89:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.073089:0.140040:0.093319:0.140040:0.093319:0.124327:0.073089:0.124327:0.000000:0.000000:0.000000
x:@0.100898:0.140040:0.108352:0.140040:0.108352:0.123634:0.100898:0.123634:0.000000
<:@0.110672:0.140622:0.126005:0.140622:0.126005:0.122968:0.110672:0.122968:0.000000
x:@0.128306:0.140040:0.135761:0.140040:0.135761:0.123634:0.128306:0.123634:0.000000
0:@0.138095:0.143212:0.143332:0.143212:0.143332:0.134052:0.138095:0.134052:0.000000
; :@0.144680:0.140040:0.151841:0.140040:0.151841:0.124327:0.144680:0.124327:0.000000:0.000000
 :@0.193581:0.140040:0.197612:0.140040:0.197612:0.124327:0.193581:0.124327:0.000000
b.       :@0.253817:0.140040:0.294478:0.140040:0.294478:0.124327:0.253817:0.124327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.294340:0.140040:0.301794:0.140040:0.301794:0.123634:0.294340:0.123634:0.000000
>:@0.304114:0.140622:0.319447:0.140622:0.319447:0.122968:0.304114:0.122968:0.000000
x:@0.321748:0.140040:0.329203:0.140040:0.329203:0.123634:0.321748:0.123634:0.000000
0:@0.331537:0.143212:0.336774:0.143212:0.336774:0.134052:0.331537:0.134052:0.000000
.:@0.338122:0.140040:0.341325:0.140040:0.341325:0.124327:0.338122:0.124327:0.000000
Para precisar la notación :@0.073094:0.167402:0.253066:0.167402:0.253066:0.151689:0.073094:0.151689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.252933:0.167402:0.260388:0.167402:0.260388:0.150996:0.252933:0.150996:0.000000
x:@0.283340:0.167403:0.290795:0.167403:0.290795:0.150997:0.283340:0.150997:0.000000
0:@0.293121:0.170575:0.298358:0.170575:0.298358:0.161415:0.293121:0.161415:0.000000
 que se lee “  tiende a  ” o también “  se aproxima a  ”, :@0.299706:0.167403:0.710379:0.167403:0.710379:0.151690:0.299706:0.151690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.385061:0.167403:0.392515:0.167403:0.392515:0.150997:0.385061:0.150997:0.000000
x:@0.460659:0.167403:0.468114:0.167403:0.468114:0.150997:0.460659:0.150997:0.000000
0:@0.470458:0.170575:0.475695:0.170575:0.475695:0.161415:0.470458:0.161415:0.000000
x:@0.567369:0.167403:0.574824:0.167403:0.574824:0.150997:0.567369:0.150997:0.000000
x:@0.683758:0.167403:0.691213:0.167403:0.691213:0.150997:0.683758:0.150997:0.000000
0:@0.693559:0.170575:0.698796:0.170575:0.698796:0.161415:0.693559:0.161415:0.000000
veamos algunos ejemplos que nos permitan comprender este significado.:@0.073083:0.184045:0.610475:0.184045:0.610475:0.168332:0.073083:0.168332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Consideremos el caso :@0.073089:0.211408:0.265536:0.211408:0.265536:0.195695:0.073089:0.195695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.265329:0.211408:0.272784:0.211408:0.272784:0.195002:0.265329:0.195002:0.000000
>:@0.275104:0.211990:0.290437:0.211990:0.290437:0.194336:0.275104:0.194336:0.000000
x:@0.292738:0.211408:0.300193:0.211408:0.300193:0.195002:0.292738:0.195002:0.000000
0:@0.302527:0.214580:0.307764:0.214580:0.307764:0.205420:0.302527:0.205420:0.000000
. Se tiene :@0.309112:0.211408:0.378482:0.211408:0.378482:0.195695:0.309112:0.195695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d x x:@0.378342:0.211408:0.425732:0.211408:0.425732:0.195002:0.378342:0.195002:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.388632:0.211990:0.394761:0.211990:0.394761:0.194336:0.388632:0.194336:0.000000
0:@0.403167:0.214580:0.408403:0.214580:0.408403:0.205420:0.403167:0.205420:0.000000
, :@0.409000:0.211408:0.417265:0.211408:0.417265:0.195695:0.409000:0.195695:0.000000:0.000000
)=∙:@0.426763:0.211990:0.454337:0.211990:0.454337:0.194336:0.426763:0.194336:0.000000:0.000000:0.000000
x x x x:@0.455349:0.211408:0.531684:0.211408:0.531684:0.195002:0.455349:0.195002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.463855:0.214580:0.469092:0.214580:0.469092:0.205420:0.463855:0.205420:0.000000
– = –:@0.469689:0.211408:0.523199:0.211408:0.523199:0.195695:0.469689:0.195695:0.000000:0.000000:0.000000:0.000000:0.000000
∙:@0.488409:0.211990:0.492495:0.211990:0.492495:0.194336:0.488409:0.194336:0.000000
0:@0.532715:0.214580:0.537952:0.214580:0.537952:0.205420:0.532715:0.205420:0.000000
>:@0.538550:0.211990:0.553883:0.211990:0.553883:0.194336:0.538550:0.194336:0.000000
