108:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Límites y continuidad de funciones:@0.073089:0.043661:0.383513:0.043661:0.383513:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una discontinuidad :@0.078581:0.862836:0.211816:0.862836:0.211816:0.848552:0.078581:0.848552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el punto c se llama :@0.078581:0.877965:0.226786:0.877965:0.226786:0.863681:0.078581:0.863681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
removible:@0.078581:0.893094:0.148570:0.893094:0.148570:0.877940:0.078581:0.877940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 si la función :@0.148478:0.893094:0.234223:0.893094:0.234223:0.878810:0.148478:0.878810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puede redefinirse en  , de :@0.078581:0.908223:0.252463:0.908223:0.252463:0.893939:0.078581:0.893939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.218309:0.908223:0.225270:0.908223:0.225270:0.893308:0.218309:0.893308:0.000000
manera que   sea continua.:@0.078581:0.923352:0.257081:0.923352:0.257081:0.909068:0.078581:0.909068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.162100:0.923352:0.166367:0.923352:0.166367:0.908437:0.162100:0.908437:0.000000
Competencia :@0.078581:0.820866:0.177272:0.820866:0.177272:0.805460:0.078581:0.805460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.835995:0.167195:0.835995:0.167195:0.820589:0.078581:0.820589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.422524:0.136836:0.498307:0.136836:0.498307:0.120167:0.422524:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos la función f definida por :@0.424104:0.174050:0.709402:0.174050:0.709402:0.158337:0.424104:0.158337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.709067:0.174050:0.727179:0.174050:0.727179:0.157644:0.709067:0.157644:0.000000:0.000000:0.000000
( )=:@0.713687:0.174632:0.749581:0.174632:0.749581:0.156978:0.713687:0.156978:0.000000:0.000000:0.000000:0.000000
∙:@0.750612:0.177209:0.757299:0.177209:0.757299:0.148320:0.750612:0.148320:0.000000
2:@0.758955:0.162127:0.767938:0.162127:0.767938:0.146414:0.758955:0.146414:0.000000
x:@0.767864:0.162127:0.775319:0.162127:0.775319:0.145721:0.767864:0.145721:0.000000
+:@0.775246:0.162709:0.790579:0.162709:0.790579:0.145055:0.775246:0.145055:0.000000
3      si:@0.790489:0.162127:0.845674:0.162127:0.845674:0.146414:0.790489:0.146414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.845551:0.162127:0.856246:0.162127:0.856246:0.145721:0.845551:0.145721:0.000000:0.000000
≠:@0.856191:0.162709:0.871524:0.162709:0.871524:0.145055:0.856191:0.145055:0.000000
1:@0.871432:0.162127:0.880415:0.162127:0.880415:0.146414:0.871432:0.146414:0.000000
2:@0.758964:0.178769:0.767946:0.178769:0.767946:0.163056:0.758964:0.163056:0.000000
	:@0.767858:0.179351:0.772460:0.179351:0.772460:0.161697:0.767858:0.161697:0.000000
				:@0.819196:0.179351:0.835946:0.179351:0.835946:0.161697:0.819196:0.161697:0.000000:0.000000:0.000000:0.000000
si:@0.835371:0.178769:0.845992:0.178769:0.845992:0.163056:0.835371:0.163056:0.000000:0.000000
 x:@0.845918:0.178769:0.856281:0.178769:0.856281:0.162363:0.845918:0.162363:0.000000:0.000000
=:@0.856208:0.179351:0.871541:0.179351:0.871541:0.161697:0.856208:0.161697:0.000000
1.:@0.871449:0.178769:0.885291:0.179088:0.885291:0.163375:0.871449:0.163056:0.000000:0.000000
