55:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6.6 Producto de números reales por funciones:@0.073089:0.136836:0.433654:0.136836:0.433654:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.073089:0.160625:0.152229:0.160625:0.152229:0.143956:0.073089:0.143956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean :@0.152350:0.160625:0.200513:0.160625:0.200513:0.144913:0.152350:0.144913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.201305:0.160070:0.211539:0.160070:0.211539:0.146355:0.201305:0.146355:0.000000
    , f   F A .:@0.211622:0.160625:0.313414:0.160625:0.313414:0.145190:0.211622:0.145190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.215579:0.160487:0.230913:0.160487:0.230913:0.146438:0.215579:0.146438:0.000000
R:@0.234944:0.159765:0.248234:0.159765:0.248234:0.146868:0.234944:0.146868:0.000000
[:@0.264359:0.160487:0.279692:0.160487:0.279692:0.146438:0.264359:0.146438:0.000000
S D:@0.291822:0.161208:0.310009:0.161208:0.310009:0.143553:0.291822:0.143553:0.000000:0.000000:0.000000
 El producto de   por   se designa con    y es la :@0.313469:0.160625:0.680234:0.160625:0.680234:0.144913:0.313469:0.144913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.433715:0.160070:0.443949:0.160070:0.443949:0.146355:0.433715:0.146355:0.000000
f:@0.479236:0.160625:0.483930:0.160625:0.483930:0.145190:0.479236:0.145190:0.000000
l:@0.610268:0.160070:0.620502:0.160070:0.620502:0.146355:0.610268:0.146355:0.000000
f:@0.620576:0.160625:0.625270:0.160625:0.625270:0.145190:0.620576:0.145190:0.000000
función definida en   como::@0.073070:0.177267:0.277759:0.177267:0.277759:0.161554:0.073070:0.161554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.218212:0.177267:0.228096:0.177267:0.228096:0.161832:0.218212:0.161832:0.000000
S D S D:@0.292632:0.201633:0.334085:0.201633:0.334085:0.183979:0.292632:0.183979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.296627:0.200496:0.306861:0.200496:0.306861:0.186781:0.296627:0.186781:0.000000
f   x     f x ,     x   A.:@0.306769:0.201051:0.456549:0.201051:0.456549:0.185616:0.306769:0.185616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 l:@0.337233:0.200496:0.365948:0.200496:0.365948:0.186781:0.337233:0.186781:0.000000:0.000000:0.000000
S D:@0.370476:0.201633:0.385939:0.201633:0.385939:0.183979:0.370476:0.183979:0.000000:0.000000:0.000000
;:@0.398860:0.200496:0.411138:0.200496:0.411138:0.186781:0.398860:0.186781:0.000000
[:@0.424925:0.200912:0.440258:0.200912:0.440258:0.186864:0.424925:0.186864:0.000000
Intervienen los siguientes elementos: :@0.073015:0.224835:0.357610:0.224835:0.357610:0.209122:0.073015:0.209122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.359046:0.224280:0.369280:0.224280:0.369280:0.210565:0.359046:0.210565:0.000000
    , f x    :@0.369427:0.224835:0.458666:0.224835:0.458666:0.209400:0.369427:0.209400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.373735:0.224696:0.389068:0.224696:0.389068:0.210648:0.373735:0.210648:0.000000
R:@0.393522:0.223975:0.406812:0.223975:0.406812:0.211078:0.393522:0.211078:0.000000
S D:@0.419532:0.225417:0.435417:0.225417:0.435417:0.207763:0.419532:0.207763:0.000000:0.000000:0.000000
[:@0.439872:0.224696:0.455205:0.224696:0.455205:0.210648:0.439872:0.210648:0.000000
R:@0.459660:0.223975:0.472950:0.223975:0.472950:0.211078:0.459660:0.211078:0.000000
 y el producto de números :@0.473097:0.224835:0.679982:0.224835:0.679982:0.209122:0.473097:0.209122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales “ ”, de modo que :@0.072942:0.241477:0.240330:0.241477:0.240330:0.225764:0.072942:0.225764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.122347:0.237691:0.126691:0.237691:0.126691:0.220744:0.122347:0.220744:0.000000
l:@0.240227:0.240922:0.250461:0.240922:0.250461:0.227206:0.240227:0.227206:0.000000
  f x     ,:@0.250369:0.241477:0.319985:0.241477:0.319985:0.226041:0.250369:0.226041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.253646:0.237691:0.261726:0.237691:0.261726:0.220744:0.253646:0.220744:0.000000:0.000000
S D:@0.266291:0.242059:0.281753:0.242059:0.281753:0.224405:0.266291:0.224405:0.000000:0.000000:0.000000
[:@0.284938:0.241338:0.300271:0.241338:0.300271:0.227290:0.284938:0.227290:0.000000
R:@0.303456:0.240617:0.316746:0.240617:0.316746:0.227720:0.303456:0.227720:0.000000
 que se escribe simplemente :@0.319912:0.241477:0.532263:0.241477:0.532263:0.225764:0.319912:0.225764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.532074:0.240922:0.542308:0.240922:0.542308:0.227206:0.532074:0.227206:0.000000
f  x . :@0.542216:0.241477:0.572054:0.241477:0.572054:0.226041:0.542216:0.226041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S D:@0.550113:0.242059:0.565575:0.242059:0.565575:0.224405:0.550113:0.224405:0.000000:0.000000:0.000000