0. :@0.554896:0.211408:0.572136:0.211408:0.572136:0.195695:0.554896:0.195695:0.000000:0.000000:0.000000
Sea :@0.103219:0.238770:0.134325:0.238770:0.134325:0.223057:0.103219:0.223057:0.000000:0.000000:0.000000:0.000000
x:@0.137033:0.238770:0.144488:0.238770:0.144488:0.222364:0.137033:0.222364:0.000000
0:@0.145897:0.241944:0.151134:0.241944:0.151134:0.232783:0.145897:0.232783:0.000000
=–:@0.152001:0.239354:0.178084:0.239354:0.178084:0.221699:0.152001:0.221699:0.000000:0.000000
2,5. Consideremos la función real  , definida como :@0.179631:0.238771:0.587001:0.238771:0.587001:0.223059:0.179631:0.223059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.452592:0.238771:0.457286:0.238771:0.457286:0.222365:0.452592:0.222365:0.000000
f h:@0.589689:0.238771:0.612974:0.238771:0.612974:0.222365:0.589689:0.222365:0.000000:0.000000:0.000000
( )=–:@0.595800:0.239354:0.648150:0.239354:0.648150:0.221699:0.595800:0.221699:0.000000:0.000000:0.000000:0.000000:0.000000
2,5:@0.649697:0.238771:0.673847:0.238771:0.673847:0.223059:0.649697:0.223059:0.000000:0.000000:0.000000
+:@0.675338:0.239354:0.690671:0.239354:0.690671:0.221699:0.675338:0.221699:0.000000
h:@0.692217:0.238771:0.701715:0.238771:0.701715:0.222365:0.692217:0.222365:0.000000
, :@0.703133:0.238771:0.710367:0.238771:0.710367:0.223059:0.703133:0.223059:0.000000:0.000000
 :@0.114251:0.255413:0.118283:0.255413:0.118283:0.239700:0.114251:0.239700:0.000000
h :@0.118202:0.255413:0.132044:0.255413:0.132044:0.239007:0.118202:0.239007:0.000000:0.000000
∈ ℝ:@0.133093:0.255996:0.166227:0.255996:0.166227:0.238341:0.133093:0.238341:0.000000:0.000000:0.000000
. Primeramente, calculemos las distancias que se muestran en la tabla 3.4: :@0.166135:0.255413:0.700158:0.255413:0.700158:0.239700:0.166135:0.239700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.216791:0.282775:0.226050:0.282775:0.226050:0.266369:0.216791:0.266369:0.000000
(–:@0.227081:0.283357:0.243427:0.283357:0.243427:0.265703:0.227081:0.265703:0.000000:0.000000
2,5;  2,49:@0.244439:0.282775:0.321418:0.282775:0.321418:0.267062:0.244439:0.267062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.277959:0.283357:0.287162:0.283357:0.287162:0.265703:0.277959:0.265703:0.000000
)=∙–:@0.322412:0.283357:0.360202:0.283357:0.360202:0.265703:0.322412:0.265703:0.000000:0.000000:0.000000:0.000000
2,5 f(0,01:@0.361215:0.282775:0.440679:0.282775:0.440679:0.267062:0.361215:0.267062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.385457:0.283357:0.394661:0.283357:0.394661:0.265703:0.385457:0.265703:0.000000
)∙=:@0.441673:0.283357:0.469247:0.283357:0.469247:0.265703:0.441673:0.265703:0.000000:0.000000:0.000000
2,5 2,49 0,01;:@0.470259:0.282775:0.592778:0.282775:0.592778:0.267062:0.470259:0.267062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.494502:0.283357:0.503705:0.283357:0.503705:0.265703:0.494502:0.265703:0.000000
=:@0.538955:0.283357:0.554288:0.283357:0.554288:0.265703:0.538955:0.265703:0.000000
d:@0.196764:0.310137:0.206023:0.310137:0.206023:0.293731:0.196764:0.293731:0.000000
(–:@0.207054:0.310719:0.223399:0.310719:0.223399:0.293065:0.207054:0.293065:0.000000:0.000000
2,5;  2,495:@0.224412:0.310137:0.311405:0.310137:0.311405:0.294424:0.224412:0.294424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.257931:0.310719:0.267135:0.310719:0.267135:0.293065:0.257931:0.293065:0.000000
)=∙–:@0.312399:0.310719:0.350189:0.310719:0.350189:0.293065:0.312399:0.293065:0.000000:0.000000:0.000000:0.000000
2,5 f(0,001:@0.351201:0.310137:0.440679:0.310137:0.440679:0.294424:0.351201:0.294424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.375443:0.310719:0.384647:0.310719:0.384647:0.293065:0.375443:0.293065:0.000000
)∙=:@0.441654:0.310719:0.469228:0.310719:0.469228:0.293065:0.441654:0.293065:0.000000:0.000000:0.000000
2,5 2,499 0,001;:@0.470241:0.310137:0.612787:0.310137:0.612787:0.294424:0.470241:0.294424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.494483:0.310719:0.503687:0.310719:0.503687:0.293065:0.494483:0.293065:0.000000
=:@0.548950:0.310719:0.564283:0.310719:0.564283:0.293065:0.548950:0.293065:0.000000
d:@0.166061:0.337499:0.175320:0.337499:0.175320:0.321093:0.166061:0.321093:0.000000
