000000 p x:@0.711802:0.114151:0.734497:0.114151:0.734497:0.097682:0.711802:0.097682:0.000000:0.000000:0.000000 x:@0.768615:0.114151:0.776090:0.114151:0.776090:0.097682:0.768615:0.097682:0.000000 3:@0.776039:0.107684:0.780992:0.107684:0.780992:0.098065:0.776039:0.098065:0.000000 x:@0.844664:0.114151:0.852139:0.114151:0.852139:0.097682:0.844664:0.097682:0.000000 :@0.856541:0.113517:0.871193:0.113517:0.871193:0.100143:0.856541:0.100143:0.000000 :@0.875618:0.112948:0.888923:0.112948:0.888923:0.100086:0.875618:0.100086:0.000000 Fijemos el punto = –2. Sea = –2 + con ≠ 0, se tiene::@0.404244:0.131386:0.819383:0.131386:0.819383:0.114888:0.404244:0.114888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.526961:0.131502:0.535939:0.131502:0.535939:0.115033:0.526961:0.115033:0.000000 x:@0.609184:0.131502:0.616659:0.131502:0.616659:0.115033:0.609184:0.115033:0.000000 h:@0.673838:0.131502:0.683239:0.131502:0.683239:0.115033:0.673838:0.115033:0.000000 h:@0.718473:0.131502:0.727875:0.131502:0.727875:0.115033:0.718473:0.115033:0.000000 p:@0.552374:0.155981:0.561641:0.155981:0.561641:0.139512:0.552374:0.139512:0.000000 (–2) = 2 · (–2) – 1 = –17,:@0.561641:0.155865:0.743637:0.155866:0.743637:0.139368:0.561641:0.139367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.662066:0.149513:0.667019:0.149513:0.667019:0.139895:0.662066:0.139895:0.000000 p:@0.460611:0.180460:0.469878:0.180460:0.469878:0.163992:0.460611:0.163992:0.000000 (–2 + ) = 2(–2 + ) – 1 = –17 + 24 – 12 + 2 .:@0.469878:0.180345:0.835387:0.180344:0.835387:0.163846:0.469878:0.163847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.513918:0.180460:0.523320:0.180460:0.523320:0.163992:0.513918:0.163992:0.000000 h:@0.600901:0.180460:0.610302:0.180460:0.610302:0.163992:0.600901:0.163992:0.000000 3:@0.616261:0.173991:0.621214:0.173991:0.621214:0.164373:0.616261:0.164373:0.000000 h:@0.731162:0.180460:0.740563:0.180460:0.740563:0.163991:0.731162:0.163991:0.000000 h:@0.776339:0.180460:0.785740:0.180460:0.785740:0.163991:0.776339:0.163991:0.000000 2:@0.785737:0.173991:0.790690:0.173991:0.790690:0.164373:0.785737:0.164373:0.000000 h:@0.818278:0.180460:0.827680:0.180460:0.827680:0.163991:0.818278:0.163991:0.000000 3:@0.827678:0.173991:0.832631:0.173991:0.832631:0.164373:0.827678:0.164373:0.000000 El cociente incremental está definido como: :@0.404230:0.212776:0.719637:0.212776:0.719637:0.196278:0.404230:0.196278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.404230:0.237370:0.431471:0.237370:0.431471:0.220901:0.404230:0.220901:0.000000:0.000000:0.000000 ( ) = = =:@0.416117:0.237255:0.834346:0.237255:0.834346:0.220757:0.416117:0.220757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 24 – 12 + 2 , ≠ 0.:@0.404230:0.261734:0.563271:0.261741:0.563271:0.245243:0.404230:0.245236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.456998:0.261849:0.466399:0.261849:0.466399:0.245381:0.456998:0.245381:0.000000 h:@0.493987:0.261849:0.503389:0.261849:0.503389:0.245381:0.493987:0.245381:0.000000 2:@0.503394:0.255388:0.508347:0.255388:0.508347:0.245769:0.503394:0.245769:0.000000 h:@0.523527:0.261856:0.532928:0.261856:0.532928:0.245387:0.523527:0.245387:0.000000 Para valores de | | no nulos y cada vez más próximos a 0, el cociente :@0.404236:0.293420:0.895920:0.293420:0.895920:0.276922:0.404236:0.276922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.519587:0.293536:0.528988:0.293536:0.528988:0.277067:0.519587:0.277067:0.000000 incremental se aproxima cada vez a 24. Calculemos la distancia de 24 :@0.404236:0.310771:0.895978:0.310771:0.895978:0.294273:0.404236:0.294273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a ( ), esto es, (24, ( )), ≠ 0. Se tiene::@0.404236:0.328122:0.699418:0.328122:0.699418:0.311624:0.404236:0.311624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.416219:0.328237:0.443460:0.328237:0.443460:0.311769:0.416219:0.311769:0.000000:0.000000:0.000000 d:@0.511679:0.328237:0.520849:0.328237:0.520849:0.311769:0.511679:0.311769:0.000000 Q h h:@0.550691:0.328237:0.606136:0.328237:0.606136:0.311769:0.550691:0.311769:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.419494:0.352716:0.428665:0.352716:0.428665:0.336248:0.419494:0.336248:0.000000 (24, ( )) = |24 – ( )| = |24 – (24 – 12 + 2 )| = |12 – 2 |.:@0.428665:0.352601:0.876517:0.352604:0.876517:0.336107:0.428665:0.336103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.458506:0.352716:0.485747:0.352716:0.485747:0.336248:0.458506:0.336248:0.000000:0.000000:0.000000 Q h:@0.557530:0.352716:0.584771:0.352716:0.584771:0.336248:0.557530:0.336248:0.000000:0.000000:0.000000 