Este elemento :@0.572017:0.241477:0.680145:0.241477:0.680145:0.225764:0.572017:0.225764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.072923:0.257564:0.083158:0.257564:0.083158:0.243848:0.072923:0.243848:0.000000
f  x:@0.083066:0.258119:0.102448:0.258119:0.102448:0.242683:0.083066:0.242683:0.000000:0.000000:0.000000:0.000000
S D:@0.090999:0.258701:0.106461:0.258701:0.106461:0.241047:0.090999:0.241047:0.000000:0.000000:0.000000
 es la imagen de la función   en :@0.106369:0.258119:0.345774:0.258119:0.345774:0.242406:0.106369:0.242406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.304321:0.257564:0.314555:0.257564:0.314555:0.243848:0.304321:0.243848:0.000000
f:@0.314463:0.258119:0.319157:0.258119:0.319157:0.242683:0.314463:0.242683:0.000000
x   A:@0.345755:0.258119:0.384116:0.258119:0.384116:0.242683:0.345755:0.242683:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.356064:0.257980:0.371397:0.257980:0.371397:0.243931:0.356064:0.243931:0.000000
, así, :@0.383877:0.258119:0.415924:0.258119:0.415924:0.242406:0.383877:0.242406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S DS D:@0.415703:0.258701:0.452812:0.258701:0.452812:0.241047:0.415703:0.241047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.419513:0.257564:0.429748:0.257564:0.429748:0.243848:0.419513:0.243848:0.000000
f x     f x     . :@0.429472:0.258119:0.543891:0.258119:0.543891:0.242683:0.429472:0.242683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 l:@0.455647:0.257564:0.484049:0.257564:0.484049:0.243848:0.455647:0.243848:0.000000:0.000000:0.000000
S D:@0.488209:0.258701:0.503303:0.258701:0.503303:0.241047:0.488209:0.241047:0.000000:0.000000:0.000000
[:@0.506138:0.257980:0.521471:0.257980:0.521471:0.243931:0.506138:0.243931:0.000000
R:@0.524490:0.257259:0.537780:0.257259:0.537780:0.244361:0.524490:0.244361:0.000000
Se tiene, entonces, :@0.543707:0.258119:0.680114:0.258119:0.680114:0.242406:0.543707:0.242406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la siguiente implicación::@0.072868:0.274760:0.242962:0.274760:0.242962:0.259048:0.072868:0.259048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.290276:0.297990:0.300510:0.297990:0.300510:0.284274:0.290276:0.284274:0.000000
    , f   F A  :@0.300418:0.298544:0.397314:0.298544:0.397314:0.283109:0.300418:0.283109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.303658:0.298406:0.318991:0.298406:0.318991:0.284357:0.303658:0.284357:0.000000
R:@0.322139:0.297685:0.335429:0.297685:0.335429:0.284787:0.322139:0.284787:0.000000
[:@0.349731:0.298406:0.365065:0.298406:0.365065:0.284357:0.349731:0.284357:0.000000
S D:@0.376201:0.299127:0.394093:0.299127:0.394093:0.281473:0.376201:0.281473:0.000000:0.000000:0.000000
⇒ :@0.397241:0.298128:0.419918:0.298128:0.419918:0.281140:0.397241:0.281140:0.000000:0.000000
l:@0.419826:0.297990:0.430061:0.297990:0.430061:0.284274:0.419826:0.284274:0.000000
 f   F A .:@0.429969:0.298544:0.488928:0.298561:0.488928:0.283126:0.429969:0.283109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.441326:0.298422:0.456660:0.298422:0.456660:0.284374:0.441326:0.284374:0.000000
S D:@0.467796:0.299143:0.485688:0.299143:0.485688:0.281489:0.467796:0.281489:0.000000:0.000000:0.000000
Ejercicios resueltos :@0.073089:0.322345:0.220001:0.322345:0.220001:0.305675:0.073089:0.305675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Sea   la función real definida como :@0.073089:0.353802:0.356916:0.353802:0.356916:0.338089:0.073089:0.338089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.132908:0.353802:0.137601:0.353802:0.137601:0.338366:0.132908:0.338366:0.000000
f x    x  :@0.356629:0.353802:0.413532:0.353802:0.413532:0.338366:0.356629:0.338366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S D:@0.361250:0.354384:0.376712:0.354384:0.376712:0.336730:0.361250:0.336730:0.000000:0.000000:0.000000
5 1:@0.379859:0.353247:0.428791:0.353247:0.428791:0.339531:0.379859:0.339531:0.000000:0.000000:0.000000
2:@0.405779:0.347738:0.410264:0.347738:0.410264:0.338577:0.405779:0.338577:0.000000
 :@0.428699:0.344981:0.432012:0.344981:0.432012:0.329546:0.428699:0.329546:0.000000
1:@0.434087:0.343303:0.443478:0.343303:0.443478:0.326877:0.434087:0.326877:0.000000
2:@0.434087:0.359687:0.443478:0.359687:0.443478:0.343260:0.434087:0.343260:0.000000
, x    .:@0.448726:0.353802:0.500892:0.353802:0.500892:0.338366:0.448726:0.338366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.465882:0.353663:0.481215:0.353663:0.481215:0.339614:0.465882:0.339614:0.000000
R:@0.484363:0.352942:0.497653:0.352942:0.497653:0.340044:0.484363:0.340044:0.000000