(–:@0.176351:0.338081:0.192696:0.338081:0.192696:0.320427:0.176351:0.320427:0.000000:0.000000
2,5;  2,499 9:@0.193709:0.337499:0.295777:0.337499:0.295777:0.321786:0.193709:0.321786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.227228:0.338081:0.236432:0.338081:0.236432:0.320427:0.227228:0.320427:0.000000
)=∙–:@0.296752:0.338081:0.334542:0.338081:0.334542:0.320427:0.296752:0.320427:0.000000:0.000000:0.000000:0.000000
2,5:@0.335555:0.337499:0.358785:0.337499:0.358785:0.321786:0.335555:0.321786:0.000000:0.000000:0.000000
– (:@0.359797:0.338081:0.381868:0.338081:0.381868:0.320427:0.359797:0.320427:0.000000:0.000000:0.000000
f:@0.370013:0.337499:0.374707:0.337499:0.374707:0.321093:0.370013:0.321093:0.000000
0,000 1:@0.382880:0.337499:0.441213:0.337499:0.441213:0.321786:0.382880:0.321786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)∙=:@0.442188:0.338081:0.469762:0.338081:0.469762:0.320427:0.442188:0.320427:0.000000:0.000000:0.000000
2,5 2,499 9 0,000 1;:@0.470775:0.337499:0.643453:0.337499:0.643453:0.321786:0.470775:0.321786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.495017:0.338081:0.504221:0.338081:0.504221:0.320427:0.495017:0.320427:0.000000
=:@0.564541:0.338081:0.579874:0.338081:0.579874:0.320427:0.564541:0.320427:0.000000
d:@0.126007:0.364861:0.135266:0.364861:0.135266:0.348455:0.126007:0.348455:0.000000
(–:@0.136296:0.365443:0.152642:0.365443:0.152642:0.347789:0.136296:0.347789:0.000000:0.000000
2,5;  2,499 998:@0.153654:0.364861:0.275750:0.364861:0.275750:0.349148:0.153654:0.349148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.187174:0.365443:0.196378:0.365443:0.196378:0.347789:0.187174:0.347789:0.000000
)=∙–:@0.276725:0.365443:0.314515:0.365443:0.314515:0.347789:0.276725:0.347789:0.000000:0.000000:0.000000:0.000000
2,5:@0.315528:0.364861:0.338758:0.364861:0.338758:0.349148:0.315528:0.349148:0.000000:0.000000:0.000000
– (:@0.339770:0.365443:0.361840:0.365443:0.361840:0.347789:0.339770:0.347789:0.000000:0.000000:0.000000
f:@0.349986:0.364861:0.354680:0.364861:0.354680:0.348455:0.349986:0.348455:0.000000
0,000 002:@0.362853:0.364861:0.441213:0.364861:0.441213:0.349148:0.362853:0.349148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)∙=:@0.442188:0.365443:0.469762:0.365443:0.469762:0.347789:0.442188:0.347789:0.000000:0.000000:0.000000
2,5 2,499 998 0,000 002.:@0.470775:0.364861:0.683507:0.364861:0.683507:0.349148:0.470775:0.349148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.495017:0.365443:0.504221:0.365443:0.504221:0.347789:0.495017:0.347789:0.000000
=:@0.584568:0.365443:0.599901:0.365443:0.599901:0.347789:0.584568:0.347789:0.000000
Se observa que los números reales  2,49;  2,495;  2,499 98 se aproximan cada :@0.073049:0.392223:0.657435:0.392223:0.657435:0.376510:0.073049:0.376510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.334763:0.392805:0.343967:0.392805:0.343967:0.375151:0.334763:0.375151:0.000000
–:@0.382162:0.392805:0.391366:0.392805:0.391366:0.375151:0.382162:0.375151:0.000000
–:@0.438580:0.392805:0.447784:0.392805:0.447784:0.375151:0.438580:0.375151:0.000000
vez más a  2,5. Para :@0.073031:0.408865:0.219214:0.408865:0.219214:0.393152:0.073031:0.393152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.147506:0.409447:0.156710:0.409447:0.156710:0.391793:0.147506:0.391793:0.000000
h:@0.219074:0.408865:0.228572:0.408865:0.228572:0.392459:0.219074:0.392459:0.000000
>:@0.229603:0.409447:0.244936:0.409447:0.244936:0.391793:0.229603:0.391793:0.000000
0 y :@0.245948:0.408865:0.271969:0.408865:0.271969:0.393152:0.245948:0.393152:0.000000:0.000000:0.000000:0.000000
x f h:@0.271866:0.408865:0.319062:0.408865:0.319062:0.392459:0.271866:0.392459:0.000000:0.000000:0.000000:0.000000:0.000000
= ( )=:@0.280352:0.409447:0.342568:0.409447:0.342568:0.391793:0.280352:0.391793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,5 h, se tiene :@0.343580:0.408865:0.462668:0.408865:0.462668:0.393152:0.343580:0.393152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.367823:0.409447:0.383156:0.409447:0.383156:0.391793:0.367823:0.391793:0.000000
d:@0.462510:0.408865:0.471769:0.408865:0.471769:0.392459:0.462510:0.392459:0.000000