La gráfica de   se rompe en el punto donde :@0.424116:0.208557:0.747546:0.208557:0.747546:0.192845:0.424116:0.192845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.521821:0.208557:0.526515:0.208557:0.526515:0.192151:0.521821:0.192151:0.000000
x:@0.747881:0.208557:0.755336:0.208557:0.755336:0.192151:0.747881:0.192151:0.000000
=:@0.756440:0.209140:0.771773:0.209140:0.771773:0.191486:0.756440:0.191486:0.000000
1. Evaluemos en este :@0.772878:0.208557:0.931011:0.208557:0.931011:0.192845:0.772878:0.192845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto las condiciones de continuidad::@0.424134:0.225199:0.702555:0.225199:0.702555:0.209487:0.424134:0.209487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  lim :@0.424104:0.259713:0.480942:0.259502:0.480942:0.243789:0.424104:0.244001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.454307:0.267794:0.459729:0.267794:0.459729:0.255862:0.454307:0.255862:0.000000
1:@0.470479:0.267794:0.477011:0.267794:0.477011:0.256366:0.470479:0.256366:0.000000
f x:@0.480832:0.259502:0.501153:0.259502:0.501153:0.243096:0.480832:0.243096:0.000000:0.000000:0.000000
( )=:@0.486556:0.260084:0.524236:0.260292:0.524236:0.242638:0.486556:0.242430:0.000000:0.000000:0.000000:0.000000
5.:@0.524144:0.259710:0.536256:0.259710:0.536256:0.243997:0.524144:0.243997:0.000000:0.000000
2. :@0.424104:0.294224:0.440173:0.294224:0.440173:0.278511:0.424104:0.278511:0.000000:0.000000:0.000000
f:@0.454307:0.294224:0.459001:0.294224:0.459001:0.277818:0.454307:0.277818:0.000000
( )=:@0.458927:0.294806:0.495245:0.294806:0.495245:0.277152:0.458927:0.277152:0.000000:0.000000:0.000000:0.000000
1:@0.464965:0.294224:0.473947:0.294224:0.473947:0.278511:0.464965:0.278511:0.000000
2.:@0.495153:0.294224:0.507265:0.294224:0.507265:0.278511:0.495153:0.278511:0.000000:0.000000
3.  lim :@0.424104:0.328734:0.480942:0.328522:0.480942:0.312810:0.424104:0.313022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.454307:0.336816:0.459729:0.336816:0.459729:0.324884:0.454307:0.324884:0.000000
1:@0.470479:0.336816:0.477011:0.336816:0.477011:0.325388:0.470479:0.325388:0.000000
f x:@0.480832:0.328522:0.501153:0.328522:0.501153:0.312116:0.480832:0.312116:0.000000:0.000000:0.000000
( ) ≠ ( ):@0.486556:0.329105:0.553798:0.329313:0.553798:0.311659:0.486556:0.311451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.508903:0.328730:0.512934:0.328730:0.512934:0.313018:0.508903:0.313018:0.000000
f:@0.528102:0.328730:0.532795:0.328730:0.532795:0.312324:0.528102:0.312324:0.000000
1 .:@0.538759:0.328730:0.556909:0.328730:0.556909:0.313018:0.538759:0.313018:0.000000:0.000000:0.000000
Observamos que la condición 3 no se cumple y, por lo tanto, :@0.424082:0.363235:0.930683:0.363235:0.930683:0.347522:0.424082:0.347522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concluimos que la función   es discontinua en 1.:@0.424082:0.379876:0.772734:0.379876:0.772734:0.364164:0.424082:0.364164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.620561:0.379876:0.625255:0.379876:0.625255:0.363470:0.620561:0.363470:0.000000
Ejemplo 2:@0.424064:0.414380:0.499846:0.414380:0.499846:0.397711:0.424064:0.397711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función   definida por :@0.293612:0.455167:0.499681:0.455167:0.499681:0.439454:0.293612:0.439454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.398846:0.455167:0.403540:0.455167:0.403540:0.438761:0.398846:0.438761:0.000000
f x:@0.499515:0.455167:0.517628:0.455167:0.517628:0.438761:0.499515:0.438761:0.000000:0.000000:0.000000
