103:@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
5.2 Teorema 2. Límites especiales de funciones trigonométricas:@0.072614:0.136836:0.566435:0.136836:0.566435:0.119889:0.072614:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.    lim:@0.072614:0.176652:0.124702:0.176785:0.124702:0.161073:0.072614:0.160939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.099815:0.185601:0.103724:0.185601:0.103724:0.173669:0.099815:0.173669:0.000000
0:@0.114474:0.185601:0.121007:0.185601:0.121007:0.174173:0.114474:0.174173:0.000000
sent:@0.135445:0.173301:0.164252:0.173301:0.164252:0.156895:0.135445:0.156895:0.000000:0.000000:0.000000:0.000000
t:@0.147170:0.187280:0.152545:0.187280:0.152545:0.170874:0.147170:0.170874:0.000000
=1  :@0.172547:0.176658:0.197145:0.176658:0.197145:0.160945:0.172547:0.160945:0.000000:0.000000:0.000000:0.000000
b.    lim:@0.253337:0.176658:0.306900:0.177080:0.306900:0.161368:0.253337:0.160945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.282013:0.185897:0.285922:0.185897:0.285922:0.173965:0.282013:0.173965:0.000000
0:@0.296672:0.185897:0.303205:0.185897:0.303205:0.174469:0.296672:0.174469:0.000000
1:@0.313722:0.172870:0.322705:0.172870:0.322705:0.157157:0.313722:0.157157:0.000000
–:@0.323736:0.173452:0.332940:0.173452:0.332940:0.155798:0.323736:0.155798:0.000000
sent:@0.333952:0.172870:0.362759:0.172870:0.362759:0.156463:0.333952:0.156463:0.000000:0.000000:0.000000:0.000000
t:@0.335572:0.186849:0.340947:0.186849:0.340947:0.170443:0.335572:0.170443:0.000000
=1 :@0.368551:0.176658:0.392388:0.176658:0.392388:0.160945:0.368551:0.160945:0.000000:0.000000:0.000000
 :@0.434081:0.176658:0.438112:0.176658:0.438112:0.160945:0.434081:0.160945:0.000000
c.    lim:@0.494309:0.176658:0.546045:0.176785:0.546045:0.161073:0.494309:0.160945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.521159:0.185601:0.525068:0.185601:0.525068:0.173669:0.521159:0.173669:0.000000
0:@0.535818:0.185601:0.542350:0.185601:0.542350:0.174173:0.535818:0.174173:0.000000
senkt:@0.555410:0.173301:0.591709:0.173301:0.591709:0.156895:0.555410:0.156895:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.570890:0.187280:0.576265:0.187280:0.576265:0.170874:0.570890:0.170874:0.000000
=:@0.598832:0.176657:0.609803:0.176657:0.609803:0.160944:0.598832:0.160944:0.000000
k:@0.609729:0.176657:0.617295:0.176657:0.617295:0.160251:0.609729:0.160251:0.000000
Veamos el comportamiento gráfico de :@0.072624:0.214683:0.356252:0.214683:0.356252:0.198971:0.072624:0.198971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f t:@0.355949:0.214683:0.371981:0.214683:0.371981:0.198277:0.355949:0.198277:0.000000:0.000000:0.000000
( )=:@0.360569:0.215266:0.393279:0.215266:0.393279:0.197612:0.360569:0.197612:0.000000:0.000000:0.000000:0.000000
sent:@0.400128:0.209489:0.428935:0.209489:0.428935:0.193083:0.400128:0.193083:0.000000:0.000000:0.000000:0.000000
t:@0.411853:0.223468:0.417228:0.223468:0.417228:0.207062:0.411853:0.207062:0.000000
 para validar el límite en el teorema.:@0.437237:0.214690:0.693961:0.214690:0.693961:0.198977:0.437237:0.198977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.408761:0.457895:0.415049:0.457895:0.415049:0.446896:0.408761:0.446896:0.000000
1.2:@0.398826:0.242976:0.413644:0.242976:0.413644:0.231977:0.398826:0.231977:0.000000:0.000000:0.000000
1:@0.407355:0.277643:0.413643:0.277643:0.413643:0.266644:0.407355:0.266644:0.000000
0.8:@0.398825:0.312309:0.413643:0.312309:0.413643:0.301310:0.398825:0.301310:0.000000:0.000000:0.000000