(–:@0.472799:0.409447:0.488041:0.409447:0.488041:0.391793:0.472799:0.391793:0.000000:0.000000
2,5; :@0.487949:0.408865:0.516056:0.408865:0.516056:0.393152:0.487949:0.393152:0.000000:0.000000:0.000000:0.000000:0.000000
f h:@0.515946:0.408865:0.537206:0.408865:0.537206:0.392459:0.515946:0.392459:0.000000:0.000000:0.000000
( ))  :@0.521671:0.409447:0.559627:0.409452:0.559627:0.391798:0.521671:0.391793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= (–:@0.073086:0.426094:0.113858:0.426094:0.113858:0.408440:0.073086:0.408440:0.000000:0.000000:0.000000:0.000000
d:@0.088327:0.425512:0.097586:0.425512:0.097586:0.409105:0.088327:0.409105:0.000000
2,5;  2,5:@0.113766:0.425512:0.171896:0.425512:0.171896:0.409799:0.113766:0.409799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.141763:0.426094:0.150967:0.426094:0.150967:0.408440:0.141763:0.408440:0.000000
+ ) =∙–:@0.171804:0.426094:0.238217:0.426094:0.238217:0.408440:0.171804:0.408440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.187045:0.425512:0.196543:0.425512:0.196543:0.409105:0.187045:0.409105:0.000000
 :@0.203612:0.425512:0.207643:0.425512:0.207643:0.409799:0.203612:0.409799:0.000000
2,5:@0.239230:0.425512:0.262460:0.425512:0.262460:0.409799:0.239230:0.409799:0.000000:0.000000:0.000000
+ –(–:@0.263472:0.426094:0.316908:0.426094:0.316908:0.408440:0.263472:0.408440:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.279818:0.425512:0.289316:0.425512:0.289316:0.409105:0.279818:0.409105:0.000000
2,5:@0.317921:0.425512:0.341151:0.425512:0.341151:0.409799:0.317921:0.409799:0.000000:0.000000:0.000000
)∙=–:@0.342163:0.426094:0.379953:0.426094:0.379953:0.408440:0.342163:0.408440:0.000000:0.000000:0.000000:0.000000
2,5:@0.380966:0.425512:0.404196:0.425512:0.404196:0.409799:0.380966:0.409799:0.000000:0.000000:0.000000
+ –(:@0.405208:0.426094:0.448428:0.426094:0.448428:0.408440:0.405208:0.408440:0.000000:0.000000:0.000000:0.000000
h:@0.421554:0.425512:0.431052:0.425512:0.431052:0.409105:0.421554:0.409105:0.000000
2,5:@0.449441:0.425512:0.472671:0.425512:0.472671:0.409799:0.449441:0.409799:0.000000:0.000000:0.000000
)=:@0.473683:0.426094:0.496158:0.426094:0.496158:0.408440:0.473683:0.408440:0.000000:0.000000
h:@0.497171:0.425512:0.506669:0.425512:0.506669:0.409105:0.497171:0.409105:0.000000
.:@0.507700:0.425512:0.510903:0.425512:0.510903:0.409799:0.507700:0.409799:0.000000
Si asignamos valores a :@0.073068:0.452873:0.249580:0.452873:0.249580:0.437161:0.073068:0.437161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.251287:0.452873:0.260785:0.452873:0.260785:0.436467:0.251287:0.436467:0.000000
>:@0.262073:0.453456:0.277407:0.453456:0.277407:0.435802:0.262073:0.435802:0.000000
0 cada vez más próximos a cero, tendremos que :@0.278769:0.452873:0.657465:0.452873:0.657465:0.437161:0.278769:0.437161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.653393:0.452873:0.657424:0.452873:0.657424:0.437161:0.653393:0.437161:0.000000
x f h:@0.073086:0.469515:0.120282:0.469515:0.120282:0.453109:0.073086:0.453109:0.000000:0.000000:0.000000:0.000000:0.000000
= ( )=–:@0.081572:0.470098:0.154004:0.470098:0.154004:0.452444:0.081572:0.452444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,5:@0.155017:0.469515:0.178247:0.469515:0.178247:0.453803:0.155017:0.453803:0.000000:0.000000:0.000000
+:@0.179259:0.470098:0.194592:0.470098:0.194592:0.452444:0.179259:0.452444:0.000000
h:@0.195605:0.469515:0.205103:0.469515:0.205103:0.453109:0.195605:0.453109:0.000000
 se aproxima cada vez más a :@0.206134:0.469515:0.414831:0.469515:0.414831:0.453803:0.206134:0.453803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.414577:0.469515:0.422032:0.469515:0.422032:0.453109:0.414577:0.453109:0.000000
0:@0.423107:0.472689:0.428343:0.472689:0.428343:0.463528:0.423107:0.463528:0.000000
= ( )=–:@0.428940:0.470099:0.500857:0.470099:0.500857:0.452445:0.428940:0.452445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.445286:0.469517:0.449980:0.469517:0.449980:0.453110:0.445286:0.453110:0.000000
0:@0.458152:0.469517:0.467135:0.469517:0.467135:0.453804:0.458152:0.453804:0.000000