Entonces, 2  es la función definida como sigue: :@0.103204:0.375810:0.444493:0.375810:0.444493:0.360098:0.103204:0.360098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.184729:0.375810:0.189423:0.375810:0.189423:0.360375:0.184729:0.360375:0.000000
S D S D    S D   :@0.230103:0.407846:0.346437:0.407846:0.346437:0.390192:0.230103:0.390192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.234098:0.407264:0.241792:0.407264:0.241792:0.391551:0.234098:0.391551:0.000000
f x:@0.241718:0.407264:0.266292:0.407264:0.266292:0.391828:0.241718:0.391828:0.000000:0.000000:0.000000
5:@0.274722:0.406709:0.290056:0.406709:0.290056:0.392993:0.274722:0.392993:0.000000
2:@0.294473:0.407264:0.302168:0.407264:0.302168:0.391551:0.294473:0.391551:0.000000
f x:@0.302094:0.407264:0.318164:0.407264:0.318164:0.391828:0.302094:0.391828:0.000000:0.000000:0.000000
5:@0.326594:0.406709:0.341927:0.406709:0.341927:0.392993:0.326594:0.392993:0.000000
2:@0.346345:0.407264:0.354039:0.407264:0.354039:0.391551:0.346345:0.391551:0.000000
3:@0.353987:0.409678:0.359931:0.409678:0.359931:0.383999:0.353987:0.383999:0.000000
x:@0.359797:0.407255:0.367252:0.407255:0.367252:0.391819:0.359797:0.391819:0.000000
2:@0.367187:0.401191:0.372424:0.401191:0.372424:0.392030:0.367187:0.392030:0.000000
 1 :@0.372376:0.406700:0.396729:0.406700:0.396729:0.392984:0.372376:0.392984:0.000000:0.000000:0.000000
 :@0.396637:0.398435:0.399950:0.398435:0.399950:0.382999:0.396637:0.382999:0.000000
1:@0.402019:0.396756:0.411410:0.396756:0.411410:0.380330:0.402019:0.380330:0.000000
2:@0.402019:0.416721:0.411410:0.416721:0.411410:0.400294:0.402019:0.400294:0.000000
4:@0.416657:0.409310:0.422230:0.409310:0.422230:0.385236:0.416657:0.385236:0.000000
   :@0.422104:0.407837:0.446457:0.407837:0.446457:0.390183:0.422104:0.390183:0.000000:0.000000:0.000000
5:@0.426614:0.406700:0.441947:0.406700:0.441947:0.392984:0.426614:0.392984:0.000000
2:@0.446365:0.407255:0.454059:0.407255:0.454059:0.391542:0.446365:0.391542:0.000000
x:@0.453986:0.407255:0.461441:0.407255:0.461441:0.391819:0.453986:0.391819:0.000000
2 :@0.461367:0.401191:0.468911:0.401191:0.468911:0.392030:0.461367:0.392030:0.000000:0.000000
1:@0.468860:0.406700:0.484194:0.406700:0.484194:0.392984:0.468860:0.392984:0.000000
 :@0.484102:0.401191:0.486452:0.401191:0.486452:0.392030:0.484102:0.392030:0.000000
1,      .:@0.486404:0.407255:0.549320:0.407255:0.549320:0.391542:0.486404:0.391542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.502382:0.407255:0.509837:0.407255:0.509837:0.391819:0.502382:0.391819:0.000000
[:@0.513721:0.407116:0.529054:0.407116:0.529054:0.393068:0.513721:0.393068:0.000000
R:@0.532919:0.406395:0.546209:0.406395:0.546209:0.393497:0.532919:0.393497:0.000000
Calculemos algunos valores de las funciones   y 2 .:@0.103220:0.434617:0.465052:0.434617:0.465052:0.418904:0.103220:0.418904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.429084:0.434617:0.433778:0.434617:0.433778:0.419181:0.429084:0.419181:0.000000
f:@0.457229:0.434617:0.461923:0.434617:0.461923:0.419181:0.457229:0.419181:0.000000
x:@0.218490:0.473845:0.227573:0.473845:0.227573:0.457432:0.218490:0.457432:0.000000
f(x)   x:@0.311939:0.475092:0.370171:0.475092:0.370171:0.458679:0.311939:0.458679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.341709:0.474512:0.357739:0.474512:0.357739:0.460173:0.341709:0.460173:0.000000
2  :@0.370107:0.468746:0.379946:0.468746:0.379946:0.459178:0.370107:0.459178:0.000000:0.000000:0.000000
1:@0.379913:0.474507:0.395943:0.474507:0.395943:0.460168:0.379913:0.460168:0.000000
 :@0.395847:0.474929:0.399160:0.474929:0.399160:0.459494:0.395847:0.459494:0.000000
1:@0.401229:0.464987:0.411544:0.464987:0.411544:0.447269:0.401229:0.447269:0.000000
2:@0.401229:0.484951:0.411544:0.484951:0.411544:0.467234:0.401229:0.467234:0.000000
2:@0.471747:0.473845:0.482062:0.473845:0.482062:0.456127:0.471747:0.456127:0.000000
f(x)    x    :@0.481985:0.473845:0.579247:0.473845:0.579247:0.457432:0.481985:0.457432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.511755:0.473265:0.527785:0.473265:0.527785:0.458926:0.511755:0.458926:0.000000
2:@0.531134:0.473845:0.541449:0.473845:0.541449:0.456127:0.531134:0.456127:0.000000
2:@0.550379:0.467506:0.556393:0.467506:0.556393:0.457177:0.550379:0.457177:0.000000
1:@0.559791:0.473265:0.575822:0.473265:0.575822:0.458926:0.559791:0.458926:0.000000
1:@0.579170:0.473845:0.589485:0.473845:0.589485:0.456127:0.579170:0.456127:0.000000
2:@0.210920:0.501487:0.226253:0.501487:0.226253:0.487771:0.210920:0.487771:0.000000
2:@0.226161:0.502041:0.235143:0.502041:0.235143:0.486329:0.226161:0.486329:0.000000
9/2:@0.351809:0.502041:0.376088:0.502041:0.376088:0.486329:0.351809:0.486329:0.000000:0.000000:0.000000
