115:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico y variacional:@0.541231:0.043660:0.930030:0.043660:0.930030:0.024915:0.541231:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El discriminante de esta ecuación debe ser cero::@0.073089:0.136836:0.420540:0.136836:0.420540:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[2 (    :@0.232201:0.171340:0.301080:0.171347:0.301080:0.155634:0.232201:0.155628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m y:@0.245896:0.171340:0.272716:0.171340:0.272716:0.155905:0.245896:0.155905:0.000000:0.000000:0.000000
0:@0.272659:0.174519:0.277896:0.174519:0.277896:0.165358:0.272659:0.165358:0.000000
2:@0.281808:0.170792:0.297141:0.170792:0.297141:0.157076:0.281808:0.157076:0.000000
mx:@0.301006:0.171347:0.323003:0.171347:0.323003:0.155911:0.301006:0.155911:0.000000:0.000000
0:@0.322929:0.174519:0.328166:0.174519:0.328166:0.165358:0.322929:0.165358:0.000000
)   4 ]    4:@0.328120:0.171347:0.414679:0.171347:0.414679:0.155634:0.328120:0.155634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.336864:0.170792:0.352197:0.170792:0.352197:0.157076:0.336864:0.157076:0.000000
c:@0.364953:0.171347:0.372611:0.171347:0.372611:0.155911:0.364953:0.155911:0.000000
2:@0.377350:0.165283:0.382586:0.165283:0.382586:0.156122:0.377350:0.156122:0.000000
2:@0.386498:0.170792:0.401831:0.170792:0.401831:0.157076:0.386498:0.157076:0.000000
m y:@0.414587:0.171347:0.446601:0.171347:0.446601:0.155911:0.414587:0.155911:0.000000:0.000000:0.000000
2:@0.429134:0.165283:0.434371:0.165283:0.434371:0.156122:0.429134:0.156122:0.000000
(    :@0.434323:0.171347:0.474948:0.171347:0.474948:0.155634:0.434323:0.155634:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.446527:0.174519:0.451764:0.174519:0.451764:0.165358:0.446527:0.165358:0.000000
2:@0.455676:0.170792:0.471009:0.170792:0.471009:0.157076:0.455676:0.157076:0.000000
mx:@0.474875:0.171347:0.496871:0.171347:0.496871:0.155911:0.474875:0.155911:0.000000:0.000000
0:@0.496798:0.174519:0.502034:0.174519:0.502034:0.165358:0.496798:0.165358:0.000000
)    0.:@0.501988:0.171347:0.547243:0.171347:0.547243:0.155634:0.501988:0.155634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.506784:0.165283:0.512021:0.165283:0.512021:0.156122:0.506784:0.156122:0.000000
5:@0.515933:0.170792:0.531266:0.170792:0.531266:0.157076:0.515933:0.157076:0.000000
La pendiente de la recta tangente   es     :@0.073091:0.206100:0.413662:0.206100:0.413662:0.190388:0.073091:0.190388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.338892:0.206100:0.346512:0.206100:0.346512:0.190665:0.338892:0.190665:0.000000
m:@0.373829:0.206100:0.388444:0.206100:0.388444:0.190665:0.373829:0.190665:0.000000
5:@0.394095:0.205546:0.409428:0.205546:0.409428:0.191830:0.394095:0.191830:0.000000
y:@0.422931:0.198900:0.430404:0.198900:0.430404:0.183465:0.422931:0.183465:0.000000
₀:@0.430404:0.198900:0.436111:0.198900:0.436111:0.183188:0.430404:0.183188:0.000000
2 ₀:@0.416746:0.213656:0.438890:0.213656:0.438890:0.197943:0.416746:0.197943:0.000000:0.000000:0.000000
x:@0.425729:0.213656:0.433184:0.213656:0.433184:0.198221:0.425729:0.198221:0.000000
. La ecuación cartesiana de la recta:@0.439240:0.206107:0.706454:0.206107:0.706454:0.190394:0.439240:0.190394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tangente   es::@0.073083:0.222748:0.173973:0.222748:0.173973:0.207036:0.073083:0.207036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.143619:0.222748:0.151240:0.222748:0.151240:0.207313:0.143619:0.207313:0.000000
( ,  )     tal que         :@0.249571:0.257502:0.446241:0.257507:0.446241:0.241795:0.249571:0.241789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.254376:0.257502:0.276299:0.257502:0.276299:0.242067:0.254376:0.242067:0.000000:0.000000:0.000000
[:@0.284985:0.257217:0.299622:0.257217:0.299622:0.243807:0.284985:0.243807:0.000000