( )=:@0.504135:0.455749:0.540030:0.455749:0.540030:0.438095:0.504135:0.438095:0.000000:0.000000:0.000000:0.000000
∙:@0.541112:0.458344:0.547799:0.458344:0.547799:0.429455:0.541112:0.429455:0.000000
3  :@0.549456:0.443262:0.571986:0.443262:0.571986:0.427549:0.549456:0.427549:0.000000:0.000000:0.000000
x:@0.559469:0.443262:0.566924:0.443262:0.566924:0.426855:0.559469:0.426855:0.000000
    si 0:@0.609703:0.443262:0.656005:0.443262:0.656005:0.427549:0.609703:0.427549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.642678:0.443262:0.645992:0.443262:0.645992:0.426855:0.642678:0.426855:0.000000
≤ ≤:@0.657036:0.443844:0.697201:0.443844:0.697201:0.426190:0.657036:0.426190:0.000000:0.000000:0.000000
x:@0.673382:0.443262:0.680837:0.443262:0.680837:0.426855:0.673382:0.426855:0.000000
6:@0.698213:0.443262:0.707196:0.443262:0.707196:0.427549:0.698213:0.427549:0.000000
1.5:@0.549446:0.459903:0.572676:0.459903:0.572676:0.444191:0.549446:0.444191:0.000000:0.000000:0.000000
x:@0.573688:0.459903:0.581143:0.459903:0.581143:0.443497:0.573688:0.443497:0.000000
+ 					:@0.582174:0.460486:0.631144:0.460486:0.631144:0.442832:0.582174:0.442832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.598519:0.459903:0.607502:0.459903:0.607502:0.444191:0.598519:0.444191:0.000000
si 6:@0.632154:0.459903:0.658238:0.459903:0.658238:0.444191:0.632154:0.444191:0.000000:0.000000:0.000000:0.000000
 :@0.644911:0.459903:0.648224:0.459903:0.648224:0.443497:0.644911:0.443497:0.000000
<:@0.659268:0.460486:0.674602:0.460486:0.674602:0.442832:0.659268:0.442832:0.000000
x:@0.675614:0.459903:0.683069:0.459903:0.683069:0.443497:0.675614:0.443497:0.000000
.:@0.710845:0.455188:0.714048:0.455188:0.714048:0.439476:0.710845:0.439476:0.000000
Analicemos la continuidad en :@0.293663:0.489692:0.513667:0.489692:0.513667:0.473980:0.293663:0.473980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.513391:0.489692:0.520846:0.489692:0.520846:0.473286:0.513391:0.473286:0.000000
=:@0.521877:0.490275:0.537210:0.490275:0.537210:0.472621:0.521877:0.472621:0.000000
6.:@0.538222:0.489692:0.550334:0.489692:0.550334:0.473980:0.538222:0.473980:0.000000:0.000000
Solo tenemos que evaluar las tres condiciones de la continuidad puntual. Veamos::@0.293663:0.524196:0.887651:0.524196:0.887651:0.508484:0.293663:0.508484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  lim :@0.293660:0.558717:0.350497:0.558505:0.350497:0.542792:0.293660:0.543004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.323861:0.566798:0.329283:0.566798:0.329283:0.554866:0.323861:0.554866:0.000000
6:@0.340033:0.566798:0.346566:0.566798:0.346566:0.555371:0.340033:0.555371:0.000000
f x:@0.350386:0.558505:0.370708:0.558505:0.370708:0.542099:0.350386:0.542099:0.000000:0.000000:0.000000
( )=:@0.356111:0.559087:0.393791:0.559295:0.393791:0.541641:0.356111:0.541433:0.000000:0.000000:0.000000:0.000000
18.:@0.393699:0.558713:0.414720:0.558713:0.414720:0.543000:0.393699:0.543000:0.000000:0.000000:0.000000
2. :@0.293660:0.593227:0.309730:0.593227:0.309730:0.577515:0.293660:0.577515:0.000000:0.000000:0.000000
f:@0.323861:0.593227:0.328555:0.593227:0.328555:0.576821:0.323861:0.576821:0.000000
( )=:@0.328482:0.593810:0.364799:0.593810:0.364799:0.576155:0.328482:0.576155:0.000000:0.000000:0.000000:0.000000
6:@0.334519:0.593227:0.343502:0.593227:0.343502:0.577515:0.334519:0.577515:0.000000
18.:@0.364707:0.593227:0.385728:0.593227:0.385728:0.577515:0.364707:0.577515:0.000000:0.000000:0.000000