h:@0.714330:0.352716:0.723731:0.352716:0.723731:0.336248:0.714330:0.336248:0.000000 h:@0.751319:0.352716:0.760720:0.352716:0.760720:0.336248:0.751319:0.336248:0.000000 2:@0.760710:0.346251:0.765664:0.346251:0.765664:0.336633:0.760710:0.336633:0.000000 h:@0.817719:0.352720:0.827120:0.352720:0.827120:0.336251:0.817719:0.336251:0.000000 h:@0.854400:0.352720:0.863801:0.352720:0.863801:0.336251:0.854400:0.336251:0.000000 2:@0.863800:0.346251:0.868753:0.346251:0.868753:0.336633:0.863800:0.336633:0.000000 Por la desigualdad triangular, se tiene::@0.404229:0.385036:0.667601:0.385036:0.667601:0.368538:0.404229:0.368538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.510246:0.409631:0.519416:0.409631:0.519416:0.393162:0.510246:0.393162:0.000000 (24, ( )) = |12 – 2 | ≤ 12| | + 2 .:@0.519416:0.409515:0.785749:0.409521:0.785749:0.393023:0.519416:0.393017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.549258:0.409631:0.576499:0.409631:0.576499:0.393162:0.549258:0.393162:0.000000:0.000000:0.000000 h:@0.629498:0.409631:0.638900:0.409631:0.638900:0.393162:0.629498:0.393162:0.000000 h:@0.666179:0.409631:0.675581:0.409631:0.675581:0.393162:0.666179:0.393162:0.000000 2:@0.675588:0.403169:0.680541:0.403169:0.680541:0.393551:0.675588:0.393551:0.000000 h:@0.726644:0.409637:0.736045:0.409637:0.736045:0.393168:0.726644:0.393168:0.000000 h:@0.768642:0.409637:0.778043:0.409637:0.778043:0.393168:0.768642:0.393168:0.000000 2:@0.778041:0.403169:0.782994:0.403169:0.782994:0.393551:0.778041:0.393551:0.000000 Notemos que si 0 < | | < 1, entonces 0 < ≤ | | < 1. Luego,:@0.404240:0.442719:0.831884:0.442714:0.831884:0.426216:0.404240:0.426221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.553235:0.442835:0.562637:0.442835:0.562637:0.426366:0.553235:0.426366:0.000000 h:@0.698572:0.442835:0.707974:0.442835:0.707974:0.426366:0.698572:0.426366:0.000000 2:@0.707967:0.436362:0.712920:0.436362:0.712920:0.426744:0.707967:0.426744:0.000000 h:@0.737022:0.442830:0.746423:0.442830:0.746423:0.426361:0.737022:0.426361:0.000000 0 < 12| | + 2 < 1 siempre que 0 < | | < . Así:@0.404234:0.467193:0.757521:0.467192:0.757521:0.450695:0.404234:0.450695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.453822:0.467309:0.463224:0.467309:0.463224:0.450840:0.453822:0.450840:0.000000 h:@0.495821:0.467309:0.505222:0.467309:0.505222:0.450840:0.495821:0.450840:0.000000 2:@0.505223:0.460841:0.510176:0.460841:0.510176:0.451222:0.505223:0.451222:0.000000 h:@0.665915:0.467308:0.675317:0.467308:0.675317:0.450839:0.665915:0.450839:0.000000 d:@0.404237:0.498988:0.413407:0.498988:0.413407:0.482519:0.404237:0.482519:0.000000 (24, ( )) = |12 – 2 | ≤ 12| | + 2 < 1 siempre que 0 < | | < 1,:@0.413407:0.498872:0.877465:0.498876:0.877465:0.482379:0.413407:0.482374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.443249:0.498988:0.470490:0.498988:0.470490:0.482519:0.443249:0.482519:0.000000:0.000000:0.000000 h:@0.523489:0.498988:0.532890:0.498988:0.532890:0.482519:0.523489:0.482519:0.000000 h:@0.560170:0.498988:0.569571:0.498988:0.569571:0.482519:0.560170:0.482519:0.000000 2:@0.569567:0.492525:0.574520:0.492525:0.574520:0.482906:0.569567:0.482906:0.000000 h:@0.620623:0.498992:0.630024:0.498992:0.630024:0.482523:0.620623:0.482523:0.000000 h:@0.662621:0.498992:0.672022:0.498992:0.672022:0.482523:0.662621:0.482523:0.000000 2:@0.672020:0.492525:0.676973:0.492525:0.676973:0.482906:0.672020:0.482906:0.000000 h:@0.832712:0.498992:0.842113:0.498992:0.842113:0.482523:0.832712:0.482523:0.000000 es decir, (24, ( )) puede hacerse tan pequeño como se quiera, to-:@0.404235:0.516227:0.891835:0.516227:0.891835:0.499729:0.404235:0.499729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.464844:0.516343:0.474014:0.516343:0.474014:0.499874:0.464844:0.499874:0.000000 Q h:@0.504280:0.516343:0.531521:0.516343:0.531521:0.499874:0.504280:0.499874:0.000000:0.000000:0.000000 mando valores de | | cada vez más cercanos a 0. En estas condiciones, :@0.404235:0.533578:0.895864:0.533578:0.895864:0.517080:0.404235:0.517080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.537975:0.533693:0.547376:0.533693:0.547376:0.517225:0.537975:0.517225:0.000000 se dice que ( ) se aproxima tanto como se quiera a 24. Se escribe::@0.404235:0.550929:0.879775:0.550929:0.879775:0.534431:0.404235:0.534431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.487594:0.551044:0.514835:0.551044:0.514835:0.534575:0.487594:0.534575:0.000000:0.000000:0.000000 lím Q