R:@0.303491:0.256647:0.316781:0.256647:0.316781:0.243750:0.303491:0.243750:0.000000
2:@0.316683:0.251443:0.321919:0.251443:0.321919:0.242283:0.316683:0.242283:0.000000
y:@0.379873:0.257507:0.387346:0.257507:0.387346:0.242072:0.379873:0.242072:0.000000
2:@0.391230:0.256952:0.406564:0.256952:0.406564:0.243237:0.391230:0.243237:0.000000
y:@0.410429:0.257507:0.417902:0.257507:0.417902:0.242072:0.410429:0.242072:0.000000
0:@0.417822:0.260679:0.423059:0.260679:0.423059:0.251519:0.417822:0.251519:0.000000
5:@0.426969:0.256952:0.442302:0.256952:0.442302:0.243237:0.426969:0.243237:0.000000
y:@0.453950:0.250302:0.461424:0.250302:0.461424:0.234867:0.453950:0.234867:0.000000
₀:@0.461424:0.250302:0.467130:0.250302:0.467130:0.234589:0.461424:0.234589:0.000000
2 ₀:@0.447766:0.265058:0.469910:0.265058:0.469910:0.249345:0.447766:0.249345:0.000000:0.000000:0.000000
x:@0.456748:0.265058:0.464203:0.265058:0.464203:0.249622:0.456748:0.249622:0.000000
 (     ).:@0.470000:0.257507:0.529865:0.257507:0.529865:0.241795:0.470000:0.241795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.478748:0.257507:0.486203:0.257507:0.486203:0.242072:0.478748:0.242072:0.000000
2:@0.490087:0.256952:0.505421:0.256952:0.505421:0.243237:0.490087:0.243237:0.000000
x:@0.509286:0.257507:0.516741:0.257507:0.516741:0.242072:0.509286:0.242072:0.000000
0:@0.516669:0.260679:0.521906:0.260679:0.521906:0.251519:0.516669:0.251519:0.000000
En la Figura 4.8. se muestran la parábola  ( ,  ), y las rectas  ,  ,  ,   del haz de rectas :@0.073089:0.292011:0.710320:0.292018:0.710320:0.276305:0.073089:0.276299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.403911:0.292018:0.411569:0.292018:0.411569:0.276582:0.403911:0.276582:0.000000
L L L L:@0.508280:0.292018:0.572271:0.292018:0.572271:0.276582:0.508280:0.276582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.531197:0.295190:0.536434:0.295190:0.536434:0.286029:0.531197:0.286029:0.000000
2:@0.551735:0.295190:0.556972:0.295190:0.556972:0.286029:0.551735:0.286029:0.000000
3:@0.572272:0.295190:0.577509:0.295190:0.577509:0.286029:0.572272:0.286029:0.000000
que pasan por el punto ( ,  )    ( ,  ).:@0.073098:0.308659:0.358552:0.308659:0.358552:0.292947:0.073098:0.292947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.251869:0.308659:0.279515:0.308659:0.279515:0.293224:0.251869:0.293224:0.000000:0.000000:0.000000
0:@0.259247:0.311832:0.264484:0.311832:0.264484:0.302671:0.259247:0.302671:0.000000
0:@0.279453:0.311832:0.284690:0.311832:0.284690:0.302671:0.279453:0.302671:0.000000
[:@0.293391:0.308369:0.308027:0.308369:0.308027:0.294959:0.293391:0.294959:0.000000
c:@0.342961:0.308659:0.350619:0.308659:0.350619:0.293224:0.342961:0.293224:0.000000
Ejercicio resuelto:@0.073074:0.343163:0.201653:0.343163:0.201653:0.326494:0.073074:0.326494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si  ( , 2)   {( ,  )   :@0.073074:0.377668:0.217186:0.377681:0.217186:0.361969:0.073074:0.361955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.138596:0.377127:0.153929:0.377127:0.153929:0.363411:0.138596:0.363411:0.000000
x y:@0.167587:0.377681:0.189713:0.377681:0.189713:0.362246:0.167587:0.362246:0.000000:0.000000:0.000000
[:@0.198607:0.377391:0.213243:0.377391:0.213243:0.363981:0.198607:0.363981:0.000000
R:@0.217315:0.376822:0.230605:0.376822:0.230605:0.363924:0.217315:0.363924:0.000000
2:@0.230507:0.371618:0.235743:0.371618:0.235743:0.362457:0.230507:0.362457:0.000000
 |     8 };     2, entonces, :@0.235697:0.377681:0.439059:0.377681:0.439059:0.361969:0.235697:0.361969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.247828:0.377681:0.255301:0.377681:0.255301:0.362246:0.247828:0.362246:0.000000
2:@0.255232:0.371618:0.260469:0.371618:0.260469:0.362457:0.255232:0.362457:0.000000
5:@0.264582:0.377127:0.279915:0.377127:0.279915:0.363411:0.264582:0.363411:0.000000