3.  lim :@0.293660:0.627739:0.350497:0.627527:0.350497:0.611814:0.293660:0.612026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.323861:0.635819:0.329283:0.635819:0.329283:0.623887:0.323861:0.623887:0.000000
6:@0.340033:0.635819:0.346566:0.635819:0.346566:0.624392:0.340033:0.624392:0.000000
f x:@0.350386:0.627527:0.370708:0.627527:0.370708:0.611121:0.350386:0.611121:0.000000:0.000000:0.000000
( ) = ( ):@0.356111:0.628109:0.423353:0.628317:0.423353:0.610663:0.356111:0.610455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.378457:0.627735:0.382489:0.627735:0.382489:0.612022:0.378457:0.612022:0.000000
f:@0.397656:0.627735:0.402350:0.627735:0.402350:0.611329:0.397656:0.611329:0.000000
6 .:@0.408314:0.627735:0.426463:0.627735:0.426463:0.612022:0.408314:0.612022:0.000000:0.000000:0.000000
Como se cumplen las tres condiciones, podemos afirmar que   es continua en 6.:@0.293637:0.662239:0.872490:0.662239:0.872490:0.646526:0.293637:0.646526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.740823:0.662239:0.745516:0.662239:0.745516:0.645833:0.740823:0.645833:0.000000
Ejemplo 3:@0.293637:0.696743:0.369419:0.696743:0.369419:0.680074:0.293637:0.680074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función f definida por :@0.293637:0.739568:0.502502:0.739568:0.502502:0.723855:0.293637:0.723855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.502780:0.739568:0.520929:0.739568:0.520929:0.723162:0.502780:0.723162:0.000000:0.000000:0.000000
( )=:@0.507419:0.740151:0.543377:0.740151:0.543377:0.722496:0.507419:0.722496:0.000000:0.000000:0.000000:0.000000
x:@0.547580:0.729746:0.555035:0.729746:0.555035:0.713340:0.547580:0.713340:0.000000
2 :@0.556074:0.723682:0.564262:0.723682:0.564262:0.714521:0.556074:0.714521:0.000000:0.000000
–:@0.564854:0.730328:0.574058:0.730328:0.574058:0.712674:0.564854:0.712674:0.000000
9:@0.575070:0.729746:0.584053:0.729746:0.584053:0.714033:0.575070:0.714033:0.000000
x:@0.551969:0.747233:0.559424:0.747233:0.559424:0.730827:0.551969:0.730827:0.000000
–:@0.560455:0.747816:0.569658:0.747816:0.569658:0.730162:0.560455:0.730162:0.000000
3:@0.570671:0.747233:0.579654:0.747233:0.579654:0.731521:0.570671:0.731521:0.000000
, :@0.588084:0.739592:0.595263:0.739592:0.595263:0.723879:0.588084:0.723879:0.000000:0.000000
x:@0.595613:0.739592:0.603068:0.739592:0.603068:0.723186:0.595613:0.723186:0.000000
≠:@0.603012:0.740175:0.618346:0.740175:0.618346:0.722520:0.603012:0.722520:0.000000
3, redefinir la función   para que la función :@0.618272:0.739592:0.930956:0.739592:0.930956:0.723879:0.618272:0.723879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.776169:0.739592:0.780863:0.739592:0.780863:0.723186:0.776169:0.723186:0.000000
sea continua en 3.:@0.293623:0.756234:0.424996:0.756234:0.424996:0.740521:0.293623:0.740521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al analizar la continuidad de esta función vemos que hay una discontinuidad en :@0.293623:0.790738:0.888737:0.790738:0.888737:0.775025:0.293623:0.775025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.889669:0.790738:0.897124:0.790738:0.897124:0.774332:0.889669:0.774332:0.000000
=:@0.898228:0.791320:0.913561:0.791320:0.913561:0.773666:0.898228:0.773666:0.000000
3, :@0.914666:0.790738:0.930882:0.790738:0.930882:0.775025:0.914666:0.775025:0.000000:0.000000:0.000000