h:@0.426564:0.580468:0.480140:0.580468:0.480140:0.563999:0.426564:0.563999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.448757:0.580353:0.505185:0.580353:0.505185:0.563855:0.448757:0.563855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím:@0.505185:0.580468:0.527379:0.580468:0.527379:0.563999:0.505185:0.563999:0.000000:0.000000:0.000000 = :@0.527379:0.580353:0.691442:0.580353:0.691442:0.563855:0.527379:0.563855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím:@0.691442:0.580468:0.713634:0.580468:0.713634:0.563999:0.691442:0.563999:0.000000:0.000000:0.000000 (24 – 12 + 2 ) = 24,:@0.714599:0.580353:0.869446:0.580349:0.869446:0.563852:0.714599:0.563855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.773319:0.580468:0.782721:0.580468:0.782721:0.563999:0.773319:0.563999:0.000000 h:@0.810308:0.580468:0.819710:0.580468:0.819710:0.563999:0.810308:0.563999:0.000000 2:@0.819701:0.573998:0.824654:0.573998:0.824654:0.564380:0.819701:0.564380:0.000000 que se lee “límite del cociente incremental igual a 24 cuando tiende :@0.404229:0.615051:0.895965:0.615051:0.895965:0.598553:0.404229:0.598553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.833237:0.615167:0.842638:0.615167:0.842638:0.598698:0.833237:0.598698:0.000000 a 0”. A este valor se le llama derivada de la función en el punto:@0.404229:0.632402:0.857361:0.632402:0.857361:0.615904:0.404229:0.615904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.762152:0.632517:0.771419:0.632517:0.771419:0.616049:0.762152:0.616049:0.000000 x:@0.404229:0.656996:0.411704:0.656996:0.411704:0.640528:0.404229:0.640528:0.000000 = –2, y se escribe (–2) = 24, o también, (–2) = 24.:@0.411704:0.656881:0.810182:0.656881:0.810182:0.640383:0.411704:0.640383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p':@0.728864:0.656996:0.740442:0.656996:0.740442:0.640528:0.728864:0.640528:0.000000:0.000000 Ejercicio resuelto:@0.404229:0.691958:0.522207:0.691958:0.522207:0.675171:0.404229:0.675171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.404229:0.709150:0.416501:0.709150:0.416501:0.692435:0.404229:0.692435:0.000000:0.000000 Sean :@0.416501:0.708933:0.466147:0.708933:0.466147:0.692435:0.416501:0.692435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c :@0.466244:0.709049:0.477668:0.709049:0.477668:0.692580:0.466244:0.692580:0.000000:0.000000 :@0.477779:0.708415:0.492432:0.708415:0.492432:0.695042:0.477779:0.695042:0.000000 con ≠ 0 y la función polinomial definida por:@0.492520:0.708934:0.857442:0.708934:0.857442:0.692436:0.492520:0.692436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.496758:0.707847:0.510063:0.707847:0.510063:0.694984:0.496758:0.694984:0.000000 c :@0.545873:0.709049:0.557297:0.709049:0.557297:0.692580:0.545873:0.692580:0.000000:0.000000 p:@0.597523:0.709049:0.606789:0.709049:0.606789:0.692580:0.597523:0.692580:0.000000 :@0.404235:0.726284:0.408377:0.726284:0.408377:0.709787:0.404235:0.709787:0.000000 p x:@0.427969:0.726400:0.450856:0.726400:0.450856:0.709931:0.427969:0.709931:0.000000:0.000000:0.000000 ( ) = :@0.437332:0.726284:0.477442:0.726284:0.477442:0.709787:0.437332:0.709787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cx:@0.478695:0.726400:0.493452:0.726400:0.493452:0.709931:0.478695:0.709931:0.000000:0.000000 4:@0.493572:0.719931:0.498525:0.719931:0.498525:0.710313:0.493572:0.710313:0.000000 + 2 – 5, :@0.498581:0.726284:0.573426:0.726284:0.573426:0.709787:0.498581:0.709787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.528866:0.726400:0.536341:0.726400:0.536341:0.709931:0.528866:0.709931:0.000000 ∀:@0.574695:0.733871:0.586268:0.733871:0.586268:0.714872:0.574695:0.714872:0.000000 x:@0.586276:0.726400:0.593751:0.726400:0.593751:0.709931:0.586276:0.709931:0.000000 . Sea , calculemos el cociente :@0.593847:0.726284:0.895891:0.726284:0.895891:0.709787:0.593847:0.709787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.599249:0.725766:0.613902:0.725766:0.613902:0.712392:0.599249:0.712392:0.000000 :@0.619391:0.725197:0.632695:0.725197:0.632695:0.712335:0.619391:0.712335:0.000000 a:@0.670834:0.726400:0.679812:0.726400:0.679812:0.709931:0.670834:0.709931:0.000000 :@0.685326:0.725766:0.699979:0.725766:0.699979:0.712392:0.685326:0.712392:0.000000 :@0.705468:0.725197:0.718772:0.725197:0.718772:0.712335:0.705468:0.712335:0.000000 incremental ( ) para :@0.427979:0.743635:0.591943:0.743635:0.591943:0.727137:0.427979:0.727137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.518371:0.743751:0.545805:0.743751:0.545805:0.727282:0.518371:0.727282:0.000000:0.000000:0.000000 h :@0.592040:0.743751:0.605679:0.743751:0.605679:0.727282:0.592040:0.727282:0.000000:0.000000 :@0.605776:0.743116:0.620428:0.743116:0.620428:0.729743:0.605776:0.729743:0.000000 , tal que ≠ 0.:@0.620516:0.743635:0.739525:0.743635:0.739525:0.727137:0.620516:0.727137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.624755:0.742548:0.638059:0.742548:0.638059:0.729686:0.624755:0.729686:0.000000 h:@0.699299:0.743751:0.708701:0.743751:0.708701:0.727282:0.699299:0.727282:0.000000 :@0.404233:0.778337:0.408375:0.778337:0.408375:0.761839:0.404233:0.761839:0.000000 Q h:@0.427968:0.778452:0.455209:0.778452:0.455209:0.761983:0.427968:0.761983:0.000000:0.000000:0.000000 ( ) = =:@0.439854:0.778337:0.613394:0.778337:0.613394:0.761839:0.439854:0.761839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.427968:0.813038:0.438775:0.813038:0.438775:0.796540:0.427968:0.796540:0.000000 :@0.404233:0.847740:0.408375:0.847740:0.408375:0.831242:0.404233:0.831242:0.000000 = :@0.427968:0.847740:0.676123:0.847740:0.676123:0.831242:0.427968:0.831242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = (4 + 6:@0.427968:0.873997:0.507005:0.874000:0.507005:0.857502:0.427968:0.857499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c a:@0.443110:0.874113:0.474012:0.874113:0.474012:0.857644:0.443110:0.857644:0.000000:0.000000:0.000000 3:@0.474119:0.867648:0.479072:0.867648:0.479072:0.858030:0.474119:0.858030:0.000000 a h:@0.507101:0.874115:0.530584:0.874115:0.530584:0.857646:0.507101:0.857646:0.000000:0.000000:0.000000 2:@0.516174:0.867648:0.521127:0.867648:0.521127:0.858030:0.516174:0.858030:0.000000 + 4:@0.530681:0.874000:0.558558:0.874000:0.558558:0.857502:0.530681:0.857502:0.000000:0.000000:0.000000:0.000000 ah:@0.558654:0.874115:0.577014:0.874115:0.577014:0.857646:0.558654:0.857646:0.000000:0.000000 2:@0.577109:0.867648:0.582062:0.867648:0.582062:0.858030:0.577109:0.858030:0.000000 + ) + 2, ≠ 0.:@0.582118:0.874000:0.705821:0.874000:0.705821:0.857502:0.582118:0.857502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.601499:0.874115:0.610900:0.874115:0.610900:0.857646:0.601499:0.857646:0.000000 3:@0.610998:0.867648:0.615951:0.867648:0.615951:0.858030:0.610998:0.858030:0.000000 h:@0.665595:0.874115:0.674997:0.874115:0.674997:0.857646:0.665595:0.857646:0.000000 Para = y = 2, se tiene::@0.404243:0.908701:0.600382:0.908701:0.600382:0.892203:0.404243:0.892203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.438728:0.908817:0.445914:0.908817:0.445914:0.892348:0.438728:0.892348:0.000000 a:@0.499895:0.908817:0.508872:0.908817:0.508872:0.892348:0.499895:0.892348:0.000000 Q h:@0.404243:0.947075:0.431484:0.947075:0.431484:0.930606:0.404243:0.930606:0.000000:0.000000:0.000000 ( ) = = (32 + 24 + 8 + ) + 2, ≠ 0. :@0.416130:0.946960:0.844579:0.946967:0.844579:0.930469:0.416130:0.930462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.675478:0.947075:0.684880:0.947075:0.684880:0.930606:0.675478:0.930606:0.000000 h:@0.712468:0.947075:0.721869:0.947075:0.721869:0.930606:0.712468:0.930606:0.000000 2:@0.721857:0.940615:0.726810:0.940615:0.726810:0.930997:0.721857:0.930997:0.000000 h:@0.745902:0.947083:0.755304:0.947083:0.755304:0.930614:0.745902:0.930614:0.000000 3:@0.755303:0.940615:0.760256:0.940615:0.760256:0.930997:0.755303:0.930997:0.000000 h:@0.800693:0.947083:0.810094:0.947083:0.810094:0.930614:0.800693:0.930614:0.000000 p:@0.461806:0.229965:0.471072:0.229965:0.471072:0.213496:0.461806:0.213496:0.000000 (–2:@0.471072:0.229849:0.496021:0.229849:0.496021:0.213351:0.471072:0.213351:0.000000:0.000000:0.000000 + h:@0.496021:0.229965:0.524591:0.229965:0.524591:0.213496:0.496021:0.213496:0.000000:0.000000:0.000000:0.000000 ) – ( 2):@0.524591:0.229849:0.589034:0.229849:0.589034:0.213351:0.524591:0.213351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p –:@0.549328:0.229965:0.574585:0.229965:0.574585:0.213496:0.549328:0.213496:0.000000:0.000000:0.000000 h:@0.520719:0.246303:0.530120:0.246303:0.530120:0.229835:0.520719:0.229835:0.000000 p a + h:@0.485549:0.771654:0.538317:0.771654:0.538317:0.755185:0.485549:0.755185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.494816:0.771538:0.500769:0.771538:0.500769:0.755041:0.494816:0.755041:0.000000 ) – ( ):@0.538317:0.771538:0.593203:0.771538:0.593203:0.755041:0.538317:0.755041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p a:@0.563053:0.771654:0.587250:0.771654:0.587250:0.755185:0.563053:0.755185:0.000000:0.000000:0.000000 h:@0.534675:0.787993:0.544077:0.787993:0.544077:0.771524:0.534675:0.771524:0.000000 –17 + 24 – 12 + 2 + 