2,5. :@0.501871:0.469517:0.533256:0.469517:0.533256:0.453804:0.501871:0.453804:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.555025:0.469517:0.559056:0.469517:0.559056:0.453804:0.555025:0.453804:0.000000
En la tabla 4 se muestran algunos de estos valores y :@0.073086:0.486158:0.450624:0.486158:0.450624:0.470446:0.073086:0.470446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.073086:0.513520:0.082345:0.513520:0.082345:0.497114:0.073086:0.497114:0.000000
(–2,5; :@0.083376:0.513520:0.132044:0.513520:0.132044:0.497808:0.083376:0.497808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f h:@0.133020:0.513520:0.155385:0.513520:0.155385:0.497114:0.133020:0.497114:0.000000:0.000000:0.000000
( ))=∙–:@0.138745:0.514103:0.201348:0.514103:0.201348:0.496449:0.138745:0.496449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,5:@0.202360:0.513520:0.225590:0.513520:0.225590:0.497808:0.202360:0.497808:0.000000:0.000000:0.000000
–(–:@0.226602:0.514103:0.253164:0.514103:0.253164:0.496449:0.226602:0.496449:0.000000:0.000000:0.000000
2,5 h:@0.254177:0.513520:0.304631:0.513520:0.304631:0.497808:0.254177:0.497808:0.000000:0.000000:0.000000:0.000000:0.000000
+ )∙=:@0.278419:0.514103:0.333236:0.514103:0.333236:0.496449:0.278419:0.496449:0.000000:0.000000:0.000000:0.000000:0.000000
h.:@0.334248:0.513520:0.348348:0.513520:0.348348:0.497808:0.334248:0.497808:0.000000:0.000000
3.4 Noción de límite de una función real:@0.073068:0.540882:0.384736:0.540882:0.384736:0.523935:0.073068:0.523935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición precisa de límite:@0.073068:0.568244:0.278774:0.568244:0.278774:0.551575:0.073068:0.551575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En los ejercicios anteriores dimos una definición intuitiva del límite de una función :@0.073068:0.595606:0.710060:0.595606:0.710060:0.579894:0.073068:0.579894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utilizando tablas y gráficos de funciones para intuir el valor del límite, lo que permitió :@0.073068:0.612248:0.710452:0.612248:0.710452:0.596535:0.073068:0.596535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concluir que lim :@0.073068:0.628890:0.200165:0.629167:0.200165:0.613455:0.073068:0.613177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a:@0.170216:0.634512:0.193121:0.634512:0.193121:0.622580:0.170216:0.622580:0.000000:0.000000:0.000000
f x:@0.201159:0.629167:0.221480:0.629167:0.221480:0.612761:0.201159:0.612761:0.000000:0.000000:0.000000
( )=:@0.206883:0.629750:0.246496:0.629472:0.246496:0.611818:0.206883:0.612095:0.000000:0.000000:0.000000:0.000000
L:@0.246514:0.628890:0.254135:0.628890:0.254135:0.612484:0.246514:0.612484:0.000000
, significa que :@0.255258:0.628890:0.360111:0.628890:0.360111:0.613177:0.255258:0.613177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.360713:0.628890:0.381237:0.628890:0.381237:0.612484:0.360713:0.612484:0.000000:0.000000:0.000000
( ):@0.366529:0.629472:0.388489:0.629472:0.388489:0.611818:0.366529:0.611818:0.000000:0.000000:0.000000
 se acerca tanto a  , siempre y cuando   se :@0.389612:0.628890:0.710327:0.628890:0.710327:0.613177:0.389612:0.613177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.523562:0.628890:0.531182:0.628890:0.531182:0.612484:0.523562:0.612484:0.000000
x:@0.677317:0.628890:0.684772:0.628890:0.684772:0.612484:0.677317:0.612484:0.000000
acerque tanto a   sin que sea igual a  . Esto significa que :@0.073044:0.645532:0.487450:0.645532:0.487450:0.629819:0.073044:0.629819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.190887:0.645532:0.200146:0.645532:0.200146:0.629126:0.190887:0.629126:0.000000
a:@0.340225:0.645532:0.349484:0.645532:0.349484:0.629126:0.340225:0.629126:0.000000
para cualquier :@0.073026:0.672894:0.180561:0.672894:0.180561:0.657181:0.073026:0.657181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ε>:@0.180377:0.673476:0.205926:0.673476:0.205926:0.655822:0.180377:0.655822:0.000000:0.000000
0, existe un :@0.206939:0.672894:0.293107:0.672894:0.293107:0.657181:0.206939:0.657181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
δ>:@0.292956:0.673476:0.318505:0.673476:0.318505:0.655822:0.292956:0.655822:0.000000:0.000000