porque la función no está definida para :@0.293605:0.807380:0.594569:0.807380:0.594569:0.791667:0.293605:0.791667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.595723:0.807380:0.603178:0.807380:0.603178:0.790974:0.595723:0.790974:0.000000
=:@0.604356:0.807962:0.619689:0.807962:0.619689:0.790308:0.604356:0.790308:0.000000
3, es decir,  3  no existe. Sin embargo, al :@0.620904:0.807380:0.930790:0.807380:0.930790:0.791667:0.620904:0.791667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.703700:0.807380:0.708394:0.807380:0.708394:0.790974:0.703700:0.790974:0.000000
( ):@0.708468:0.807962:0.729912:0.807962:0.729912:0.790308:0.708468:0.790308:0.000000:0.000000:0.000000
redefinir   en :@0.293586:0.824022:0.388973:0.824022:0.388973:0.808309:0.293586:0.808309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.357717:0.824022:0.362411:0.824022:0.362411:0.807616:0.357717:0.807616:0.000000
x:@0.388862:0.824022:0.396317:0.824022:0.396317:0.807616:0.388862:0.807616:0.000000
=:@0.397348:0.824604:0.412681:0.824604:0.412681:0.806950:0.397348:0.806950:0.000000
3 podemos lograr que se dé la continuidad en este punto.:@0.413694:0.824022:0.834403:0.824022:0.834403:0.808309:0.413694:0.808309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Evaluemos primero: lim:@0.293568:0.863061:0.464180:0.863290:0.464180:0.847577:0.293568:0.847348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.441502:0.872049:0.446924:0.872049:0.446924:0.860117:0.441502:0.860117:0.000000
3:@0.457674:0.872049:0.464207:0.872049:0.464207:0.860621:0.457674:0.860621:0.000000
x:@0.471886:0.857014:0.479341:0.857014:0.479341:0.840608:0.471886:0.840608:0.000000
2 :@0.480380:0.850950:0.488568:0.850950:0.488568:0.841790:0.480380:0.841790:0.000000:0.000000
–:@0.489160:0.857597:0.498364:0.857597:0.498364:0.839942:0.489160:0.839942:0.000000
9:@0.499376:0.857014:0.508359:0.857014:0.508359:0.841301:0.499376:0.841301:0.000000
x:@0.476275:0.874502:0.483730:0.874502:0.483730:0.858096:0.476275:0.858096:0.000000
–:@0.484761:0.875084:0.493965:0.875084:0.493965:0.857430:0.484761:0.857430:0.000000
3:@0.494977:0.874502:0.503960:0.874502:0.503960:0.858789:0.494977:0.858789:0.000000
=:@0.511267:0.863643:0.526601:0.863643:0.526601:0.845989:0.511267:0.845989:0.000000
x:@0.526517:0.872049:0.531939:0.872049:0.531939:0.860117:0.526517:0.860117:0.000000
3:@0.542689:0.872049:0.549221:0.872049:0.549221:0.860621:0.542689:0.860621:0.000000
lim:@0.526517:0.863290:0.549195:0.863290:0.549195:0.847577:0.526517:0.847577:0.000000:0.000000:0.000000
( – )( + ):@0.555667:0.857597:0.646783:0.857597:0.646783:0.839942:0.555667:0.839942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.562809:0.857014:0.570264:0.857014:0.570264:0.840608:0.562809:0.840608:0.000000
3:@0.581511:0.857014:0.590494:0.857014:0.590494:0.841301:0.581511:0.841301:0.000000
x:@0.605809:0.857014:0.613264:0.857014:0.613264:0.840608:0.605809:0.840608:0.000000
3:@0.630640:0.857014:0.639623:0.857014:0.639623:0.841301:0.630640:0.841301:0.000000
x:@0.587383:0.874502:0.594838:0.874502:0.594838:0.858096:0.587383:0.858096:0.000000
–:@0.595869:0.875084:0.605072:0.875084:0.605072:0.857430:0.595869:0.857430:0.000000
3:@0.606085:0.874502:0.615068:0.874502:0.615068:0.858789:0.606085:0.858789:0.000000
=:@0.649342:0.863643:0.664675:0.863643:0.664675:0.845989:0.649342:0.845989:0.000000
x:@0.664580:0.870514:0.670001:0.870514:0.670001:0.858582:0.664580:0.858582:0.000000
3:@0.680751:0.870514:0.687284:0.870514:0.687284:0.859087:0.680751:0.859087:0.000000