0.6:@0.398825:0.346975:0.413643:0.346975:0.413643:0.335976:0.398825:0.335976:0.000000:0.000000:0.000000
0.4:@0.398825:0.381642:0.413643:0.381642:0.413643:0.370643:0.398825:0.370643:0.000000:0.000000:0.000000
0.2:@0.398825:0.416308:0.413643:0.416308:0.413643:0.405309:0.398825:0.405309:0.000000:0.000000:0.000000
0.2   0.4    0.6    0.8     1     1.2    1.4   1.6   1.8     2:@0.431549:0.457548:0.631010:0.457548:0.631010:0.448121:0.431549:0.448121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−2.4  −2.2 −2  −1.8 −1.6 −1.4 −1.2   −1 −0.8 −0.6 −0.4 −0.2:@0.151829:0.457881:0.404888:0.457881:0.404888:0.448454:0.151829:0.448454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h (x)= :@0.163409:0.416889:0.200685:0.416889:0.200685:0.404625:0.163409:0.404625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.171110:0.419365:0.175197:0.419365:0.175197:0.412215:0.171110:0.412215:0.000000
sin(x):@0.202021:0.409192:0.231862:0.409192:0.231862:0.396928:0.202021:0.396928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.213860:0.423448:0.220023:0.423448:0.220023:0.411184:0.213860:0.411184:0.000000
Figura 5.7:@0.352516:0.491414:0.426469:0.491414:0.426469:0.474745:0.352516:0.474745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuando   se acerca a 0 tanto por la izquierda como por la derecha las imágenes se :@0.072616:0.522354:0.710512:0.522354:0.710512:0.506642:0.072616:0.506642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.137152:0.522354:0.144607:0.522354:0.144607:0.505948:0.137152:0.505948:0.000000
acercan a 1. De esta manera, validamos gráficamente el teorema 2 o 2a. Tengamos en :@0.072616:0.538996:0.709890:0.538996:0.709890:0.523284:0.072616:0.523284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuenta que la imagen de 0 no está definida. :@0.072616:0.555638:0.393970:0.555638:0.393970:0.539925:0.072616:0.539925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ahora, consideremos la evaluación de los límites en los siguientes ejemplos::@0.072616:0.590142:0.622100:0.590142:0.622100:0.574429:0.072616:0.574429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  lim:@0.072614:0.619186:0.126046:0.619313:0.126046:0.603601:0.072614:0.603473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.101159:0.628128:0.105068:0.628128:0.105068:0.616197:0.101159:0.616197:0.000000
0:@0.115818:0.628128:0.122351:0.628128:0.122351:0.616701:0.115818:0.616701:0.000000
sen t:@0.136529:0.615829:0.175368:0.615829:0.175368:0.599422:0.136529:0.599422:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.159980:0.615829:0.168963:0.615829:0.168963:0.600116:0.159980:0.600116:0.000000
t:@0.153261:0.629808:0.158636:0.629808:0.158636:0.613402:0.153261:0.613402:0.000000
=5:@0.186855:0.619185:0.208391:0.619185:0.208391:0.603472:0.186855:0.603472:0.000000:0.000000
2.  lim:@0.072614:0.659749:0.126046:0.659875:0.126046:0.644163:0.072614:0.644036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.101159:0.668690:0.105068:0.668690:0.105068:0.656759:0.101159:0.656759:0.000000
0:@0.115818:0.668690:0.122351:0.668690:0.122351:0.657263:0.115818:0.657263:0.000000
sen t:@0.136529:0.656391:0.175368:0.656391:0.175368:0.639984:0.136529:0.639984:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.159980:0.656391:0.168963:0.656391:0.168963:0.640678:0.159980:0.640678:0.000000
4:@0.148255:0.670370:0.157237:0.670370:0.157237:0.654657:0.148255:0.654657:0.000000
t:@0.158268:0.670370:0.163643:0.670370:0.163643:0.653964:0.158268:0.653964:0.000000
=:@0.186855:0.659747:0.197825:0.659747:0.197825:0.644034:0.186855:0.644034:0.000000