9:@0.526125:0.502041:0.535108:0.502041:0.535108:0.486329:0.526125:0.486329:0.000000
2:@0.195365:0.522927:0.210699:0.522927:0.210699:0.509211:0.195365:0.509211:0.000000
1/    2:@0.210607:0.523482:0.250698:0.523482:0.250698:0.507769:0.210607:0.507769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.359429:0.523482:0.368412:0.523482:0.368412:0.507769:0.359429:0.507769:0.000000
2:@0.526107:0.523482:0.535090:0.523482:0.535090:0.507769:0.526107:0.507769:0.000000
0:@0.218522:0.544922:0.227504:0.544922:0.227504:0.529209:0.218522:0.529209:0.000000
1/2:@0.351790:0.544922:0.376069:0.544922:0.376069:0.529209:0.351790:0.529209:0.000000:0.000000:0.000000
1:@0.526107:0.544922:0.535090:0.544922:0.535090:0.529209:0.526107:0.529209:0.000000
1:@0.218522:0.566362:0.227504:0.566362:0.227504:0.550649:0.218522:0.550649:0.000000
3/2:@0.351790:0.566362:0.376069:0.566362:0.376069:0.550649:0.351790:0.550649:0.000000:0.000000:0.000000
3:@0.526107:0.566362:0.535090:0.566362:0.535090:0.550649:0.526107:0.550649:0.000000
En la Figura 6.5 se representan gráficamente las funciones  y 2 . Identifica estas :@0.103182:0.594514:0.710419:0.594514:0.710419:0.578802:0.103182:0.578802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f    f :@0.547441:0.594514:0.585157:0.594514:0.585157:0.579079:0.547441:0.579079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones.:@0.103182:0.611156:0.177485:0.611156:0.177485:0.595444:0.103182:0.595444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Considera la función real   definida como :@0.073089:0.648858:0.403899:0.648858:0.403899:0.633145:0.073089:0.633145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.285651:0.648858:0.290345:0.648858:0.290345:0.633422:0.285651:0.633422:0.000000
f x:@0.403715:0.648858:0.419784:0.648858:0.419784:0.633422:0.403715:0.633422:0.000000:0.000000:0.000000
S D:@0.408335:0.649440:0.423797:0.649440:0.423797:0.631786:0.408335:0.631786:0.000000:0.000000:0.000000
   :@0.423705:0.648858:0.446935:0.648858:0.446935:0.633145:0.423705:0.633145:0.000000:0.000000:0.000000
5:@0.427663:0.648303:0.442996:0.648303:0.442996:0.634587:0.427663:0.634587:0.000000
2:@0.454445:0.634684:0.469779:0.634684:0.469779:0.620969:0.454445:0.620969:0.000000
1 si:@0.469687:0.635239:0.492162:0.635239:0.492162:0.619526:0.469687:0.619526:0.000000:0.000000:0.000000:0.000000
,   x    ,:@0.475006:0.635239:0.536671:0.635239:0.536671:0.619804:0.475006:0.619804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
#:@0.505949:0.634684:0.521282:0.634684:0.521282:0.620969:0.505949:0.620969:0.000000
0:@0.524430:0.635239:0.533412:0.635239:0.533412:0.619526:0.524430:0.619526:0.000000
x :@0.454445:0.657248:0.465140:0.657248:0.465140:0.641813:0.454445:0.641813:0.000000:0.000000
1:@0.465085:0.656693:0.480418:0.656693:0.480418:0.642977:0.465085:0.642977:0.000000
2:@0.480326:0.657248:0.488020:0.657248:0.488020:0.641535:0.480326:0.641535:0.000000
, si x    .:@0.487947:0.657248:0.549095:0.657248:0.549095:0.641813:0.487947:0.641813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.518374:0.656693:0.533707:0.656693:0.533707:0.642977:0.518374:0.642977:0.000000
0:@0.536855:0.657248:0.545837:0.657248:0.545837:0.641535:0.536855:0.641535:0.000000
Para:@0.133336:0.679795:0.163866:0.679795:0.163866:0.664082:0.133336:0.664082:0.000000:0.000000:0.000000:0.000000
l:@0.167791:0.679240:0.178026:0.679240:0.178026:0.665525:0.167791:0.665525:0.000000
    ,:@0.177934:0.679795:0.216184:0.679795:0.216184:0.664360:0.177934:0.664360:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.181173:0.679656:0.196507:0.679656:0.196507:0.665608:0.181173:0.665608:0.000000
R:@0.199654:0.678935:0.212944:0.678935:0.212944:0.666038:0.199654:0.666038:0.000000
 la función real   está definida como:@0.216110:0.679795:0.483641:0.679795:0.483641:0.664082:0.216110:0.664082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.325707:0.679240:0.335942:0.679240:0.335942:0.665525:0.325707:0.665525:0.000000
f:@0.335850:0.679795:0.340543:0.679795:0.340543:0.664360:0.335850:0.664360:0.000000
 :@0.073089:0.716905:0.077120:0.716905:0.077120:0.701192:0.073089:0.701192:0.000000
S DS D:@0.133331:0.717487:0.171544:0.717487:0.171544:0.699833:0.133331:0.699833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.137325:0.716350:0.147559:0.716350:0.147559:0.702635:0.137325:0.702635:0.000000
f x     f x    :@0.147467:0.716905:0.245099:0.716905:0.245099:0.701470:0.147467:0.701470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 l:@0.174692:0.716350:0.203407:0.716350:0.203407:0.702635:0.174692:0.702635:0.000000:0.000000:0.000000
S D:@0.207935:0.717487:0.223397:0.717487:0.223397:0.699833:0.207935:0.699833:0.000000:0.000000:0.000000
5:@0.226545:0.716350:0.241878:0.716350:0.241878:0.702635:0.226545:0.702635:0.000000