x x:@0.292874:0.377681:0.319785:0.377681:0.319785:0.362246:0.292874:0.362246:0.000000:0.000000:0.000000
0:@0.319721:0.380854:0.324958:0.380854:0.324958:0.371693:0.319721:0.371693:0.000000
5:@0.329072:0.377127:0.344406:0.377127:0.344406:0.363411:0.329072:0.363411:0.000000
y:@0.439111:0.377681:0.446584:0.377681:0.446584:0.362246:0.439111:0.362246:0.000000
0 :@0.446506:0.380854:0.454050:0.380854:0.454050:0.371693:0.446506:0.371693:0.000000:0.000000
2:@0.453041:0.371620:0.458278:0.371620:0.458278:0.362460:0.453041:0.362460:0.000000
   8    16. Elegimos      4. La :@0.458234:0.377681:0.710412:0.377681:0.710412:0.361969:0.458234:0.361969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.462394:0.377127:0.477728:0.377127:0.477728:0.363411:0.462394:0.363411:0.000000
x:@0.490686:0.377681:0.498141:0.377681:0.498141:0.362246:0.490686:0.362246:0.000000
0:@0.498073:0.380854:0.503310:0.380854:0.503310:0.371693:0.498073:0.371693:0.000000
5:@0.507424:0.377127:0.522757:0.377127:0.522757:0.363411:0.507424:0.363411:0.000000
y:@0.622266:0.377681:0.629740:0.377681:0.629740:0.362246:0.622266:0.362246:0.000000
0:@0.629661:0.380854:0.634898:0.380854:0.634898:0.371693:0.629661:0.371693:0.000000
5 2:@0.639010:0.377127:0.673745:0.377127:0.673745:0.363411:0.639010:0.363411:0.000000:0.000000:0.000000
pendiente de la recta tangente   a la parábola  ( , 2) en el punto (2, :@0.073098:0.394323:0.671300:0.394323:0.671300:0.378611:0.073098:0.378611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.343684:0.394323:0.351305:0.394323:0.351305:0.378888:0.343684:0.378888:0.000000
2:@0.675721:0.393768:0.691054:0.393768:0.691054:0.380053:0.675721:0.380053:0.000000
4) :@0.691809:0.394323:0.710367:0.394323:0.710367:0.378611:0.691809:0.378611:0.000000:0.000000:0.000000
 :@0.706332:0.394323:0.710364:0.394323:0.710364:0.378611:0.706332:0.378611:0.000000
es   :@0.073086:0.412837:0.111244:0.412837:0.111244:0.397125:0.073086:0.397125:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.092671:0.412837:0.107287:0.412837:0.107287:0.397402:0.092671:0.397402:0.000000
5 :@0.111171:0.412283:0.131014:0.412283:0.131014:0.398567:0.111171:0.398567:0.000000:0.000000
y:@0.138720:0.404007:0.146193:0.404007:0.146193:0.388572:0.138720:0.388572:0.000000
₀:@0.146193:0.404007:0.151899:0.404007:0.151899:0.388294:0.146193:0.388294:0.000000
2 ₀:@0.132535:0.418763:0.154679:0.418763:0.154679:0.403050:0.132535:0.403050:0.000000:0.000000:0.000000
x:@0.141517:0.418763:0.148972:0.418763:0.148972:0.403327:0.141517:0.403327:0.000000
    1.:@0.154769:0.412844:0.205272:0.412844:0.205272:0.397131:0.154769:0.397131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.158720:0.412289:0.193252:0.412289:0.193252:0.398573:0.158720:0.398573:0.000000:0.000000:0.000000
La ecuación cartesiana de la recta tangente a la parábola  ( , 2) en el punto (2,  4) es: ( , :@0.073089:0.447348:0.710384:0.447354:0.710384:0.431641:0.073089:0.431635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.636331:0.446799:0.651664:0.446799:0.651664:0.433084:0.636331:0.433084:0.000000
x:@0.695768:0.447354:0.703223:0.447354:0.703223:0.431919:0.695768:0.431919:0.000000
y:@0.073106:0.463996:0.080579:0.463996:0.080579:0.448560:0.073106:0.448560:0.000000
):@0.080506:0.463996:0.085384:0.463996:0.085384:0.448283:0.080506:0.448283:0.000000
[:@0.089244:0.463706:0.103880:0.463706:0.103880:0.450296:0.089244:0.450296:0.000000
   tal que     4   :@0.103792:0.463996:0.246808:0.463996:0.246808:0.448283:0.103792:0.448283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.107750:0.463136:0.121040:0.463136:0.121040:0.450239:0.107750:0.450239:0.000000
2:@0.120941:0.457932:0.126178:0.457932:0.126178:0.448771:0.120941:0.448771:0.000000
y:@0.184132:0.463996:0.191605:0.463996:0.191605:0.448560:0.184132:0.448560:0.000000