lim x 3 6.:@0.664580:0.862778:0.753027:0.863069:0.753027:0.847357:0.664580:0.847066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ =:@0.698928:0.863361:0.738411:0.863361:0.738411:0.845706:0.698928:0.845706:0.000000:0.000000:0.000000
De este resultado se deduce que debemos definir  3:@0.293655:0.897574:0.677962:0.897574:0.677962:0.881861:0.293655:0.881861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.658321:0.897574:0.663015:0.897574:0.663015:0.881167:0.658321:0.881167:0.000000
( )=:@0.662941:0.898156:0.699259:0.898156:0.699259:0.880502:0.662941:0.880502:0.000000:0.000000:0.000000:0.000000
6 para que se dé la continuidad :@0.699167:0.897574:0.931080:0.897574:0.931080:0.881861:0.699167:0.881861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en 3.:@0.293655:0.914215:0.328371:0.914215:0.328371:0.898503:0.293655:0.898503:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 6.4:@0.117939:0.432254:0.191892:0.432254:0.191892:0.415584:0.117939:0.415584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.186374:0.182626:0.194473:0.182626:0.194473:0.166914:0.186374:0.166914:0.000000
x:@0.369618:0.380858:0.377515:0.380858:0.377515:0.365146:0.369618:0.365146:0.000000
5:@0.194289:0.267389:0.203272:0.267389:0.203272:0.251676:0.194289:0.251676:0.000000
0:@0.196112:0.380858:0.205094:0.380858:0.205094:0.365146:0.196112:0.365146:0.000000
f x:@0.073089:0.151047:0.091209:0.151047:0.091209:0.134641:0.073089:0.134641:0.000000:0.000000:0.000000
( )=:@0.077716:0.151630:0.113611:0.151630:0.113611:0.133976:0.077716:0.133976:0.000000:0.000000:0.000000:0.000000
∙:@0.114630:0.154207:0.121317:0.154207:0.121317:0.125318:0.114630:0.125318:0.000000
2:@0.122974:0.140040:0.131957:0.140040:0.131957:0.124327:0.122974:0.124327:0.000000
x:@0.131883:0.140040:0.139338:0.140040:0.139338:0.123634:0.131883:0.123634:0.000000
+:@0.139264:0.140622:0.154598:0.140622:0.154598:0.122968:0.139264:0.122968:0.000000
3      si:@0.154506:0.140040:0.209691:0.140040:0.209691:0.124327:0.154506:0.124327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.209569:0.140040:0.220264:0.140040:0.220264:0.123634:0.209569:0.123634:0.000000:0.000000
≠:@0.220208:0.140622:0.235542:0.140622:0.235542:0.122968:0.220208:0.122968:0.000000
1:@0.235450:0.140040:0.244432:0.140040:0.244432:0.124327:0.235450:0.124327:0.000000
2:@0.122981:0.156682:0.131964:0.156682:0.131964:0.140969:0.122981:0.140969:0.000000
	:@0.131876:0.157264:0.136478:0.157264:0.136478:0.139610:0.131876:0.139610:0.000000
				:@0.183213:0.157264:0.201344:0.157264:0.201344:0.139610:0.183213:0.139610:0.000000:0.000000:0.000000:0.000000
si:@0.201256:0.156682:0.211895:0.156682:0.211895:0.140969:0.201256:0.140969:0.000000:0.000000
 x:@0.211803:0.156682:0.222498:0.156682:0.222498:0.140276:0.211803:0.140276:0.000000:0.000000
=:@0.222442:0.157264:0.237776:0.157264:0.237776:0.139610:0.222442:0.139610:0.000000
1:@0.237684:0.156682:0.246666:0.156682:0.246666:0.140969:0.237684:0.140969:0.000000
Continuidad de :@0.080269:0.621023:0.194658:0.621023:0.194658:0.605617:0.080269:0.605617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones:@0.080269:0.637665:0.150585:0.637665:0.150585:0.622258:0.080269:0.622258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t.ly/9FP3o:@0.104476:0.750940:0.176669:0.750940:0.176669:0.735227:0.104476:0.735227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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