2l:@0.255463:0.701886:0.280938:0.701886:0.280938:0.688170:0.255463:0.688170:0.000000:0.000000
,   x    ,:@0.280846:0.702440:0.342511:0.702440:0.342511:0.687005:0.280846:0.687005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si:@0.287362:0.702440:0.298002:0.702440:0.298002:0.686728:0.287362:0.686728:0.000000:0.000000
#:@0.311789:0.701886:0.327122:0.701886:0.327122:0.688170:0.311789:0.688170:0.000000
0:@0.330270:0.702440:0.339253:0.702440:0.339253:0.686728:0.330270:0.686728:0.000000
l 1 l:@0.255463:0.729248:0.312580:0.729248:0.312580:0.715532:0.255463:0.715532:0.000000:0.000000:0.000000:0.000000:0.000000
x    , si x   :@0.265605:0.729802:0.361470:0.729802:0.361470:0.714367:0.265605:0.714367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.294725:0.729802:0.302420:0.729802:0.302420:0.714090:0.294725:0.714090:0.000000
.:@0.342916:0.729248:0.358249:0.729248:0.358249:0.715532:0.342916:0.715532:0.000000
0:@0.361396:0.729802:0.370379:0.729802:0.370379:0.714090:0.361396:0.714090:0.000000
 :@0.073089:0.754447:0.076991:0.754447:0.076991:0.737778:0.073089:0.737778:0.000000
Particularmente, para       :@0.133331:0.754447:0.344167:0.754447:0.344167:0.738735:0.133331:0.738735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l 5 2:@0.291596:0.753893:0.340228:0.753893:0.340228:0.740177:0.291596:0.740177:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.344094:0.745627:0.347407:0.745627:0.347407:0.730192:0.344094:0.730192:0.000000
1:@0.349463:0.745006:0.355101:0.745006:0.355101:0.728579:0.349463:0.728579:0.000000
4:@0.349463:0.764970:0.358854:0.764970:0.358854:0.748543:0.349463:0.748543:0.000000
 :@0.364101:0.754447:0.367415:0.754447:0.367415:0.739012:0.364101:0.739012:0.000000
tenemos: :@0.367341:0.754447:0.439083:0.754447:0.439083:0.738735:0.367341:0.738735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.073089:0.794249:0.077120:0.794249:0.077120:0.778537:0.073089:0.778537:0.000000
2:@0.137362:0.799064:0.152696:0.799064:0.152696:0.785348:0.137362:0.785348:0.000000
   f  x  :@0.152604:0.799619:0.210583:0.800562:0.210583:0.785126:0.152604:0.784183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.159038:0.791327:0.168429:0.791327:0.168429:0.774900:0.159038:0.774900:0.000000
4:@0.159038:0.811291:0.168429:0.811291:0.168429:0.794864:0.159038:0.794864:0.000000
 :@0.187942:0.794252:0.191973:0.794252:0.191973:0.778539:0.187942:0.778539:0.000000
S D:@0.191900:0.801144:0.207362:0.801144:0.207362:0.783490:0.191900:0.783490:0.000000:0.000000:0.000000
5:@0.210510:0.800007:0.225843:0.800007:0.225843:0.786291:0.210510:0.786291:0.000000
 :@0.225751:0.794252:0.229064:0.794252:0.229064:0.778816:0.225751:0.778816:0.000000
1:@0.241578:0.773176:0.250969:0.773176:0.250969:0.756749:0.241578:0.756749:0.000000
4:@0.241578:0.789559:0.250969:0.789559:0.250969:0.773132:0.241578:0.773132:0.000000
 ,   x    ,:@0.256216:0.782618:0.321120:0.782618:0.321120:0.767182:0.256216:0.767182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si:@0.265972:0.782618:0.276612:0.782618:0.276612:0.766905:0.265972:0.766905:0.000000:0.000000
#:@0.290399:0.782063:0.305732:0.782063:0.305732:0.768347:0.290399:0.768347:0.000000
0:@0.308880:0.782618:0.317862:0.782618:0.317862:0.766905:0.308880:0.766905:0.000000
2:@0.239429:0.825720:0.254762:0.825720:0.254762:0.812004:0.239429:0.812004:0.000000
  x    ,   x    .:@0.254670:0.826275:0.382266:0.826276:0.382266:0.810841:0.254670:0.810839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.260067:0.816108:0.269458:0.816108:0.269458:0.799681:0.260067:0.799681:0.000000
4:@0.260067:0.832491:0.269458:0.832491:0.269458:0.816064:0.260067:0.816064:0.000000
2:@0.285343:0.825721:0.300677:0.825721:0.300677:0.812006:0.285343:0.812006:0.000000
1:@0.305963:0.815969:0.311601:0.815969:0.311601:0.799542:0.305963:0.799542:0.000000
2:@0.305963:0.832353:0.314007:0.832353:0.314007:0.815926:0.305963:0.815926:0.000000
si:@0.327118:0.826276:0.337757:0.826276:0.337757:0.810563:0.327118:0.810563:0.000000:0.000000
.:@0.351544:0.825721:0.366877:0.825721:0.366877:0.812006:0.351544:0.812006:0.000000
0:@0.370025:0.826276:0.379008:0.826276:0.379008:0.810563:0.370025:0.810563:0.000000
Para:@0.103210:0.863010:0.133814:0.863010:0.133814:0.847298:0.103210:0.847298:0.000000:0.000000:0.000000:0.000000
  x      ,      f     :@0.133719:0.863010:0.262291:0.863010:0.262291:0.847575:0.133719:0.847575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2 2:@0.150856:0.862455:0.218227:0.862455:0.218227:0.848740:0.150856:0.848740:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.187818:0.863010:0.193212:0.863010:0.193212:0.847298:0.187818:0.847298:0.000000
1:@0.223520:0.852707:0.229159:0.852707:0.229159:0.836281:0.223520:0.836281:0.000000