17:@0.615501:0.229849:0.816632:0.229849:0.816632:0.213351:0.615501:0.213351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.679076:0.229965:0.688477:0.229965:0.688477:0.213496:0.679076:0.213496:0.000000 h:@0.724253:0.229965:0.733654:0.229965:0.733654:0.213496:0.724253:0.213496:0.000000 2:@0.733654:0.223497:0.738607:0.223497:0.738607:0.213879:0.733654:0.213879:0.000000 h:@0.766193:0.229965:0.775595:0.229965:0.775595:0.213496:0.766193:0.213496:0.000000 3:@0.775595:0.223497:0.780548:0.223497:0.780548:0.213879:0.775595:0.213879:0.000000 h:@0.711367:0.246303:0.720769:0.246303:0.720769:0.229835:0.711367:0.229835:0.000000 c a + h:@0.620670:0.771654:0.669932:0.771654:0.669932:0.755185:0.620670:0.755185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.627856:0.771538:0.633809:0.771538:0.633809:0.755041:0.627856:0.755041:0.000000 ) + 2(:@0.669932:0.771538:0.712937:0.771538:0.712937:0.755041:0.669932:0.755041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.675870:0.765185:0.680823:0.765185:0.680823:0.755567:0.675870:0.755567:0.000000 a + h:@0.712937:0.771654:0.749059:0.771654:0.749059:0.755185:0.712937:0.755185:0.000000:0.000000:0.000000:0.000000:0.000000 ) – 5 – (:@0.749059:0.771538:0.804177:0.771538:0.804177:0.755041:0.749059:0.755041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ca + a – 5:@0.804177:0.771654:0.885422:0.771654:0.885422:0.755185:0.804177:0.755185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.820284:0.765185:0.825237:0.765185:0.825237:0.755567:0.820284:0.755567:0.000000 2:@0.839551:0.771538:0.851477:0.771538:0.851477:0.755041:0.839551:0.755041:0.000000:0.000000 ):@0.885422:0.771538:0.891375:0.771538:0.891375:0.755041:0.885422:0.755041:0.000000 h:@0.751317:0.787993:0.760718:0.787993:0.760718:0.771524:0.751317:0.771524:0.000000 c a + a h + a h:@0.443504:0.806488:0.572564:0.806488:0.572564:0.790019:0.443504:0.790019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.450690:0.806372:0.456643:0.806372:0.456643:0.789874:0.450690:0.789874:0.000000 4:@0.465619:0.800019:0.470572:0.800019:0.470572:0.790401:0.465619:0.790401:0.000000 4:@0.489741:0.806372:0.498237:0.806372:0.498237:0.789874:0.489741:0.789874:0.000000 3:@0.507213:0.800019:0.512166:0.800019:0.512166:0.790401:0.507213:0.790401:0.000000 6:@0.521568:0.806372:0.549233:0.806372:0.549233:0.789874:0.521568:0.789874:0.000000:0.000000:0.000000 2 2:@0.558209:0.800019:0.577517:0.800019:0.577517:0.790401:0.558209:0.790401:0.000000:0.000000:0.000000 + 4:@0.577518:0.806372:0.605106:0.806372:0.605106:0.789874:0.577518:0.789874:0.000000:0.000000:0.000000:0.000000 ah + h:@0.605106:0.806488:0.656892:0.806488:0.656892:0.790019:0.605106:0.790019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.623368:0.800019:0.628321:0.800019:0.628321:0.790401:0.623368:0.790401:0.000000 :@0.628321:0.806372:0.632463:0.806372:0.632463:0.789874:0.628321:0.789874:0.000000 4:@0.656891:0.800019:0.661844:0.800019:0.661844:0.790401:0.656891:0.790401:0.000000 ) + 2 + 2:@0.661844:0.806372:0.731951:0.806372:0.731951:0.789874:0.661844:0.789874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.695385:0.806488:0.704363:0.806488:0.704363:0.790019:0.695385:0.790019:0.000000 h – 5 ca – a + 5:@0.731951:0.806488:0.870678:0.806488:0.870678:0.790019:0.731951:0.790019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.767746:0.806372:0.786529:0.806372:0.786529:0.789874:0.767746:0.789874:0.000000:0.000000:0.000000 4:@0.802689:0.800019:0.807642:0.800019:0.807642:0.790401:0.802689:0.790401:0.000000 2:@0.821822:0.806372:0.834460:0.806372:0.834460:0.789874:0.821822:0.789874:0.000000:0.000000 h:@0.654869:0.822826:0.664270:0.822826:0.664270:0.806357:0.654869:0.806357:0.000000 ch a + a h:@0.448347:0.841321:0.544078:0.841321:0.544078:0.824852:0.448347:0.824852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (4:@0.464703:0.841205:0.479152:0.841205:0.479152:0.824708:0.464703:0.824708:0.000000:0.000000 3:@0.488129:0.834854:0.493082:0.834854:0.493082:0.825236:0.488129:0.825236:0.000000 6:@0.512251:0.841205:0.520747:0.841205:0.520747:0.824708:0.512251:0.824708:0.000000 2:@0.529723:0.834854:0.534677:0.834854:0.534677:0.825236:0.529723:0.825236:0.000000 + 4:@0.544078:0.841205:0.571666:0.841205:0.571666:0.824708:0.544078:0.824708:0.000000:0.000000:0.000000:0.000000 ah + h:@0.571666:0.841321:0.623452:0.841321:0.623452:0.824852:0.571666:0.824852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.589928:0.834854:0.594881:0.834854:0.594881:0.825236:0.589928:0.825236:0.000000 :@0.594882:0.841205:0.599024:0.841205:0.599024:0.824708:0.594882:0.824708:0.000000 