1 5 2 1:@0.195489:0.463441:0.288648:0.463441:0.288648:0.449725:0.195489:0.449725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.261976:0.463996:0.269431:0.463996:0.269431:0.448560:0.261976:0.448560:0.000000
   2, o bien,     :@0.269357:0.463996:0.392318:0.463996:0.392318:0.448283:0.269357:0.448283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.361688:0.463996:0.369161:0.463996:0.369161:0.448560:0.361688:0.448560:0.000000
5 2 2:@0.373045:0.463441:0.434158:0.463441:0.434158:0.449725:0.373045:0.449725:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.407485:0.463996:0.414940:0.463996:0.414940:0.448560:0.407485:0.448560:0.000000
   2.:@0.414867:0.463996:0.450135:0.463996:0.450135:0.448283:0.414867:0.448283:0.000000:0.000000:0.000000:0.000000:0.000000
En la Figura 4.9. se muestran la parábola  ( , 2), el punto (2,  4) y la recta   que pasa por :@0.073099:0.498500:0.710405:0.498506:0.710405:0.482793:0.073099:0.482787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.500231:0.497951:0.515565:0.497951:0.515565:0.484236:0.500231:0.484236:0.000000
L:@0.600477:0.498506:0.608098:0.498506:0.608098:0.483071:0.600477:0.483071:0.000000
(2,  4) y es tangente a  ( , 2). :@0.073091:0.515148:0.293093:0.515148:0.293093:0.499435:0.073091:0.499435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.093854:0.514593:0.109188:0.514593:0.109188:0.500878:0.093854:0.500878:0.000000
Problema 2:@0.073089:0.549658:0.162892:0.549658:0.162892:0.532711:0.073089:0.532711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Consideremos la parábola:@0.162806:0.549658:0.358609:0.549658:0.358609:0.533946:0.162806:0.533946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )   {( ,  )   :@0.084881:0.584170:0.198990:0.584170:0.198990:0.568457:0.084881:0.568457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.104262:0.584170:0.111919:0.584170:0.111919:0.568735:0.104262:0.568735:0.000000
5:@0.120700:0.583615:0.136033:0.583615:0.136033:0.569900:0.120700:0.569900:0.000000
x y:@0.149581:0.584170:0.171614:0.584170:0.171614:0.568735:0.149581:0.568735:0.000000:0.000000:0.000000
[:@0.180410:0.583880:0.195047:0.583880:0.195047:0.570470:0.180410:0.570470:0.000000
R:@0.199008:0.583310:0.212298:0.583310:0.212298:0.570413:0.199008:0.570413:0.000000
2:@0.212210:0.578106:0.217447:0.578106:0.217447:0.568946:0.212210:0.568946:0.000000
 |     4 }, donde   > 0, y ( ,  )   :@0.217399:0.584170:0.473233:0.584170:0.473233:0.568457:0.217399:0.568457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.229327:0.584170:0.236800:0.584170:0.236800:0.568735:0.229327:0.568735:0.000000
2:@0.236733:0.578106:0.241970:0.578106:0.241970:0.568946:0.236733:0.568946:0.000000
5:@0.245972:0.583615:0.261305:0.583615:0.261305:0.569900:0.245972:0.569900:0.000000
cx:@0.274172:0.584170:0.289211:0.584170:0.289211:0.568735:0.274172:0.568735:0.000000:0.000000
c:@0.353397:0.584170:0.361054:0.584170:0.361054:0.568735:0.353397:0.568735:0.000000
x y:@0.412926:0.584170:0.440684:0.584170:0.440684:0.568735:0.412926:0.568735:0.000000:0.000000:0.000000
0:@0.420305:0.587342:0.425542:0.587342:0.425542:0.578182:0.420305:0.578182:0.000000
0:@0.440614:0.587342:0.445850:0.587342:0.445850:0.578182:0.440614:0.578182:0.000000
[:@0.454653:0.583880:0.469290:0.583880:0.469290:0.570470:0.454653:0.570470:0.000000
R:@0.473251:0.583310:0.486541:0.583310:0.486541:0.570413:0.473251:0.570413:0.000000
2:@0.486451:0.578106:0.491688:0.578106:0.491688:0.568946:0.486451:0.568946:0.000000
, tal que ( ,  )    ( ,  ) y si   :@0.491642:0.584170:0.710372:0.584170:0.710372:0.568457:0.491642:0.568457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.557853:0.584170:0.585628:0.584170:0.585628:0.568735:0.557853:0.568735:0.000000:0.000000:0.000000
0:@0.565247:0.587342:0.570484:0.587342:0.570484:0.578182:0.565247:0.578182:0.000000
0:@0.585556:0.587342:0.590793:0.587342:0.590793:0.578182:0.585556:0.578182:0.000000