0, tal que,:@0.319517:0.672894:0.389763:0.672894:0.389763:0.657181:0.319517:0.657181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si 0:@0.257117:0.700256:0.280623:0.700256:0.280623:0.684543:0.257117:0.684543:0.000000:0.000000:0.000000:0.000000
<∙ – ∙<δ:@0.281617:0.700838:0.362701:0.700838:0.362701:0.683184:0.281617:0.683184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x a:@0.303061:0.700256:0.331022:0.700256:0.331022:0.683850:0.303061:0.683850:0.000000:0.000000:0.000000
 entonces :@0.363713:0.700256:0.439139:0.700256:0.439139:0.684543:0.363713:0.684543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙ ( )– ∙<ε:@0.438999:0.700838:0.522108:0.700838:0.522108:0.683184:0.438999:0.683184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x L:@0.444098:0.700256:0.490429:0.700256:0.490429:0.683850:0.444098:0.683850:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.109774:0.742520:0.117873:0.742520:0.117873:0.726807:0.109774:0.726807:0.000000
x:@0.265982:0.861084:0.273879:0.861084:0.273879:0.845371:0.265982:0.845371:0.000000
y:@0.313697:0.742520:0.321796:0.742520:0.321796:0.726807:0.313697:0.726807:0.000000
x:@0.469906:0.861084:0.477803:0.861084:0.477803:0.845371:0.469906:0.845371:0.000000
y:@0.518289:0.742520:0.526388:0.742520:0.526388:0.726807:0.518289:0.726807:0.000000
x:@0.674498:0.861084:0.682395:0.861084:0.682395:0.845371:0.674498:0.845371:0.000000
(a):@0.172422:0.888942:0.185594:0.888942:0.185594:0.877515:0.172422:0.877515:0.000000:0.000000:0.000000
(b):@0.375357:0.888942:0.389841:0.888942:0.389841:0.877515:0.375357:0.877515:0.000000:0.000000:0.000000
(c):@0.580487:0.888942:0.593499:0.888942:0.593499:0.877515:0.580487:0.877515:0.000000:0.000000:0.000000
L + ε:@0.085508:0.766161:0.110997:0.766161:0.110997:0.754734:0.085508:0.754734:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.232445:0.800927:0.239179:0.800927:0.239179:0.788996:0.232445:0.788996:0.000000
 + δ:@0.239179:0.800927:0.260089:0.800927:0.260089:0.789500:0.239179:0.789500:0.000000:0.000000:0.000000:0.000000
a:@0.138374:0.834140:0.145107:0.834140:0.145107:0.822209:0.138374:0.822209:0.000000
 − δ:@0.145107:0.834140:0.166018:0.834140:0.166018:0.822713:0.145107:0.822713:0.000000:0.000000:0.000000:0.000000
δ:@0.242954:0.876633:0.250022:0.876633:0.250022:0.865205:0.242954:0.865205:0.000000
δ:@0.181012:0.876633:0.188080:0.876633:0.188080:0.865205:0.181012:0.865205:0.000000
a:@0.212217:0.860132:0.218951:0.860132:0.218951:0.848200:0.212217:0.848200:0.000000
 :@0.218951:0.860132:0.221882:0.860132:0.221882:0.848705:0.218951:0.848705:0.000000
f x:@0.251495:0.835078:0.263878:0.835078:0.263878:0.823147:0.251495:0.823147:0.000000:0.000000:0.000000
( ):@0.254908:0.835078:0.267425:0.835078:0.267425:0.823651:0.254908:0.823651:0.000000:0.000000:0.000000
ε:@0.111653:0.780342:0.117302:0.780342:0.117302:0.768915:0.111653:0.768915:0.000000
L :@0.104839:0.790952:0.113768:0.790952:0.113768:0.779525:0.104839:0.779525:0.000000:0.000000
ε:@0.111653:0.802188:0.117302:0.802188:0.117302:0.790761:0.111653:0.790761:0.000000
L − ε:@0.085521:0.813283:0.111010:0.813283:0.111010:0.801855:0.085521:0.801855:0.000000:0.000000:0.000000:0.000000:0.000000
δ:@0.447165:0.876638:0.454233:0.876638:0.454233:0.865210:0.447165:0.865210:0.000000
δ:@0.385223:0.876638:0.392291:0.876638:0.392291:0.865210:0.385223:0.865210:0.000000
a:@0.416428:0.860137:0.423162:0.860137:0.423162:0.848205:0.416428:0.848205:0.000000
 :@0.423162:0.860137:0.426094:0.860137:0.426094:0.848710:0.423162:0.848710:0.000000
f x:@0.454166:0.835083:0.466549:0.835083:0.466549:0.823152:0.454166:0.823152:0.000000:0.000000:0.000000
( ):@0.457580:0.835083:0.470097:0.835083:0.470097:0.823656:0.457580:0.823656:0.000000:0.000000:0.000000
L + ε:@0.290536:0.775062:0.316025:0.775062:0.316025:0.763635:0.290536:0.763635:0.000000:0.000000:0.000000:0.000000:0.000000
L :@0.308769:0.790978:0.317698:0.790978:0.317698:0.779550:0.308769:0.779550:0.000000:0.000000
L − ε:@0.290536:0.805259:0.316025:0.805259:0.316025:0.793832:0.290536:0.793832:0.000000:0.000000:0.000000:0.000000:0.000000
δ:@0.651091:0.876638:0.658159:0.876638:0.658159:0.865210:0.651091:0.865210:0.000000
δ:@0.589148:0.876638:0.596217:0.876638:0.596217:0.865210:0.589148:0.865210:0.000000
a:@0.620354:0.860137:0.627087:0.860137:0.627087:0.848205:0.620354:0.848205:0.000000