1:@0.204393:0.654390:0.213376:0.654390:0.213376:0.638677:0.204393:0.638677:0.000000
4:@0.204393:0.668369:0.213376:0.668369:0.213376:0.652656:0.204393:0.652656:0.000000
 lim:@0.220076:0.659757:0.250564:0.659875:0.250564:0.644163:0.220076:0.644044:0.000000:0.000000:0.000000:0.000000
t:@0.225677:0.668690:0.229586:0.668690:0.229586:0.656759:0.225677:0.656759:0.000000
0:@0.240336:0.668690:0.246869:0.668690:0.246869:0.657263:0.240336:0.657263:0.000000
sen t:@0.261046:0.656391:0.299885:0.656391:0.299885:0.639984:0.261046:0.639984:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.284497:0.656391:0.293479:0.656391:0.293479:0.640678:0.284497:0.640678:0.000000
t:@0.277778:0.670370:0.283153:0.670370:0.283153:0.653964:0.277778:0.653964:0.000000
=:@0.311371:0.659747:0.322342:0.659747:0.322342:0.644034:0.311371:0.644034:0.000000
1:@0.328912:0.654390:0.337894:0.654390:0.337894:0.638677:0.328912:0.638677:0.000000
4:@0.328912:0.668369:0.337894:0.668369:0.337894:0.652656:0.328912:0.652656:0.000000
.7=:@0.344595:0.659757:0.370917:0.659757:0.370917:0.644044:0.344595:0.644044:0.000000:0.000000:0.000000
7:@0.377467:0.654390:0.386449:0.654390:0.386449:0.638677:0.377467:0.638677:0.000000
4:@0.377467:0.668369:0.386449:0.668369:0.386449:0.652656:0.377467:0.652656:0.000000
3.  lim:@0.072614:0.713686:0.126046:0.713812:0.126046:0.698100:0.072614:0.697974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.101159:0.722628:0.105068:0.722628:0.105068:0.710696:0.101159:0.710696:0.000000
0:@0.115818:0.722628:0.122351:0.722628:0.122351:0.711200:0.115818:0.711200:0.000000
sen t:@0.136529:0.710328:0.175368:0.710328:0.175368:0.693922:0.136529:0.693922:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.159980:0.710328:0.168963:0.710328:0.168963:0.694615:0.159980:0.694615:0.000000
tant:@0.141297:0.724307:0.170583:0.724307:0.170583:0.707901:0.141297:0.707901:0.000000:0.000000:0.000000:0.000000
= lim:@0.186855:0.713684:0.229892:0.714351:0.229892:0.698638:0.186855:0.697971:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.205006:0.723166:0.208915:0.723166:0.208915:0.711234:0.205006:0.711234:0.000000
0:@0.219665:0.723166:0.226198:0.723166:0.226198:0.711738:0.219665:0.711738:0.000000
sen t:@0.241176:0.692579:0.280015:0.692579:0.280015:0.676173:0.241176:0.676173:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.264627:0.692579:0.273610:0.692579:0.273610:0.676866:0.264627:0.676866:0.000000
t:@0.257908:0.706558:0.263283:0.706558:0.263283:0.690152:0.257908:0.690152:0.000000
tant:@0.245940:0.724207:0.275226:0.724207:0.275226:0.707801:0.245940:0.707801:0.000000:0.000000:0.000000:0.000000
t:@0.257905:0.738186:0.263280:0.738186:0.263280:0.721780:0.257905:0.721780:0.000000
 = :@0.292768:0.713695:0.314967:0.713695:0.314967:0.697982:0.292768:0.697982:0.000000:0.000000:0.000000
t:@0.318908:0.705439:0.322817:0.705439:0.322817:0.693507:0.318908:0.693507:0.000000
0:@0.333567:0.705439:0.340100:0.705439:0.340100:0.694011:0.333567:0.694011:0.000000
lim:@0.318908:0.696623:0.343795:0.696623:0.343795:0.680911:0.318908:0.680911:0.000000:0.000000:0.000000
sen t:@0.354277:0.693139:0.393116:0.693139:0.393116:0.676733:0.354277:0.676733:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.377728:0.693139:0.386710:0.693139:0.386710:0.677426:0.377728:0.677426:0.000000
t:@0.371009:0.707118:0.376384:0.707118:0.376384:0.690712:0.371009:0.690712:0.000000
t:@0.316537:0.735437:0.320446:0.735437:0.320446:0.723505:0.316537:0.723505:0.000000
0:@0.331196:0.735437:0.337729:0.735437:0.337729:0.724009:0.331196:0.724009:0.000000