Ó:@0.599600:0.584031:0.614934:0.584031:0.614934:0.569983:0.599600:0.569983:0.000000
c:@0.650063:0.584170:0.657720:0.584170:0.657720:0.568735:0.650063:0.568735:0.000000
x:@0.693173:0.584170:0.700628:0.584170:0.700628:0.568735:0.693173:0.568735:0.000000
0:@0.700568:0.587342:0.705804:0.587342:0.705804:0.578182:0.700568:0.578182:0.000000
> 0,   > 4:@0.073094:0.600812:0.149017:0.600812:0.149017:0.585099:0.073094:0.585099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.104755:0.600812:0.112228:0.600812:0.112228:0.585377:0.104755:0.585377:0.000000
0:@0.112169:0.603984:0.117406:0.603984:0.117406:0.594824:0.112169:0.594824:0.000000
2:@0.115217:0.594751:0.120453:0.594751:0.120453:0.585590:0.115217:0.585590:0.000000
cx:@0.148944:0.600812:0.164001:0.600812:0.164001:0.585377:0.148944:0.585377:0.000000:0.000000
0:@0.163943:0.603984:0.169179:0.603984:0.169179:0.594824:0.163943:0.594824:0.000000
. En la Figura 4.10. se muestran la parábola  ( ,  ), el punto ( ,  ) y  ,  ,   :@0.169137:0.600812:0.710372:0.600812:0.710372:0.585099:0.169137:0.585099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.512521:0.600812:0.520178:0.600812:0.520178:0.585377:0.512521:0.585377:0.000000
x y:@0.603453:0.600812:0.631540:0.600812:0.631540:0.585377:0.603453:0.585377:0.000000:0.000000:0.000000
0:@0.610844:0.603984:0.616081:0.603984:0.616081:0.594824:0.610844:0.594824:0.000000
0:@0.631483:0.603984:0.636720:0.603984:0.636720:0.594824:0.631483:0.594824:0.000000
L L L:@0.658233:0.600812:0.701162:0.600812:0.701162:0.585377:0.658233:0.585377:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.680853:0.603984:0.686090:0.603984:0.686090:0.594824:0.680853:0.594824:0.000000
2:@0.701103:0.603984:0.706340:0.603984:0.706340:0.594824:0.701103:0.594824:0.000000
que son tres rectas de un haz de rectas que pasan por ( ,  ), una de ellas tangente a  (:@0.073094:0.617454:0.706341:0.617454:0.706341:0.601741:0.073094:0.601741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.472072:0.617454:0.499751:0.617454:0.499751:0.602018:0.472072:0.602018:0.000000:0.000000:0.000000
0:@0.479446:0.620626:0.484683:0.620626:0.484683:0.611465:0.479446:0.611465:0.000000
0:@0.499691:0.620626:0.504928:0.620626:0.504928:0.611465:0.499691:0.611465:0.000000
,  ) y ( ,  )    . :@0.080498:0.634095:0.205794:0.634095:0.205794:0.618383:0.080498:0.618383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.087570:0.634095:0.095228:0.634095:0.095228:0.618660:0.087570:0.618660:0.000000
x y:@0.120667:0.634095:0.147796:0.634095:0.147796:0.618660:0.120667:0.618660:0.000000:0.000000:0.000000
1:@0.128064:0.637268:0.133301:0.637268:0.133301:0.628107:0.128064:0.628107:0.000000
1:@0.147734:0.637268:0.152971:0.637268:0.152971:0.628107:0.147734:0.628107:0.000000
[:@0.161672:0.633806:0.176308:0.633806:0.176308:0.620396:0.161672:0.620396:0.000000
R:@0.180178:0.633236:0.193468:0.633236:0.193468:0.620338:0.180178:0.620338:0.000000
2:@0.193369:0.628032:0.198606:0.628032:0.198606:0.618871:0.193369:0.618871:0.000000
Notemos que ( ,  )     es tal que   > 0 y   > 4:@0.073096:0.668600:0.431929:0.668606:0.431929:0.652893:0.073096:0.652887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.180834:0.668600:0.207650:0.668606:0.207650:0.653171:0.180834:0.653164:0.000000:0.000000:0.000000
1:@0.188213:0.671778:0.193450:0.671778:0.193450:0.662618:0.188213:0.662618:0.000000
1:@0.207578:0.671778:0.212815:0.671778:0.212815:0.662618:0.207578:0.662618:0.000000
[:@0.221211:0.668316:0.235847:0.668316:0.235847:0.654906:0.221211:0.654906:0.000000
R:@0.239404:0.667746:0.252694:0.667746:0.252694:0.654849:0.239404:0.654849:0.000000
2:@0.252602:0.662542:0.257839:0.662542:0.257839:0.653381:0.252602:0.653381:0.000000
x:@0.334146:0.668606:0.341601:0.668606:0.341601:0.653171:0.334146:0.653171:0.000000