3:@0.623451:0.834854:0.628405:0.834854:0.628405:0.825236:0.623451:0.825236:0.000000 ) + 2:@0.628405:0.841205:0.661946:0.841205:0.661946:0.824708:0.628405:0.824708:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.661946:0.841321:0.671347:0.841321:0.671347:0.824852:0.661946:0.824852:0.000000 h:@0.555139:0.857660:0.564541:0.857660:0.564541:0.841191:0.555139:0.841191:0.000000 1:@0.706607:0.459770:0.715103:0.459770:0.715103:0.443273:0.706607:0.443273:0.000000 14:@0.702369:0.476109:0.719360:0.476109:0.719360:0.459611:0.702369:0.459611:0.000000:0.000000 p:@0.537620:0.572787:0.546887:0.572787:0.546887:0.556318:0.537620:0.556318:0.000000 (–2:@0.546887:0.572671:0.571836:0.572671:0.571836:0.556173:0.546887:0.556173:0.000000:0.000000:0.000000 + h:@0.571836:0.572787:0.600406:0.572787:0.600406:0.556318:0.571836:0.556318:0.000000:0.000000:0.000000:0.000000 ) – (–2):@0.600406:0.572671:0.665311:0.572671:0.665311:0.556173:0.600406:0.556173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.625143:0.572787:0.634409:0.572787:0.634409:0.556318:0.625143:0.556318:0.000000 h:@0.596765:0.589125:0.606166:0.589125:0.606166:0.572657:0.596765:0.572657:0.000000 h:@0.427787:0.588211:0.433918:0.588211:0.433918:0.577471:0.427787:0.577471:0.000000 →:@0.433918:0.587529:0.444666:0.587529:0.444666:0.577518:0.433918:0.577518:0.000000 0:@0.444663:0.588136:0.450204:0.588136:0.450204:0.577377:0.444663:0.577377:0.000000 h:@0.503175:0.588211:0.509306:0.588211:0.509306:0.577471:0.503175:0.577471:0.000000 →:@0.509304:0.587529:0.520051:0.587529:0.520051:0.577518:0.509304:0.577518:0.000000 0:@0.520049:0.588136:0.525590:0.588136:0.525590:0.577377:0.520049:0.577377:0.000000 h:@0.691727:0.588211:0.697859:0.588211:0.697859:0.577471:0.691727:0.577471:0.000000 →:@0.697860:0.587529:0.708608:0.587529:0.708608:0.577518:0.697860:0.577518:0.000000 0:@0.708605:0.588136:0.714146:0.588136:0.714146:0.577377:0.708605:0.577377:0.000000 dp:@0.547647:0.648850:0.566007:0.648850:0.566007:0.632381:0.547647:0.632381:0.000000:0.000000 dx:@0.548591:0.665188:0.565082:0.665188:0.565082:0.648720:0.548591:0.648720:0.000000:0.000000 Dada una función :@0.199880:0.141226:0.327707:0.141226:0.327707:0.126163:0.199880:0.126163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.320003:0.141331:0.323925:0.141331:0.323925:0.126295:0.320003:0.126295:0.000000 definida en un subconjunto :@0.153337:0.157068:0.351098:0.157068:0.351098:0.142005:0.153337:0.142005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.337026:0.157173:0.347316:0.157173:0.347316:0.142137:0.337026:0.142137:0.000000 de , esta es derivable en :@0.153337:0.172910:0.320085:0.172910:0.320085:0.157847:0.153337:0.157847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.173326:0.171907:0.185421:0.171907:0.185421:0.160214:0.173326:0.160214:0.000000 x A:@0.320050:0.173015:0.357881:0.173015:0.357881:0.157979:0.320050:0.157979:0.000000:0.000000:0.000000:0.000000 :@0.330588:0.172410:0.343845:0.172410:0.343845:0.160310:0.330588:0.160310:0.000000 :@0.343844:0.172910:0.361662:0.172910:0.361662:0.157847:0.343844:0.157847:0.000000:0.000000:0.000000 si y solo si existe:@0.153344:0.188752:0.256648:0.188752:0.256648:0.173689:0.153344:0.173689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím .:@0.194012:0.211828:0.320836:0.211828:0.320836:0.196791:0.194012:0.196791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En tal caso, este límite es notado :@0.153344:0.238258:0.365320:0.238258:0.365320:0.223195:0.153344:0.223195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.361538:0.238258:0.365320:0.238258:0.365320:0.223195:0.361538:0.223195:0.000000 ( ), ( ) llamado derivada :@0.153344:0.261229:0.346007:0.261229:0.346007:0.246166:0.153344:0.246166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x f' x:@0.184601:0.261334:0.222086:0.261334:0.222086:0.246298:0.184601:0.246298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de en .:@0.153344:0.287764:0.209966:0.287764:0.209966:0.272701:0.153344:0.272701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.173326:0.287870:0.177249:0.287870:0.177249:0.272833:0.173326:0.272833:0.000000 x:@0.200661:0.287870:0.207486:0.287870:0.207486:0.272833:0.200661:0.272833:0.000000 El proceso de cálculo de la :@0.153344:0.310735:0.327464:0.310735:0.327464:0.295672:0.153344:0.295672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derivada consiste en formar el :@0.153344:0.326577:0.349116:0.326577:0.349116:0.311514:0.153344:0.311514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cociente