4:@0.223520:0.872672:0.232911:0.872672:0.232911:0.856245:0.223520:0.856245:0.000000
S:@0.262272:0.863593:0.266359:0.863593:0.266359:0.845938:0.262272:0.845938:0.000000
2 5:@0.266267:0.862455:0.309395:0.862455:0.309395:0.848740:0.266267:0.848740:0.000000:0.000000:0.000000
1:@0.281508:0.863010:0.286901:0.863010:0.286901:0.847298:0.281508:0.847298:0.000000
D:@0.286828:0.863593:0.290914:0.863593:0.290914:0.845938:0.286828:0.845938:0.000000
    , :@0.290822:0.863010:0.335891:0.863010:0.335891:0.847575:0.290822:0.847575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.314681:0.853569:0.320320:0.853569:0.320320:0.837142:0.314681:0.837142:0.000000
4:@0.314681:0.869952:0.324072:0.869952:0.324072:0.853525:0.314681:0.853525:0.000000
para:@0.335836:0.863010:0.367920:0.863010:0.367920:0.847298:0.335836:0.847298:0.000000:0.000000:0.000000:0.000000
 :@0.073089:0.904766:0.076402:0.904766:0.076402:0.889331:0.073089:0.889331:0.000000
x   2,   :@0.133331:0.905291:0.188276:0.905291:0.188276:0.889579:0.133331:0.889579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.145093:0.904736:0.160426:0.904736:0.160426:0.891021:0.145093:0.891021:0.000000
2:@0.188166:0.904736:0.203499:0.904736:0.203499:0.891021:0.188166:0.891021:0.000000
   f   :@0.203407:0.905291:0.241077:0.905291:0.241077:0.889856:0.203407:0.889856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.208786:0.894989:0.214424:0.894989:0.214424:0.878562:0.208786:0.878562:0.000000
4:@0.208786:0.914954:0.218177:0.914954:0.218177:0.898527:0.208786:0.898527:0.000000
S D:@0.241040:0.905874:0.258030:0.905874:0.258030:0.888219:0.241040:0.888219:0.000000:0.000000:0.000000
2     1:@0.245035:0.905291:0.305319:0.905291:0.305319:0.889579:0.245035:0.889579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.261896:0.904736:0.296428:0.904736:0.296428:0.891021:0.261896:0.891021:0.000000:0.000000:0.000000
,:@0.305245:0.905291:0.308577:0.905291:0.308577:0.889856:0.305245:0.889856:0.000000
 :@0.384272:0.904766:0.387586:0.904766:0.387586:0.889331:0.384272:0.889331:0.000000
mientras que  1     1 2    4.:@0.387519:0.904766:0.619395:0.904766:0.619395:0.889054:0.387519:0.889054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.487268:0.904766:0.491961:0.904766:0.491961:0.889331:0.487268:0.889331:0.000000
S D:@0.491888:0.905349:0.508878:0.905349:0.508878:0.887695:0.491888:0.887695:0.000000:0.000000:0.000000
5 2:@0.512743:0.904212:0.547275:0.904212:0.547275:0.890496:0.512743:0.890496:0.000000:0.000000:0.000000
, f:@0.556092:0.904766:0.567284:0.904766:0.567284:0.889331:0.556092:0.889331:0.000000:0.000000:0.000000
S D:@0.567229:0.905349:0.584219:0.905349:0.584219:0.887695:0.567229:0.887695:0.000000:0.000000:0.000000
5:@0.588084:0.904212:0.603417:0.904212:0.603417:0.890496:0.588084:0.890496:0.000000
En la Figura 6.6 se muestran las gráficas de  y de :@0.073123:0.939257:0.428548:0.939257:0.428548:0.923544:0.073123:0.923544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  :@0.382622:0.939257:0.393796:0.939257:0.393796:0.923821:0.382622:0.923821:0.000000:0.000000:0.000000
2:@0.428438:0.938702:0.443771:0.938702:0.443771:0.924986:0.428438:0.924986:0.000000
1:@0.445783:0.929293:0.451421:0.929293:0.451421:0.912866:0.445783:0.912866:0.000000
4:@0.445783:0.949257:0.455174:0.949257:0.455174:0.932831:0.445783:0.932831:0.000000
 :@0.460421:0.932958:0.463735:0.932958:0.463735:0.917523:0.460421:0.917523:0.000000
f.:@0.463661:0.939268:0.471024:0.939268:0.471024:0.923833:0.463661:0.923833:0.000000:0.000000
Las propiedades del :@0.744288:0.399886:0.880078:0.399886:0.880078:0.385601:0.744288:0.385601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto de escalares :@0.744288:0.415015:0.893310:0.415015:0.893310:0.400730:0.744288:0.400730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por funciones son las :@0.744288:0.430144:0.887614:0.430144:0.887614:0.415859:0.744288:0.415859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuatro que se detallan a :@0.744288:0.445272:0.905514:0.445272:0.905514:0.430988:0.744288:0.430988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
continuación.:@0.744288:0.460401:0.834684:0.460401:0.834684:0.446117:0.744288:0.446117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.744288:0.476287:0.780209:0.476287:0.780209:0.462003:0.744288:0.462003:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.780082:0.475782:0.808613:0.475782:0.808613:0.463314:0.780082:0.463314:0.000000:0.000000:0.000000
,   :@0.790223:0.475909:0.812713:0.475909:0.812713:0.460464:0.790223:0.460464:0.000000:0.000000:0.000000:0.000000
[:@0.812606:0.476161:0.826545:0.476161:0.826545:0.463389:0.812606:0.463389:0.000000