1:@0.341537:0.671778:0.346774:0.671778:0.346774:0.662618:0.341537:0.662618:0.000000
y:@0.389118:0.668606:0.396592:0.668606:0.396592:0.653171:0.389118:0.653171:0.000000
1:@0.396527:0.671778:0.401763:0.671778:0.401763:0.662618:0.396527:0.662618:0.000000
2:@0.399574:0.662545:0.404811:0.662545:0.404811:0.653385:0.399574:0.653385:0.000000
cx:@0.431837:0.668606:0.446875:0.668606:0.446875:0.653171:0.431837:0.653171:0.000000:0.000000
1:@0.446822:0.671778:0.452059:0.671778:0.452059:0.662618:0.446822:0.662618:0.000000
. Un punto como este se denomina :@0.452013:0.668606:0.710528:0.668606:0.710528:0.652893:0.452013:0.652893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interior a la parábola:@0.073081:0.685248:0.229434:0.685248:0.229434:0.668578:0.073081:0.668578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.229285:0.685248:0.232488:0.685248:0.232488:0.669535:0.229285:0.669535:0.000000
Determinemos si existe una recta   que pasa por el punto ( ,  ) y es tangente a la :@0.073081:0.719752:0.710400:0.719758:0.710400:0.704045:0.073081:0.704039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.332126:0.719752:0.339747:0.719752:0.339747:0.704316:0.332126:0.704316:0.000000
x y:@0.525587:0.719752:0.555237:0.719758:0.555237:0.704323:0.525587:0.704316:0.000000:0.000000:0.000000
0:@0.533174:0.722930:0.538411:0.722930:0.538411:0.713770:0.533174:0.713770:0.000000
0:@0.555369:0.722930:0.560606:0.722930:0.560606:0.713770:0.555369:0.713770:0.000000
parábola  ( ,  ). Para el efecto, supongamos que la ecuación cartesiana de la recta está :@0.073089:0.736400:0.710299:0.736400:0.710299:0.720687:0.073089:0.720687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.173006:0.736400:0.180663:0.736400:0.180663:0.720965:0.173006:0.720965:0.000000
definida como ( ,  )    , así,          (     ), donde       es la pendiente. Entonces, :@0.073091:0.753042:0.710397:0.753042:0.710397:0.737329:0.073091:0.737329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.185246:0.753042:0.206525:0.753042:0.206525:0.737606:0.185246:0.737606:0.000000:0.000000:0.000000
[:@0.214536:0.752752:0.229172:0.752752:0.229172:0.739342:0.214536:0.739342:0.000000
R:@0.232433:0.752182:0.245723:0.752182:0.245723:0.739284:0.232433:0.739284:0.000000
2:@0.245530:0.746978:0.250767:0.746978:0.250767:0.737817:0.245530:0.737817:0.000000
y:@0.282202:0.753042:0.289676:0.753042:0.289676:0.737606:0.282202:0.737606:0.000000
2:@0.292971:0.752487:0.308304:0.752487:0.308304:0.738771:0.292971:0.738771:0.000000
y:@0.311562:0.753042:0.319035:0.753042:0.319035:0.737606:0.311562:0.737606:0.000000
0:@0.318890:0.756214:0.324127:0.756214:0.324127:0.747054:0.318890:0.747054:0.000000
5:@0.327473:0.752487:0.342806:0.752487:0.342806:0.738771:0.327473:0.738771:0.000000
m x:@0.346064:0.753042:0.372718:0.753042:0.372718:0.737606:0.346064:0.737606:0.000000:0.000000:0.000000
2:@0.376031:0.752487:0.391364:0.752487:0.391364:0.738771:0.376031:0.738771:0.000000
x:@0.394622:0.753042:0.402077:0.753042:0.402077:0.737606:0.394622:0.737606:0.000000
0:@0.401901:0.756214:0.407138:0.756214:0.407138:0.747054:0.401901:0.747054:0.000000
m:@0.469461:0.753042:0.484076:0.753042:0.484076:0.737606:0.469461:0.737606:0.000000
[:@0.487371:0.752752:0.502008:0.752752:0.502008:0.739342:0.487371:0.739342:0.000000
R:@0.505268:0.752182:0.518558:0.752182:0.518558:0.739284:0.505268:0.739284:0.000000
y:@0.073103:0.769684:0.080576:0.769684:0.080576:0.754248:0.073103:0.754248:0.000000
    (     )    , y reemplazando en la ecuación de la parábola     4 , se tiene (    :@0.080502:0.769684:0.710374:0.769684:0.710374:0.753971:0.080502:0.753971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.084092:0.769129:0.099425:0.769129:0.099425:0.755413:0.084092:0.755413:0.000000
m x:@0.102922:0.769684:0.129723:0.769684:0.129723:0.754248:0.102922:0.754248:0.000000:0.000000:0.000000