incremental::@0.153344:0.342419:0.292020:0.342419:0.292020:0.327356:0.153344:0.327356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.202631:0.365496:0.312199:0.365496:0.312199:0.350459:0.202631:0.350459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde :@0.153344:0.395490:0.227302:0.395481:0.227302:0.380418:0.153344:0.380427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.199729:0.395595:0.206554:0.395595:0.206554:0.380559:0.199729:0.380559:0.000000 :@0.210264:0.394981:0.223521:0.394981:0.223521:0.382881:0.210264:0.382881:0.000000 A, h :@0.227266:0.395586:0.273521:0.395586:0.273521:0.380550:0.227266:0.380550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.256483:0.394981:0.269740:0.394981:0.269740:0.382881:0.256483:0.382881:0.000000 :@0.273487:0.394478:0.285582:0.394478:0.285582:0.382785:0.273487:0.382785:0.000000 con ≠ 0, :@0.285582:0.395481:0.357473:0.395481:0.357473:0.380418:0.285582:0.380418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.317579:0.395586:0.326162:0.395586:0.326162:0.380550:0.317579:0.380550:0.000000 x h:@0.153341:0.411428:0.186040:0.411428:0.186040:0.396392:0.153341:0.396392:0.000000:0.000000:0.000000 + :@0.160130:0.411323:0.189787:0.411323:0.189787:0.396260:0.160130:0.396260:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.189754:0.410823:0.206989:0.410823:0.206989:0.398723:0.189754:0.398723:0.000000:0.000000 A:@0.206990:0.411428:0.217280:0.411428:0.217280:0.396392:0.206990:0.396392:0.000000 .:@0.217245:0.411323:0.219760:0.411323:0.219760:0.396260:0.217245:0.396260:0.000000 A continuación, se realizan :@0.153341:0.434294:0.329274:0.434294:0.329274:0.419231:0.153341:0.419231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los cálculos pertinentes en el :@0.153341:0.450136:0.341744:0.450136:0.341744:0.435073:0.153341:0.435073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cociente incremental, para :@0.153341:0.465978:0.327920:0.465978:0.327920:0.450915:0.153341:0.450915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 simplificar. Luego, se hace | | :@0.153341:0.481820:0.342767:0.481820:0.342767:0.466757:0.153341:0.466757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.325862:0.481925:0.334446:0.481925:0.334446:0.466889:0.325862:0.466889:0.000000 suficientemente pequeño, y se :@0.153341:0.497662:0.353144:0.497662:0.353144:0.482599:0.153341:0.482599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calcula::@0.153341:0.513504:0.200306:0.513504:0.200306:0.498441:0.153341:0.498441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím .:@0.195310:0.536580:0.319529:0.536580:0.319529:0.521544:0.195310:0.521544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El cociente incremental se :@0.153341:0.566574:0.324998:0.566574:0.324998:0.551511:0.153341:0.551511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 denomina también tasa de :@0.153341:0.582416:0.331702:0.582416:0.331702:0.567353:0.153341:0.567353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 variación de la función en .:@0.153341:0.598258:0.339900:0.598258:0.339900:0.583195:0.153341:0.583195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.303260:0.598364:0.307183:0.598364:0.307183:0.583327:0.303260:0.583327:0.000000 x:@0.330595:0.598364:0.337420:0.598364:0.337420:0.583327:0.330595:0.583327:0.000000 f x h – f x:@0.222925:0.205312:0.303470:0.205312:0.303470:0.190275:0.222925:0.190275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ):@0.226848:0.205206:0.270559:0.205206:0.270559:0.190143:0.226848:0.190143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.291209:0.205206:0.308905:0.205206:0.308905:0.190143:0.291209:0.190143:0.000000:0.000000:0.000000 h:@0.261623:0.221655:0.270207:0.221655:0.270207:0.206619:0.261623:0.206619:0.000000 f x h – f x:@0.222925:0.528576:0.303470:0.528576:0.303470:0.513540:0.222925:0.513540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ):@0.226848:0.528471:0.270559:0.528471:0.270559:0.513408:0.226848:0.513408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.291209:0.528471:0.308905:0.528471:0.308905:0.513408:0.291209:0.513408:0.000000:0.000000:0.000000 h:@0.261623:0.544920:0.270207:0.544920:0.270207:0.529883:0.261623:0.529883:0.000000 f x h – f x:@0.215536:0.359356:0.296080:0.359356:0.296080:0.344319:0.215536:0.344319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ):@0.219458:0.359250:0.263169:0.359250:0.263169:0.344187:0.219458:0.344187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.283820:0.359250:0.301516:0.359250:0.301516:0.344187:0.283820:0.344187:0.000000:0.000000:0.000000 