   , f, g   F A .:@0.826461:0.476444:0.917410:0.476444:0.917410:0.461711:0.826461:0.461711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.829537:0.475505:0.841619:0.475505:0.841619:0.463780:0.829537:0.463780:0.000000
[:@0.872702:0.476161:0.886641:0.476161:0.886641:0.463389:0.872702:0.463389:0.000000
S D:@0.897239:0.477000:0.914318:0.477000:0.914318:0.460149:0.897239:0.460149:0.000000:0.000000:0.000000
Se verifican las siguientes :@0.744288:0.491416:0.914294:0.491416:0.914294:0.477131:0.744288:0.477131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades::@0.744288:0.506545:0.830360:0.506545:0.830360:0.492260:0.744288:0.492260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.744288:0.522272:0.752046:0.522272:0.752046:0.508702:0.744288:0.508702:0.000000
.     :@0.751977:0.521913:0.789468:0.521913:0.789468:0.507241:0.751977:0.507241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.758519:0.521793:0.785573:0.521793:0.785573:0.509948:0.758519:0.509948:0.000000:0.000000:0.000000
S:@0.772048:0.523144:0.775949:0.523144:0.775949:0.506292:0.772048:0.506292:0.000000
f       f .:@0.789389:0.522588:0.859041:0.522588:0.859041:0.507854:0.789389:0.507854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.793799:0.523144:0.797700:0.523144:0.797700:0.506292:0.793799:0.506292:0.000000
5:@0.800705:0.522058:0.815341:0.522058:0.815341:0.508966:0.800705:0.508966:0.000000
S:@0.818346:0.523144:0.822246:0.523144:0.822246:0.506292:0.818346:0.506292:0.000000
a b:@0.822179:0.521793:0.844625:0.521793:0.844625:0.509948:0.822179:0.509948:0.000000:0.000000:0.000000
D:@0.844546:0.523144:0.848446:0.523144:0.848446:0.506292:0.844546:0.506292:0.000000
2.:@0.744288:0.543519:0.754748:0.543519:0.754748:0.529948:0.744288:0.529948:0.000000:0.000000
      :@0.754673:0.543159:0.783730:0.543159:0.783730:0.528487:0.754673:0.528487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.758519:0.543039:0.768232:0.543039:0.768232:0.531194:0.758519:0.531194:0.000000
S:@0.775942:0.544390:0.779843:0.544390:0.779843:0.527538:0.775942:0.527538:0.000000
f   g     f    .:@0.783650:0.543834:0.893655:0.543834:0.893655:0.529100:0.783650:0.529100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.791170:0.543304:0.805806:0.543304:0.805806:0.530212:0.791170:0.530212:0.000000
D:@0.817596:0.544390:0.821496:0.544390:0.821496:0.527538:0.817596:0.527538:0.000000
5:@0.824501:0.543304:0.839137:0.543304:0.839137:0.530212:0.824501:0.530212:0.000000
a:@0.842149:0.543039:0.851863:0.543039:0.851863:0.531194:0.842149:0.531194:0.000000
 :@0.851783:0.543159:0.855757:0.543159:0.855757:0.528487:0.851783:0.528487:0.000000
1:@0.863197:0.543304:0.877834:0.543304:0.877834:0.530212:0.863197:0.530212:0.000000
b:@0.880843:0.543039:0.890556:0.543039:0.890556:0.531194:0.880843:0.531194:0.000000
3.:@0.744288:0.564765:0.754748:0.564765:0.754748:0.551195:0.744288:0.551195:0.000000:0.000000
 S:@0.754673:0.565636:0.762421:0.565636:0.762421:0.548784:0.754673:0.548784:0.000000:0.000000
 :@0.762332:0.564405:0.766307:0.564405:0.766307:0.549733:0.762332:0.549733:0.000000
a:@0.766227:0.564286:0.775940:0.564286:0.775940:0.552440:0.766227:0.552440:0.000000
        f    f.:@0.775860:0.565080:0.882344:0.565080:0.882344:0.550346:0.775860:0.550346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 5:@0.778952:0.564550:0.823971:0.564550:0.823971:0.551458:0.778952:0.551458:0.000000:0.000000:0.000000
b:@0.796608:0.564286:0.806321:0.564286:0.806321:0.552440:0.796608:0.552440:0.000000
a:@0.826989:0.564286:0.836702:0.564286:0.836702:0.552440:0.826989:0.552440:0.000000
 :@0.836622:0.564405:0.840597:0.564405:0.840597:0.549733:0.836622:0.549733:0.000000
1:@0.848036:0.564550:0.862673:0.564550:0.862673:0.551458:0.848036:0.551458:0.000000
b:@0.865682:0.564286:0.875395:0.564286:0.875395:0.552440:0.865682:0.552440:0.000000
4.:@0.744288:0.586011:0.754748:0.586011:0.754748:0.572441:0.744288:0.572441:0.000000:0.000000
      :@0.754673:0.585651:0.782269:0.585651:0.782269:0.570979:0.754673:0.570979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.758519:0.586011:0.766674:0.586011:0.766674:0.571614:0.758519:0.571614:0.000000
.:@0.770505:0.581867:0.774479:0.581867:0.774479:0.567195:0.770505:0.567195:0.000000
f   f .:@0.782185:0.586326:0.818029:0.586326:0.818029:0.571592:0.782185:0.571592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.789705:0.585796:0.804342:0.585796:0.804342:0.572704:0.789705:0.572704:0.000000