2:@0.133239:0.769129:0.148572:0.769129:0.148572:0.755413:0.133239:0.755413:0.000000
x:@0.152070:0.769684:0.159525:0.769684:0.159525:0.754248:0.152070:0.754248:0.000000
0:@0.159453:0.772856:0.164690:0.772856:0.164690:0.763695:0.159453:0.763695:0.000000
1:@0.173036:0.769129:0.188369:0.769129:0.188369:0.755413:0.173036:0.755413:0.000000
y:@0.191866:0.769684:0.199340:0.769684:0.199340:0.754248:0.191866:0.754248:0.000000
0:@0.199263:0.772856:0.204500:0.772856:0.204500:0.763695:0.199263:0.763695:0.000000
y:@0.544767:0.769684:0.552240:0.769684:0.552240:0.754248:0.544767:0.754248:0.000000
2:@0.552167:0.763620:0.557403:0.763620:0.557403:0.754459:0.552167:0.754459:0.000000
5:@0.560947:0.769129:0.576280:0.769129:0.576280:0.755413:0.560947:0.755413:0.000000
cx:@0.588687:0.769684:0.603725:0.769684:0.603725:0.754248:0.588687:0.754248:0.000000:0.000000
y:@0.674833:0.769684:0.682306:0.769684:0.682306:0.754248:0.674833:0.754248:0.000000
0:@0.682231:0.772856:0.687467:0.772856:0.687467:0.763695:0.682231:0.763695:0.000000
1:@0.691009:0.769129:0.706342:0.769129:0.706342:0.755413:0.691009:0.755413:0.000000
m x:@0.073096:0.786325:0.099897:0.786325:0.099897:0.770890:0.073096:0.770890:0.000000:0.000000:0.000000
(     ))    4    0.:@0.087638:0.786325:0.232628:0.786325:0.232628:0.770613:0.087638:0.770613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.103781:0.785771:0.119114:0.785771:0.119114:0.772055:0.103781:0.772055:0.000000
x:@0.122980:0.786325:0.130435:0.786325:0.130435:0.770890:0.122980:0.770890:0.000000
0:@0.130355:0.789498:0.135592:0.789498:0.135592:0.780337:0.130355:0.780337:0.000000
2:@0.145140:0.780262:0.150377:0.780262:0.150377:0.771101:0.145140:0.771101:0.000000
2:@0.154287:0.785771:0.169620:0.785771:0.169620:0.772055:0.154287:0.772055:0.000000
cx:@0.182377:0.786325:0.197415:0.786325:0.197415:0.770890:0.182377:0.770890:0.000000:0.000000
5:@0.201318:0.785771:0.216651:0.785771:0.216651:0.772055:0.201318:0.772055:0.000000
Procediendo en forma similar al desarrollo realizado en el problema 1, se obtiene la :@0.073111:0.820829:0.710396:0.820829:0.710396:0.805117:0.073111:0.805117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación siguiente que permite hallar  .:@0.073111:0.837471:0.369155:0.837471:0.369155:0.821759:0.073111:0.821759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.351410:0.837471:0.366026:0.837471:0.366026:0.822036:0.351410:0.822036:0.000000
x m:@0.315166:0.871975:0.342346:0.871989:0.342346:0.856554:0.315166:0.856540:0.000000:0.000000:0.000000
0:@0.322541:0.875162:0.327778:0.875162:0.327778:0.866001:0.322541:0.866001:0.000000
2:@0.342280:0.865925:0.347517:0.865925:0.347517:0.856765:0.342280:0.856765:0.000000
   :@0.347470:0.871989:0.370700:0.871989:0.370700:0.856277:0.347470:0.856277:0.000000:0.000000:0.000000
2:@0.351427:0.871435:0.366760:0.871435:0.366760:0.857719:0.351427:0.857719:0.000000
y m:@0.370626:0.871989:0.397825:0.871989:0.397825:0.856554:0.370626:0.856554:0.000000:0.000000:0.000000
0:@0.378019:0.875162:0.383256:0.875162:0.383256:0.866001:0.378019:0.866001:0.000000
   c   0, :@0.397751:0.871989:0.468325:0.871989:0.468325:0.856277:0.397751:0.856277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 5:@0.401709:0.871435:0.448316:0.871435:0.448316:0.857719:0.401709:0.857719:0.000000:0.000000:0.000000
x:@0.270616:0.647545:0.277054:0.647545:0.277054:0.634215:0.270616:0.634215:0.000000
Figura 4.8:@0.728378:0.275111:0.779704:0.275111:0.779704:0.263684:0.728378:0.263684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ):@0.849327:0.175798:0.880157:0.175798:0.880157:0.164371:0.849327:0.164371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.852874:0.175798:0.872801:0.175798:0.872801:0.164573:0.852874:0.164573:0.000000:0.000000:0.000000
0:@0.858296:0.178105:0.862105:0.178105:0.862105:0.171443:0.858296:0.171443:0.000000