lim:@0.316537:0.726622:0.341424:0.726622:0.341424:0.710909:0.316537:0.710909:0.000000:0.000000:0.000000
sent:@0.356909:0.723137:0.385716:0.723137:0.385716:0.706731:0.356909:0.706731:0.000000:0.000000:0.000000:0.000000
cost:@0.357204:0.737116:0.385429:0.737116:0.385429:0.720710:0.357204:0.720710:0.000000:0.000000:0.000000:0.000000
=:@0.408339:0.714275:0.423672:0.714275:0.423672:0.696621:0.408339:0.696621:0.000000
t:@0.468561:0.705439:0.472470:0.705439:0.472470:0.693507:0.468561:0.693507:0.000000
0:@0.483220:0.705439:0.489753:0.705439:0.489753:0.694011:0.483220:0.694011:0.000000
lim:@0.468561:0.696623:0.493447:0.696623:0.493447:0.680911:0.468561:0.680911:0.000000:0.000000:0.000000
sen t:@0.503930:0.693139:0.542769:0.693139:0.542769:0.676733:0.503930:0.676733:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.527380:0.693139:0.536363:0.693139:0.536363:0.677426:0.527380:0.677426:0.000000
t:@0.520662:0.707118:0.526037:0.707118:0.526037:0.690712:0.520662:0.690712:0.000000
t:@0.425237:0.735437:0.429146:0.735437:0.429146:0.723505:0.425237:0.723505:0.000000
0:@0.439896:0.735437:0.446429:0.735437:0.446429:0.724009:0.439896:0.724009:0.000000
lim:@0.425237:0.726622:0.450123:0.726622:0.450123:0.710909:0.425237:0.710909:0.000000:0.000000:0.000000
sent:@0.465609:0.723137:0.494416:0.723137:0.494416:0.706731:0.465609:0.706731:0.000000:0.000000:0.000000:0.000000
t:@0.477334:0.737116:0.482709:0.737116:0.482709:0.720710:0.477334:0.720710:0.000000
 lim:@0.509087:0.726493:0.536773:0.726622:0.536773:0.710909:0.509087:0.710780:0.000000:0.000000:0.000000:0.000000
t:@0.511886:0.735437:0.515796:0.735437:0.515796:0.723505:0.511886:0.723505:0.000000
0:@0.526545:0.735437:0.533078:0.735437:0.533078:0.724009:0.526545:0.724009:0.000000
t:@0.563986:0.723137:0.569361:0.723137:0.569361:0.706731:0.563986:0.706731:0.000000
cost:@0.552555:0.737116:0.580780:0.737116:0.580780:0.720710:0.552555:0.720710:0.000000:0.000000:0.000000:0.000000
=:@0.597837:0.714275:0.613170:0.714275:0.613170:0.696621:0.597837:0.696621:0.000000
7:@0.626850:0.703088:0.635833:0.703088:0.635833:0.687376:0.626850:0.687376:0.000000
1. :@0.614738:0.728759:0.630807:0.728759:0.630807:0.713046:0.614738:0.713046:0.000000:0.000000:0.000000
1:@0.633338:0.722581:0.642320:0.722581:0.642320:0.706868:0.633338:0.706868:0.000000
1:@0.633338:0.736560:0.642320:0.736560:0.642320:0.720847:0.633338:0.720847:0.000000
4.  lim 1:@0.072614:0.768544:0.145181:0.767674:0.145181:0.751961:0.072614:0.752831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.101159:0.776770:0.105068:0.776770:0.105068:0.764839:0.101159:0.764839:0.000000
0:@0.115818:0.776770:0.122351:0.776770:0.122351:0.765343:0.115818:0.765343:0.000000
–:@0.146211:0.768256:0.155415:0.768256:0.155415:0.750602:0.146211:0.750602:0.000000
cos t:@0.156427:0.767674:0.194678:0.767674:0.194678:0.751268:0.156427:0.751268:0.000000:0.000000:0.000000:0.000000:0.000000
2 =:@0.179289:0.767674:0.211594:0.768548:0.211594:0.752835:0.179289:0.751961:0.000000:0.000000:0.000000
3:@0.157753:0.781653:0.166735:0.781653:0.166735:0.765940:0.157753:0.765940:0.000000
t:@0.167766:0.781653:0.173141:0.781653:0.173141:0.765247:0.167766:0.765247:0.000000
1:@0.218147:0.764078:0.227130:0.764078:0.227130:0.748366:0.218147:0.748366:0.000000
3:@0.218147:0.778057:0.227130:0.778057:0.227130:0.762345:0.218147:0.762345:0.000000
 lim:@0.233830:0.768544:0.264316:0.768705:0.264316:0.752993:0.233830:0.752831:0.000000:0.000000:0.000000:0.000000
t:@0.239429:0.777520:0.243338:0.777520:0.243338:0.765589:0.239429:0.765589:0.000000