 :@0.627087:0.860137:0.630019:0.860137:0.630019:0.848710:0.627087:0.848710:0.000000
f x:@0.658761:0.835083:0.671144:0.835083:0.671144:0.823152:0.658761:0.823152:0.000000:0.000000:0.000000
( ):@0.662175:0.835083:0.674692:0.835083:0.674692:0.823656:0.662175:0.823656:0.000000:0.000000:0.000000
L + ε:@0.495091:0.779631:0.520580:0.779631:0.520580:0.768203:0.495091:0.768203:0.000000:0.000000:0.000000:0.000000:0.000000
L :@0.513324:0.791220:0.522253:0.791220:0.522253:0.779792:0.513324:0.779792:0.000000:0.000000
L − ε:@0.495091:0.802607:0.520580:0.802607:0.520580:0.791179:0.495091:0.791179:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 3.1:@0.352754:0.916236:0.426707:0.916236:0.426707:0.899566:0.352754:0.899566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.710862:0.395038:0.718905:0.395038:0.718905:0.381388:0.710862:0.381388:0.000000
f h:@0.756977:0.396343:0.774116:0.396343:0.774116:0.382693:0.756977:0.382693:0.000000:0.000000:0.000000
( )=–:@0.761164:0.396819:0.798921:0.396819:0.798921:0.382375:0.761164:0.382375:0.000000:0.000000:0.000000:0.000000:0.000000
2,5:@0.798815:0.396343:0.817204:0.396343:0.817204:0.382704:0.798815:0.382704:0.000000:0.000000:0.000000
+:@0.817114:0.396819:0.829659:0.396819:0.829659:0.382375:0.817114:0.382375:0.000000
h d:@0.829569:0.396343:0.857009:0.396343:0.857009:0.382693:0.829569:0.382693:0.000000:0.000000:0.000000
(–:@0.856949:0.396819:0.869419:0.396819:0.869419:0.382375:0.856949:0.382375:0.000000:0.000000
2,5; :@0.869344:0.396343:0.893983:0.396343:0.893983:0.382704:0.869344:0.382704:0.000000:0.000000:0.000000:0.000000:0.000000
f h:@0.893907:0.396343:0.911091:0.396343:0.911091:0.382693:0.893907:0.382693:0.000000:0.000000:0.000000
( )):@0.898109:0.396819:0.920986:0.396819:0.920986:0.382375:0.898109:0.382375:0.000000:0.000000:0.000000:0.000000
0,1:@0.682277:0.418469:0.701284:0.418469:0.701284:0.405613:0.682277:0.405613:0.000000:0.000000:0.000000
–2,4:@0.756962:0.418469:0.784342:0.418469:0.784342:0.405613:0.756962:0.405613:0.000000:0.000000:0.000000:0.000000
0,1 :@0.847084:0.418469:0.869389:0.418469:0.869389:0.405613:0.847084:0.405613:0.000000:0.000000:0.000000:0.000000
0,01:@0.682277:0.439914:0.709477:0.439914:0.709477:0.427058:0.682277:0.427058:0.000000:0.000000:0.000000:0.000000
–2,49:@0.756962:0.439914:0.792535:0.439914:0.792535:0.427058:0.756962:0.427058:0.000000:0.000000:0.000000:0.000000:0.000000
0,01 :@0.847084:0.439914:0.877582:0.439914:0.877582:0.427058:0.847084:0.427058:0.000000:0.000000:0.000000:0.000000:0.000000
0,001:@0.682277:0.461360:0.717670:0.461360:0.717670:0.448504:0.682277:0.448504:0.000000:0.000000:0.000000:0.000000:0.000000
–2,499:@0.756962:0.461360:0.800728:0.461360:0.800728:0.448504:0.756962:0.448504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,001:@0.847084:0.461360:0.882476:0.461360:0.882476:0.448504:0.847084:0.448504:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 1:@0.682277:0.482805:0.730004:0.482805:0.730004:0.469949:0.682277:0.469949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2,499 9:@0.756962:0.482805:0.813063:0.482805:0.813063:0.469949:0.756962:0.469949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,0001 :@0.847084:0.482805:0.893968:0.482805:0.893968:0.469949:0.847084:0.469949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 01:@0.682277:0.504250:0.738197:0.504250:0.738197:0.491394:0.682277:0.491394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2,499 99:@0.756962:0.504250:0.821256:0.504250:0.821256:0.491394:0.756962:0.491394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 01:@0.847084:0.504250:0.903004:0.504250:0.903004:0.491394:0.847084:0.491394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 002 –2,499 998:@0.682277:0.525695:0.829448:0.525695:0.829448:0.512840:0.682277:0.512840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 002:@0.847084:0.525695:0.911197:0.525695:0.911197:0.512840:0.847084:0.512840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.859799:0.541053:0.871266:0.541053:0.871266:0.531001:0.859799:0.531001:0.000000
 :@0.871735:0.541712:0.874667:0.541712:0.874667:0.530284:0.871735:0.530284:0.000000