0:@0.872801:0.178105:0.876609:0.178105:0.876609:0.171443:0.872801:0.171443:0.000000
y:@0.777510:0.141086:0.783964:0.141086:0.783964:0.127756:0.777510:0.127756:0.000000
x:@0.941155:0.214003:0.947594:0.214003:0.947594:0.200672:0.941155:0.200672:0.000000
0:@0.781404:0.210563:0.788753:0.210563:0.788753:0.197708:0.781404:0.197708:0.000000
y:@0.887425:0.241386:0.894219:0.241386:0.894219:0.227354:0.887425:0.227354:0.000000
2:@0.894219:0.235873:0.898979:0.235873:0.898979:0.227546:0.894219:0.227546:0.000000
   4:@0.898979:0.241386:0.928414:0.241386:0.928414:0.227102:0.898979:0.227102:0.000000:0.000000:0.000000:0.000000
5:@0.902644:0.240882:0.916583:0.240882:0.916583:0.228413:0.902644:0.228413:0.000000
cx:@0.928414:0.241386:0.942153:0.241386:0.942153:0.227354:0.928414:0.227354:0.000000:0.000000
L:@0.744576:0.166258:0.751504:0.166258:0.751504:0.152226:0.744576:0.152226:0.000000
1:@0.751495:0.169142:0.756256:0.169142:0.756256:0.160814:0.751495:0.160814:0.000000
L:@0.736908:0.215427:0.743836:0.215427:0.743836:0.201395:0.736908:0.201395:0.000000
L:@0.759633:0.241903:0.766561:0.241903:0.766561:0.227871:0.759633:0.227871:0.000000
3:@0.766556:0.244787:0.771317:0.244787:0.771317:0.236459:0.766556:0.236459:0.000000
L:@0.813176:0.149869:0.820104:0.149869:0.820104:0.135836:0.813176:0.135836:0.000000
2:@0.820104:0.152752:0.824865:0.152752:0.824865:0.144425:0.820104:0.144425:0.000000
Figura 4.9:@0.728378:0.539047:0.779704:0.539047:0.779704:0.527619:0.728378:0.527619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.793512:0.427211:0.800045:0.427211:0.800045:0.415784:0.793512:0.415784:0.000000
2:@0.782836:0.456112:0.793988:0.456112:0.793988:0.446137:0.782836:0.446137:0.000000
1:@0.793988:0.456516:0.800521:0.456516:0.800521:0.445088:0.793988:0.445088:0.000000
2:@0.782836:0.470051:0.793988:0.470051:0.793988:0.460076:0.782836:0.460076:0.000000
2:@0.793988:0.470455:0.800521:0.470455:0.800521:0.459027:0.793988:0.459027:0.000000
2:@0.782836:0.484343:0.793988:0.484343:0.793988:0.474368:0.782836:0.474368:0.000000
3:@0.793988:0.484746:0.800521:0.484746:0.800521:0.473319:0.793988:0.473319:0.000000
2:@0.782836:0.498635:0.793988:0.498635:0.793988:0.488660:0.782836:0.488660:0.000000
4:@0.793988:0.499038:0.800521:0.499038:0.800521:0.487611:0.793988:0.487611:0.000000
2:@0.782836:0.512927:0.793988:0.512927:0.793988:0.502952:0.782836:0.502952:0.000000
5:@0.793988:0.513330:0.800521:0.513330:0.800521:0.501903:0.793988:0.501903:0.000000
2:@0.793519:0.412904:0.800052:0.412904:0.800052:0.401477:0.793519:0.401477:0.000000
3:@0.793519:0.398612:0.800052:0.398612:0.800052:0.387185:0.793519:0.387185:0.000000
4:@0.793519:0.384320:0.800052:0.384320:0.800052:0.372893:0.793519:0.372893:0.000000
5:@0.793519:0.370029:0.800052:0.370029:0.800052:0.358601:0.793519:0.358601:0.000000
1 2 3 4:@0.822716:0.451432:0.886158:0.451432:0.886158:0.440005:0.822716:0.440005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.774831:0.451029:0.785982:0.451029:0.785982:0.441054:0.774831:0.441054:0.000000
1:@0.785982:0.451432:0.792515:0.451432:0.792515:0.440005:0.785982:0.440005:0.000000
2:@0.755968:0.451029:0.767120:0.451029:0.767120:0.441054:0.755968:0.441054:0.000000
2:@0.767120:0.451432:0.773653:0.451432:0.773653:0.440005:0.767120:0.440005:0.000000
2:@0.737106:0.451029:0.748257:0.451029:0.748257:0.441054:0.737106:0.441054:0.000000
3:@0.748257:0.451432:0.754790:0.451432:0.754790:0.440005:0.748257:0.440005:0.000000
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:@0.855650:0.496736:0.860665:0.496736:0.860665:0.484323:0.855650:0.484323:0.000000
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Figura 4.10:@0.724524:0.729004:0.782383:0.729004:0.782383:0.717577:0.724524:0.717577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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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