0:@0.254088:0.777520:0.260621:0.777520:0.260621:0.766093:0.254088:0.766093:0.000000
1:@0.274150:0.764314:0.283133:0.764314:0.283133:0.748601:0.274150:0.748601:0.000000
–:@0.284164:0.764897:0.293367:0.764897:0.293367:0.747242:0.284164:0.747242:0.000000
cos t:@0.294380:0.764314:0.332630:0.764314:0.332630:0.747908:0.294380:0.747908:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.317241:0.764314:0.326224:0.764314:0.326224:0.748601:0.317241:0.748601:0.000000
2:@0.295705:0.778293:0.304688:0.778293:0.304688:0.762581:0.295705:0.762581:0.000000
t:@0.305719:0.778293:0.311093:0.778293:0.311093:0.761887:0.305719:0.761887:0.000000
=:@0.338575:0.768544:0.349546:0.768544:0.349546:0.752831:0.338575:0.752831:0.000000
1:@0.356098:0.763184:0.365080:0.763184:0.365080:0.747472:0.356098:0.747472:0.000000
3:@0.356098:0.777164:0.365080:0.777164:0.365080:0.761451:0.356098:0.761451:0.000000
.0=0:@0.371781:0.768551:0.408669:0.768551:0.408669:0.752839:0.371781:0.752839:0.000000:0.000000:0.000000:0.000000
5.  lim 1:@0.072614:0.818848:0.150023:0.818873:0.150023:0.803160:0.072614:0.803135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.101159:0.828715:0.105068:0.828715:0.105068:0.816784:0.101159:0.816784:0.000000
0:@0.115818:0.828715:0.122351:0.828715:0.122351:0.817288:0.115818:0.817288:0.000000
+:@0.123096:0.824552:0.129597:0.824552:0.129597:0.817067:0.123096:0.817067:0.000000
+:@0.151054:0.819455:0.166387:0.819455:0.166387:0.801801:0.151054:0.801801:0.000000
sent:@0.166295:0.818873:0.195103:0.818873:0.195103:0.802467:0.166295:0.802467:0.000000:0.000000:0.000000:0.000000
t:@0.165393:0.832852:0.170768:0.832852:0.170768:0.816446:0.165393:0.816446:0.000000
=lim:@0.203257:0.818859:0.240957:0.819846:0.240957:0.804133:0.203257:0.803146:0.000000:0.000000:0.000000:0.000000
t:@0.215796:0.829408:0.219705:0.829408:0.219705:0.817476:0.215796:0.817476:0.000000
0:@0.230455:0.829408:0.236988:0.829408:0.236988:0.817980:0.230455:0.817980:0.000000
+:@0.237732:0.825244:0.244233:0.825244:0.244233:0.817759:0.237732:0.817759:0.000000
1:@0.249764:0.816361:0.258747:0.816361:0.258747:0.800649:0.249764:0.800649:0.000000
t:@0.251568:0.830341:0.256943:0.830341:0.256943:0.813934:0.251568:0.813934:0.000000
+:@0.263220:0.819440:0.278553:0.819440:0.278553:0.801786:0.263220:0.801786:0.000000
t:@0.280116:0.828908:0.284025:0.828908:0.284025:0.816977:0.280116:0.816977:0.000000
0:@0.294775:0.828908:0.301308:0.828908:0.301308:0.817481:0.294775:0.817481:0.000000
+:@0.302052:0.824745:0.308553:0.824745:0.308553:0.817260:0.302052:0.817260:0.000000
lim:@0.280388:0.819347:0.305275:0.819347:0.305275:0.803634:0.280388:0.803634:0.000000:0.000000:0.000000
sent:@0.316018:0.815862:0.344826:0.815862:0.344826:0.799456:0.316018:0.799456:0.000000:0.000000:0.000000:0.000000
t:@0.327744:0.829841:0.333119:0.829841:0.333119:0.813435:0.327744:0.813435:0.000000
=∞+ =∞:@0.351213:0.819440:0.438592:0.819440:0.438592:0.801786:0.351213:0.801786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.398851:0.818858:0.407834:0.818858:0.407834:0.803145:0.398851:0.803145:0.000000
Límites de funciones exponenciales y logarítmicas:@0.072619:0.867660:0.451501:0.867660:0.451501:0.850990:0.072619:0.850990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los límites de funciones exponenciales y logarítmicas siguen reglas específicas debido a :@0.072619:0.898600:0.710909:0.898600:0.710909:0.882887:0.072619:0.882887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las propiedades únicas de estas funciones. A continuación, se detallan algunas de las :@0.072619:0.915242:0.710500:0.915242:0.710500:0.899529:0.072619:0.899529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