h:@0.254234:0.375700:0.262817:0.375700:0.262817:0.360663:0.254234:0.360663:0.000000 h:@0.193550:0.220172:0.199148:0.220172:0.199148:0.210366:0.193550:0.210366:0.000000 →:@0.199147:0.219549:0.208959:0.219549:0.208959:0.210409:0.199147:0.210409:0.000000 0:@0.208959:0.220103:0.214017:0.220103:0.214017:0.210280:0.208959:0.210280:0.000000 h:@0.193553:0.543437:0.199151:0.543437:0.199151:0.533631:0.193553:0.533631:0.000000 →:@0.199147:0.542814:0.208959:0.542814:0.208959:0.533674:0.199147:0.533674:0.000000 0:@0.208959:0.543368:0.214017:0.543368:0.214017:0.533545:0.208959:0.533545:0.000000 df:@0.157880:0.254574:0.170176:0.254574:0.170176:0.239537:0.157880:0.239537:0.000000:0.000000 dx:@0.156491:0.270918:0.171548:0.270918:0.171548:0.255881:0.156491:0.255881:0.000000:0.000000 1:@0.469535:0.900853:0.478031:0.900853:0.478031:0.884355:0.469535:0.884355:0.000000 4:@0.469535:0.917192:0.478031:0.917192:0.478031:0.900694:0.469535:0.900694:0.000000 1:@0.601919:0.939323:0.610415:0.939323:0.610415:0.922825:0.601919:0.922825:0.000000 4:@0.601919:0.955662:0.610415:0.955662:0.610415:0.939164:0.601919:0.939164:0.000000 p + h:@0.463814:0.939375:0.516100:0.939375:0.516100:0.922906:0.463814:0.922906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2:@0.473081:0.939259:0.487530:0.939259:0.487530:0.922762:0.473081:0.922762:0.000000:0.000000 ) – (2):@0.516100:0.939259:0.570505:0.939259:0.570505:0.922762:0.516100:0.922762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.540837:0.939375:0.550103:0.939375:0.550103:0.922906:0.540837:0.922906:0.000000 h:@0.512459:0.955714:0.521861:0.955714:0.521861:0.939245:0.512459:0.939245:0.000000 Competencia :@0.199646:0.758641:0.297269:0.758641:0.297269:0.743169:0.199646:0.743169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.199646:0.771209:0.283709:0.771209:0.283709:0.755737:0.199646:0.755737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las notaciones que se :@0.199884:0.795684:0.359263:0.795684:0.359263:0.780620:0.199884:0.780620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 usan más comúnmente para :@0.153341:0.811526:0.343381:0.811526:0.343381:0.796462:0.153341:0.796462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 denotar la derivada de una :@0.153341:0.827368:0.331000:0.827368:0.331000:0.812304:0.153341:0.812304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función son::@0.153341:0.843210:0.233303:0.843210:0.233303:0.828146:0.153341:0.828146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , ', [ ( )] , ,:@0.153341:0.866180:0.329821:0.866180:0.329821:0.851117:0.153341:0.851117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.193674:0.866286:0.200693:0.866286:0.200693:0.851249:0.193674:0.851249:0.000000 f x:@0.244879:0.866286:0.261062:0.866286:0.261062:0.851249:0.244879:0.851249:0.000000:0.000000:0.000000 D f D y f' x:@0.153341:0.896386:0.245002:0.896383:0.245002:0.881347:0.153341:0.881349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.163970:0.899332:0.167949:0.899332:0.167949:0.890566:0.163970:0.890566:0.000000 , :@0.174178:0.896278:0.188039:0.896278:0.188039:0.881215:0.174178:0.881215:0.000000:0.000000:0.000000:0.000000 x:@0.198662:0.899332:0.202641:0.899332:0.202641:0.890566:0.198662:0.890566:0.000000 , ( ).:@0.211968:0.896278:0.252953:0.896278:0.252953:0.881215:0.211968:0.881215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Y se lee como “derivada de la :@0.153341:0.919249:0.346088:0.919249:0.346088:0.904185:0.153341:0.904185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función y con respecto a x\.:@0.153341:0.935091:0.331721:0.935091:0.331721:0.920027:0.153341:0.920027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dy:@0.156359:0.859478:0.171698:0.859478:0.171698:0.844441:0.156359:0.844441:0.000000:0.000000 dx:@0.156500:0.875821:0.171557:0.875821:0.171557:0.860785:0.156500:0.860785:0.000000:0.000000 d:@0.221903:0.859478:0.230276:0.859478:0.230276:0.844441:0.221903:0.844441:0.000000 dx:@0.218561:0.875821:0.233618:0.875821:0.233618:0.860785:0.218561:0.860785:0.000000:0.000000 df(x):@0.290940:0.859478:0.319981:0.859478:0.319981:0.844441:0.290940:0.844441:0.000000:0.000000:0.000000:0.000000:0.000000 dx:@0.297923:0.875821:0.312980:0.875821:0.312980:0.860785:0.297923:0.860785:0.000000:0.000000 Competencia :@0.199644:0.104916:0.297267:0.104916:0.297267:0.089444:0.199644:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.199644:0.117484:0.283707:0.117484:0.283707:0.102012:0.199644:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000