Tabla 3.4:@0.874854:0.541712:0.926951:0.541712:0.926951:0.530284:0.874854:0.530284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Del punto de vista :@0.740294:0.769197:0.864747:0.769197:0.864747:0.754913:0.740294:0.754913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intuitivo, a medida que :@0.740294:0.784326:0.895905:0.784326:0.895905:0.770042:0.740294:0.770042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙ ∙:@0.740294:0.799984:0.757212:0.799984:0.757212:0.783935:0.740294:0.783935:0.000000:0.000000:0.000000
h:@0.743925:0.799455:0.752560:0.799455:0.752560:0.784540:0.743925:0.784540:0.000000
 se hace cada vez más :@0.757128:0.799455:0.905887:0.799455:0.905887:0.785171:0.757128:0.785171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pequeño o próximo a cero, :@0.740294:0.814584:0.922666:0.814584:0.922666:0.800300:0.740294:0.800300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la distancia de :@0.740294:0.829713:0.837785:0.829713:0.837785:0.815428:0.740294:0.815428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f h:@0.837618:0.829713:0.856946:0.829713:0.856946:0.814798:0.837618:0.814798:0.000000:0.000000:0.000000
( ):@0.842822:0.830242:0.863455:0.830242:0.863455:0.814193:0.842822:0.814193:0.000000:0.000000:0.000000
 a L es :@0.863371:0.829713:0.907080:0.829713:0.907080:0.815428:0.863371:0.815428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
también muy pequeña.:@0.740277:0.844842:0.895484:0.844842:0.895484:0.830557:0.740277:0.830557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.740277:0.185245:0.880711:0.185245:0.880711:0.170961:0.740277:0.170961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.740277:0.200374:0.899051:0.200374:0.899051:0.186090:0.740277:0.186090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.740277:0.215503:0.747054:0.215503:0.747054:0.200588:0.740277:0.200588:0.000000
0 se lee “  tiende :@0.768827:0.215502:0.882431:0.215502:0.882431:0.201217:0.768827:0.201217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.824818:0.215502:0.831595:0.215502:0.831595:0.200587:0.824818:0.200587:0.000000
a cero” o también “  se :@0.740279:0.230631:0.890900:0.230631:0.890900:0.216346:0.740279:0.216346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.861633:0.230631:0.868410:0.230631:0.868410:0.215716:0.861633:0.215716:0.000000
aproxima a cero”.:@0.740279:0.245760:0.850741:0.245760:0.850741:0.231475:0.740279:0.231475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.740279:0.260888:0.747056:0.260888:0.747056:0.245974:0.740279:0.245974:0.000000
x:@0.768827:0.260888:0.775604:0.260888:0.775604:0.245974:0.768827:0.245974:0.000000
0:@0.776548:0.263772:0.781308:0.263772:0.781308:0.255445:0.776548:0.255445:0.000000
 que se lee “  tiende :@0.781265:0.260888:0.916222:0.260888:0.916222:0.246604:0.781265:0.246604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.858609:0.260888:0.865386:0.260888:0.865386:0.245974:0.858609:0.245974:0.000000
a  ” o también “  se :@0.740284:0.276017:0.875045:0.276017:0.875045:0.261733:0.740284:0.261733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.751395:0.276017:0.758172:0.276017:0.758172:0.261103:0.751395:0.261103:0.000000
0:@0.759129:0.278901:0.763890:0.278901:0.763890:0.270574:0.759129:0.270574:0.000000
x:@0.845777:0.276017:0.852555:0.276017:0.852555:0.261103:0.845777:0.261103:0.000000
aproxima a  ”.:@0.740287:0.291146:0.834825:0.291146:0.834825:0.276862:0.740287:0.276862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.816744:0.291146:0.823521:0.291146:0.823521:0.276232:0.816744:0.276232:0.000000
0:@0.824468:0.294030:0.829229:0.294030:0.829229:0.285703:0.824468:0.285703:0.000000
Competencia :@0.740295:0.729381:0.838987:0.729381:0.838987:0.713975:0.740295:0.713975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740295:0.744510:0.828910:0.744510:0.828910:0.729104:0.740295:0.729104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740295:0.145429:0.838987:0.145429:0.838987:0.130023:0.740295:0.130023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740295:0.160558:0.828910:0.160558:0.828910:0.145152:0.740295:0.145152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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