situaciones más comunes para cada tipo::@0.072619:0.931883:0.370761:0.931883:0.370761:0.916171:0.072619:0.916171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cuerpo elimina :@0.741944:0.190942:0.859794:0.190942:0.859794:0.176658:0.741944:0.176658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sustancias como :@0.741944:0.206071:0.855215:0.206071:0.855215:0.191787:0.741944:0.191787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medicamentos o alcohol :@0.741944:0.221200:0.909845:0.221200:0.909845:0.206916:0.741944:0.206916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a través de procesos :@0.741944:0.236329:0.879396:0.236329:0.879396:0.222045:0.741944:0.222045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
metabólicos, y este :@0.741944:0.251458:0.871735:0.251458:0.871735:0.237174:0.741944:0.237174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proceso se puede modelar :@0.741944:0.266587:0.922395:0.266587:0.922395:0.252303:0.741944:0.252303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
usando una función :@0.741944:0.281716:0.878023:0.281716:0.878023:0.267432:0.741944:0.267432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponencial. La fórmula :@0.741944:0.296845:0.902686:0.296845:0.902686:0.282561:0.741944:0.282561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para la cantidad de :@0.741944:0.311974:0.871631:0.311974:0.871631:0.297690:0.741944:0.297690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medicamento que queda :@0.741944:0.327103:0.914681:0.327103:0.914681:0.312819:0.741944:0.312819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el cuerpo después de :@0.741944:0.342232:0.908355:0.342232:0.908355:0.327948:0.741944:0.327948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cierto tiempo es::@0.741944:0.357361:0.852508:0.357361:0.852508:0.343076:0.741944:0.343076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C t:@0.796145:0.380710:0.815456:0.380710:0.815456:0.365795:0.796145:0.365795:0.000000:0.000000:0.000000
( )=:@0.805081:0.381239:0.834817:0.381239:0.834817:0.365190:0.805081:0.365190:0.000000:0.000000:0.000000:0.000000
C:@0.834733:0.380710:0.843736:0.380710:0.843736:0.365795:0.834733:0.365795:0.000000
0:@0.843697:0.383594:0.848458:0.383594:0.848458:0.375266:0.843697:0.375266:0.000000
e:@0.848419:0.383594:0.852546:0.383594:0.852546:0.374898:0.848419:0.374898:0.000000
–λ:@0.852507:0.375508:0.862760:0.375508:0.862760:0.366152:0.852507:0.366152:0.000000:0.000000
t:@0.862712:0.375200:0.865560:0.375200:0.865560:0.366505:0.862712:0.366505:0.000000
Donde::@0.741944:0.404057:0.790532:0.404057:0.790532:0.389773:0.741944:0.389773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.741944:0.427406:0.749675:0.427406:0.749675:0.413122:0.741944:0.413122:0.000000:0.000000
C t:@0.756174:0.427406:0.775485:0.427406:0.775485:0.412492:0.756174:0.412492:0.000000:0.000000:0.000000
( ):@0.765110:0.427936:0.780990:0.427936:0.780990:0.411887:0.765110:0.411887:0.000000:0.000000:0.000000
 es la concentración :@0.780907:0.427406:0.916217:0.427406:0.916217:0.413122:0.780907:0.413122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de medicamento en el :@0.756157:0.442535:0.909751:0.442535:0.909751:0.428251:0.756157:0.428251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuerpo en el tiempo t.:@0.756157:0.457664:0.902522:0.457664:0.902522:0.443380:0.756157:0.443380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.741944:0.481013:0.749675:0.481013:0.749675:0.466729:0.741944:0.466729:0.000000:0.000000
