107:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tema 6. Continuidad:@0.073089:0.098522:0.378947:0.098522:0.378947:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Observa la gráfica y determina dónde no sería continua. ¿En qué punto o puntos la :@0.293660:0.170554:0.919625:0.170554:0.919625:0.154841:0.293660:0.154841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función no es continua? Explica por qué.:@0.293660:0.187195:0.587046:0.187195:0.587046:0.171483:0.293660:0.171483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.074954:0.142022:0.081486:0.142022:0.081486:0.130594:0.074954:0.130594:0.000000 3:@0.074954:0.154125:0.081486:0.154125:0.081486:0.142697:0.074954:0.142697:0.000000 2:@0.074954:0.166228:0.081486:0.166228:0.081486:0.154801:0.074954:0.154801:0.000000 1:@0.074954:0.178331:0.081486:0.178331:0.081486:0.166904:0.074954:0.166904:0.000000 0:@0.074954:0.190434:0.081486:0.190434:0.081486:0.179007:0.074954:0.179007:0.000000 -3 -2 -1 0 1 2 3 4 5 6:@0.085431:0.196111:0.261443:0.196111:0.261443:0.183256:0.085431:0.183256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • (1, 3):@0.133911:0.153595:0.169529:0.153595:0.169529:0.140739:0.133911:0.140739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En matemáticas, la continuidad de una función describe cómo se comporta esta en :@0.293660:0.235472:0.931460:0.235472:0.931460:0.219759:0.293660:0.219759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relación con los valores cercanos a un punto o en un intervalo de su dominio. Así, una :@0.293660:0.252114:0.931243:0.252114:0.931243:0.236401:0.293660:0.236401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función se considera continua si no presenta rompimientos, saltos, puntos indefinidos o :@0.293660:0.268756:0.931460:0.268756:0.931460:0.253043:0.293660:0.253043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 discontinuidades en su gráfica.:@0.293660:0.285397:0.516859:0.285397:0.516859:0.269685:0.293660:0.269685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si observamos las tres gráficas dadas, la única que nos da la idea de continuidad es la :@0.293660:0.319901:0.931063:0.319901:0.931063:0.304189:0.293660:0.304189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 6.3. En la Figura 6.1 se presentan saltos y en la Figura 6.2 hay un rompimiento y un :@0.293660:0.336543:0.931449:0.336543:0.931449:0.320831:0.293660:0.320831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 salto.:@0.293660:0.353185:0.330646:0.353185:0.330646:0.337472:0.293660:0.337472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.382706:0.375931:0.388596:0.375931:0.388596:0.364504:0.382706:0.364504:0.000000 x:@0.483765:0.452948:0.489508:0.452948:0.489508:0.441520:0.483765:0.441520:0.000000 2:@0.382853:0.411121:0.389386:0.411121:0.389386:0.399694:0.382853:0.399694:0.000000 0:@0.384165:0.451556:0.390698:0.451556:0.390698:0.440129:0.384165:0.440129:0.000000 1:@0.414367:0.451667:0.420899:0.451667:0.420899:0.440240:0.414367:0.440240:0.000000 :@0.493688:0.509637:0.517507:0.509637:0.517507:0.493925:0.493688:0.493925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.550962:0.375931:0.556852:0.375931:0.556852:0.364504:0.550962:0.364504:0.000000 x:@0.678206:0.476821:0.683949:0.476821:0.683949:0.465394:0.678206:0.465394:0.000000 1:@0.598590:0.477764:0.607572:0.477764:0.607572:0.462052:0.598590:0.462052:0.000000 1:@0.551117:0.439530:0.560100:0.439530:0.560100:0.423817:0.551117:0.423817:0.000000 :@0.707049:0.509637:0.726910:0.509637:0.726910:0.493925:0.707049:0.493925:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.805477:0.375931:0.811367:0.375931:0.811367:0.364504:0.805477:0.364504:0.000000 x:@0.906536:0.452948:0.912279:0.452948:0.912279:0.441520:0.906536:0.441520:0.000000 1:@0.805624:0.428056:0.812157:0.428056:0.812157:0.416628:0.805624:0.416628:0.000000 0:@0.806936:0.451546:0.813469:0.451546:0.813469:0.440119:0.806936:0.440119:0.000000 1:@0.837138:0.451657:0.843671:0.451657:0.843671:0.440229:0.837138:0.440229:0.000000 Figura 