La demostración se deja :@0.744288:0.606658:0.907929:0.606658:0.907929:0.592374:0.744288:0.592374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como investigación para :@0.744288:0.621787:0.910442:0.621787:0.910442:0.607503:0.744288:0.607503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el estudiante.:@0.744288:0.636916:0.832245:0.636916:0.832245:0.622632:0.744288:0.622632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.356603:0.848854:0.356603:0.848854:0.339656:0.740294:0.339656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.373245:0.837769:0.373245:0.837769:0.356298:0.740294:0.356298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.794291:0.243516:0.797991:0.243516:0.797991:0.236210:0.794291:0.236210:0.000000
2:@0.794291:0.220722:0.797991:0.220722:0.797991:0.213415:0.794291:0.213415:0.000000
3:@0.794291:0.201250:0.797991:0.201250:0.797991:0.193943:0.794291:0.193943:0.000000
4:@0.794291:0.181426:0.797991:0.181426:0.797991:0.174119:0.794291:0.174119:0.000000
y = f (x) :@0.718642:0.214063:0.744988:0.214063:0.744988:0.206756:0.718642:0.206756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = 2 f (x) :@0.839304:0.162482:0.871222:0.162482:0.871222:0.155176:0.839304:0.155176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.906798:0.265322:0.910164:0.265322:0.910164:0.258016:0.906798:0.258016:0.000000
y:@0.794756:0.145924:0.798231:0.145924:0.798231:0.138618:0.794756:0.138618:0.000000
0:@0.795926:0.263724:0.799626:0.263724:0.799626:0.256417:0.795926:0.256417:0.000000
–3:@0.718567:0.267248:0.726711:0.267248:0.726711:0.259942:0.718567:0.259942:0.000000:0.000000
–2:@0.744879:0.267248:0.753024:0.267248:0.753024:0.259942:0.744879:0.259942:0.000000:0.000000
–1:@0.771192:0.267248:0.779336:0.267248:0.779336:0.259942:0.771192:0.259942:0.000000:0.000000
1:@0.826031:0.267248:0.829731:0.267248:0.829731:0.259942:0.826031:0.259942:0.000000
2:@0.852343:0.267248:0.856044:0.267248:0.856044:0.259942:0.852343:0.259942:0.000000
3:@0.878656:0.267248:0.882356:0.267248:0.882356:0.259942:0.878656:0.259942:0.000000
1:@0.791588:0.823049:0.794924:0.823049:0.794924:0.816462:0.791588:0.816462:0.000000
–1:@0.788327:0.862553:0.795669:0.862553:0.795669:0.855966:0.788327:0.855966:0.000000:0.000000
–2:@0.787213:0.876010:0.794555:0.876010:0.794555:0.869423:0.787213:0.869423:0.000000:0.000000
–3:@0.787213:0.893881:0.794555:0.893881:0.794555:0.887294:0.787213:0.887294:0.000000:0.000000
–4:@0.787213:0.911752:0.794555:0.911752:0.794555:0.905165:0.787213:0.905165:0.000000:0.000000
2:@0.791588:0.804821:0.794924:0.804821:0.794924:0.798234:0.791588:0.798234:0.000000
3:@0.791588:0.787267:0.794924:0.787267:0.794924:0.780680:0.791588:0.780680:0.000000
4:@0.791588:0.769396:0.794924:0.769396:0.794924:0.762809:0.791588:0.762809:0.000000
x:@0.915178:0.845015:0.918212:0.845015:0.918212:0.838428:0.915178:0.838428:0.000000
y:@0.791998:0.744154:0.795131:0.744154:0.795131:0.737567:0.791998:0.737567:0.000000
0:@0.793052:0.843568:0.796388:0.843568:0.796388:0.836982:0.793052:0.836982:0.000000
–3:@0.723315:0.846745:0.730657:0.846745:0.730657:0.840159:0.723315:0.840159:0.000000:0.000000
–2:@0.747035:0.846745:0.754377:0.846745:0.754377:0.840159:0.747035:0.840159:0.000000:0.000000
–1:@0.770755:0.846745:0.778097:0.846745:0.778097:0.840159:0.770755:0.840159:0.000000:0.000000
1:@0.820191:0.846745:0.823527:0.846745:0.823527:0.840159:0.820191:0.840159:0.000000
2:@0.843912:0.846745:0.847247:0.846745:0.847247:0.840159:0.843912:0.840159:0.000000
3:@0.867632:0.846745:0.870968:0.846745:0.870968:0.840159:0.867632:0.840159:0.000000
4:@0.891352:0.846745:0.894688:0.846745:0.894688:0.840159:0.891352:0.840159:0.000000
y =      :@0.736977:0.824635:0.764800:0.824635:0.764800:0.815121:0.736977:0.815121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.752509:0.821996:0.757328:0.821996:0.757328:0.812482:0.752509:0.812482:0.000000
4:@0.752509:0.829306:0.757328:0.829306:0.757328:0.819792:0.752509:0.819792:0.000000
y = –     x – :@0.843573:0.881681:0.892226:0.881681:0.892226:0.872167:0.843573:0.872167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.868732:0.878780:0.873551:0.878780:0.873551:0.869266:0.868732:0.869266:0.000000
4:@0.868732:0.886696:0.873551:0.886696:0.873551:0.877182:0.868732:0.877182:0.000000
1:@0.892682:0.879133:0.897501:0.879133:0.897501:0.869619:0.892682:0.869619:0.000000
2:@0.892682:0.886689:0.897501:0.886689:0.897501:0.877175:0.892682:0.877175:0.000000
y = x + 2:@0.853165:0.774039:0.889125:0.774039:0.889125:0.764525:0.853165:0.764525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = –1:@0.737575:0.866641:0.763822:0.866641:0.763822:0.857126:0.737575:0.857126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura  6.5:@0.865157:0.320992:0.919415:0.320992:0.919415:0.309565:0.865157:0.309565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura  6.6:@0.872654:0.940008:0.926911:0.940008:0.926911:0.928580:0.872654:0.928580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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