C:@0.756174:0.481013:0.765177:0.481013:0.765177:0.466099:0.756174:0.466099:0.000000
0:@0.765117:0.483897:0.769878:0.483897:0.769878:0.475570:0.765117:0.475570:0.000000
 es la concentración :@0.769836:0.481013:0.905146:0.481013:0.905146:0.466729:0.769836:0.466729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inicial de medicamento :@0.756181:0.496142:0.915288:0.496142:0.915288:0.481858:0.756181:0.481858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el cuerpo.:@0.756181:0.511271:0.841711:0.511271:0.841711:0.496987:0.756181:0.496987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•   es la constante :@0.741944:0.534620:0.871045:0.534620:0.871045:0.520336:0.741944:0.520336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.756174:0.535150:0.765478:0.535150:0.765478:0.519100:0.756174:0.519100:0.000000
de eliminación (que :@0.756174:0.549749:0.891377:0.549749:0.891377:0.535465:0.756174:0.535465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
depende de la sustancia :@0.756174:0.564878:0.920149:0.564878:0.920149:0.550594:0.756174:0.550594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y del cuerpo).:@0.756174:0.580007:0.845761:0.580007:0.845761:0.565723:0.756174:0.565723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  es el tiempo que ha :@0.741944:0.603355:0.898353:0.603355:0.898353:0.589071:0.741944:0.589071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t :@0.756174:0.603355:0.764006:0.603355:0.764006:0.588440:0.756174:0.588440:0.000000:0.000000
pasado.:@0.756174:0.618484:0.807057:0.618484:0.807057:0.604199:0.756174:0.604199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este modelo exponencial :@0.741950:0.641833:0.912562:0.641833:0.912562:0.627548:0.741950:0.627548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayuda a los médicos :@0.741950:0.656962:0.879161:0.656962:0.879161:0.642677:0.741950:0.642677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a decidir las dosis y la :@0.741950:0.672091:0.885594:0.672091:0.885594:0.657806:0.741950:0.657806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
frecuencia con que :@0.741950:0.687219:0.872444:0.687219:0.872444:0.672935:0.741950:0.672935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se debe administrar :@0.741950:0.702348:0.875922:0.702348:0.875922:0.688064:0.741950:0.688064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el medicamento :@0.741950:0.717477:0.854312:0.717477:0.854312:0.703193:0.741950:0.703193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para mantener su :@0.741950:0.732606:0.861909:0.732606:0.861909:0.718322:0.741950:0.718322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concentración en un nivel :@0.741950:0.747735:0.917934:0.747735:0.917934:0.733451:0.741950:0.733451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
terapéutico.:@0.741950:0.762864:0.820804:0.762864:0.820804:0.748580:0.741950:0.748580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cátedra :@0.743130:0.142740:0.802709:0.142740:0.802709:0.127334:0.743130:0.127334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de salud y :@0.743130:0.155348:0.818667:0.155348:0.818667:0.139941:0.743130:0.139941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bienestar:@0.743130:0.167955:0.810819:0.167955:0.810819:0.152549:0.743130:0.152549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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