6.1 Figura 6.2 Figura 6.3:@0.361809:0.533428:0.859186:0.533428:0.859186:0.516758:0.361809:0.516758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6.1 Continuidad puntual:@0.293660:0.578659:0.485403:0.578659:0.485403:0.561712:0.293660:0.561712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Considerando una función definida en un intervalo abierto que contiene a . La función :@0.293660:0.606021:0.930882:0.606021:0.930882:0.590309:0.293660:0.590309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.488335:0.606021:0.493029:0.606021:0.493029:0.589615:0.488335:0.589615:0.000000 a:@0.836085:0.606021:0.845344:0.606021:0.845344:0.589615:0.836085:0.589615:0.000000 f:@0.293660:0.622663:0.298354:0.622663:0.298354:0.606257:0.293660:0.606257:0.000000 es continua en si se cumplen las siguientes condiciones::@0.298280:0.622663:0.721953:0.622663:0.721953:0.606950:0.298280:0.606950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.413105:0.622663:0.422364:0.622663:0.422364:0.606257:0.413105:0.606257:0.000000 1. lim :@0.293660:0.650028:0.350497:0.649816:0.350497:0.634103:0.293660:0.634315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x a:@0.323861:0.658108:0.346767:0.658108:0.346767:0.646176:0.323861:0.646176:0.000000:0.000000:0.000000 f x:@0.350386:0.649816:0.370708:0.649816:0.370708:0.633410:0.350386:0.633410:0.000000:0.000000:0.000000 ( ):@0.356111:0.650398:0.377868:0.650398:0.377868:0.632744:0.356111:0.632744:0.000000:0.000000:0.000000 existe.:@0.391821:0.650024:0.440383:0.650024:0.440383:0.634311:0.391821:0.634311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. :@0.293660:0.677391:0.309730:0.677391:0.309730:0.661678:0.293660:0.661678:0.000000:0.000000:0.000000 f a:@0.323861:0.677391:0.343778:0.677391:0.343778:0.660985:0.323861:0.660985:0.000000:0.000000:0.000000 ( ):@0.328482:0.677973:0.349834:0.677973:0.349834:0.660319:0.328482:0.660319:0.000000:0.000000:0.000000 existe (la función f está definida para :@0.349742:0.677391:0.621058:0.677391:0.621058:0.661678:0.349742:0.661678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x a:@0.620697:0.677391:0.652578:0.677391:0.652578:0.660985:0.620697:0.660985:0.000000:0.000000:0.000000 =:@0.628078:0.677973:0.643411:0.677973:0.643411:0.660319:0.628078:0.660319:0.000000 ).:@0.652505:0.677391:0.660512:0.677391:0.660512:0.661678:0.652505:0.661678:0.000000:0.000000 3. lim :@0.293660:0.704753:0.350497:0.704541:0.350497:0.688828:0.293660:0.689040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x a:@0.323861:0.712834:0.346767:0.712834:0.346767:0.700902:0.323861:0.700902:0.000000:0.000000:0.000000 f x:@0.350386:0.704541:0.370708:0.704541:0.370708:0.688135:0.350386:0.688135:0.000000:0.000000:0.000000 ( ) = ( ):@0.356111:0.705123:0.433035:0.705331:0.433035:0.687677:0.356111:0.687469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f a:@0.407062:0.704749:0.426979:0.704749:0.426979:0.688343:0.407062:0.688343:0.000000:0.000000:0.000000 .:@0.432943:0.704749:0.436146:0.704749:0.436146:0.689036:0.432943:0.689036:0.000000 Si una o más de las tres condiciones no se cumplen en , entonces decimos que la :@0.293618:0.735689:0.930898:0.735689:0.930898:0.719976:0.293618:0.719976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.718347:0.735689:0.727606:0.735689:0.727606:0.719283:0.718347:0.719283:0.000000 función es discontinua en .:@0.293637:0.752331:0.505523:0.752331:0.505523:0.736618:0.293637:0.736618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.353203:0.752331:0.357896:0.752331:0.357896:0.735925:0.353203:0.735925:0.000000 a:@0.493135:0.752331:0.502393:0.752331:0.502393:0.735925:0.493135:0.735925:0.000000 Con base en la definición dada, observemos cuáles condiciones se cumplen en las :@0.293618:0.786835:0.930618:0.786835:0.930618:0.771122:0.293618:0.771122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gráficas anteriores.:@0.293618:0.803477:0.427918:0.803477:0.427918:0.787764:0.293618:0.787764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfica 1: :@0.293618:0.837981:0.367426:0.837981:0.367426:0.821311:0.293618:0.821311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función no es continua en :@0.367303:0.837981:0.577513:0.837981:0.577513:0.822268:0.367303:0.822268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.577237:0.837981:0.584692:0.837981:0.584692:0.821575:0.577237:0.821575:0.000000 =:@0.584619:0.838563:0.599952:0.838563:0.599952:0.820909:0.584619:0.820909:0.000000 2 porque lim :@0.599860:0.837981:0.696729:0.837784:0.696729:0.822071:0.599860:0.822268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.670093:0.846076:0.675515:0.846076:0.675515:0.834144:0.670093:0.834144:0.000000 2:@0.686265:0.846076:0.692798:0.846076:0.692798:0.834649:0.686265:0.834649:0.000000 f x:@0.696618:0.837784:0.716940:0.837784:0.716940:0.821378:0.696618:0.821378:0.000000:0.000000:0.000000 ( ):@0.702343:0.838366:0.724100:0.838366:0.724100:0.820712:0.702343:0.820712:0.000000:0.000000:0.000000 no existe.:@0.724505:0.837992:0.796538:0.837992:0.796538:0.822279:0.724505:0.822279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfica 2::@0.293647:0.865354:0.362921:0.865354:0.362921:0.848684:0.293647:0.848684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función no es continua en :@0.362876:0.865354:0.573547:0.865354:0.573547:0.849641:0.362876:0.849641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.573161:0.865354:0.580616:0.865354:0.580616:0.848948:0.573161:0.848948:0.000000 =:@0.580524:0.865936:0.595857:0.865936:0.595857:0.848282:0.580524:0.848282:0.000000 2 porque, aunque lim :@0.595728:0.865354:0.753989:0.865146:0.753989:0.849433:0.595728:0.849641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.727353:0.873439:0.732775:0.873439:0.732775:0.861507:0.727353:0.861507:0.000000 2:@0.743525:0.873439:0.750058:0.873439:0.750058:0.862012:0.743525:0.862012:0.000000 f x:@0.753878:0.865146:0.774200:0.865146:0.774200:0.848740:0.753878:0.848740:0.000000:0.000000:0.000000 ( ) =:@0.759603:0.865728:0.800577:0.865936:0.800577:0.848282:0.759603:0.848074:0.000000:0.000000:0.000000:0.000000:0.000000 2, este no es igual :@0.781728:0.865354:0.930831:0.865354:0.930831:0.849641:0.781728:0.849641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a 2:@0.293623:0.881996:0.325486:0.881996:0.325486:0.866283:0.293623:0.866283:0.000000:0.000000:0.000000:0.000000 f:@0.305846:0.881996:0.310540:0.881996:0.310540:0.865590:0.305846:0.865590:0.000000 ( )=:@0.310466:0.882578:0.346783:0.882578:0.346783:0.864924:0.310466:0.864924:0.000000:0.000000:0.000000:0.000000 1.:@0.346691:0.881996:0.358803:0.881996:0.358803:0.866283:0.346691:0.866283:0.000000:0.000000 Gráfica 3::@0.293623:0.909358:0.367985:0.909358:0.367985:0.892688:0.293623:0.892688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se observa que para cualquier punto del dominio se cumplen las tres :@0.368173:0.909358:0.930849:0.909358:0.930849:0.893645:0.368173:0.893645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.665211:0.909358:0.672665:0.909358:0.672665:0.892952:0.665211:0.892952:0.000000 condiciones.:@0.293623:0.926000:0.385045:0.926000:0.385045:0.910287:0.293623:0.910287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 EBC 11. 1. Comprende el concepto de función continua.:@0.084472:0.970432:0.379012:0.970432:0.379012:0.959005:0.084472:0.959005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Características de :@0.080269:0.800654:0.209446:0.800654:0.209446:0.785247:0.080269:0.785247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las funciones:@0.080269:0.817296:0.173560:0.817296:0.173560:0.801889:0.080269:0.801889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t.ly/9vHk9:@0.104255:0.930570:0.176882:0.930570:0.176882:0.914857:0.104255:0.914857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función no es continua en x=1 debido al punto aislado (1,3), que indica un salto en el valor de la función.:@0.302768:0.197078:0.864925:0.197078:0.864925:0.185651:0.302768:0.185651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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