110:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
Función exponencial. Propiedades:@0.404235:0.119073:0.819510:0.119073:0.819510:0.074413:0.404235:0.074413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.74. Reconocer y graficar funciones exponenciales analizando sus características: monotonía, concavidad y comportamiento al infinito.:@0.148948:0.939630:0.750475:0.939630:0.750475:0.929588:0.148948:0.929588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos funciones muy importantes que intervienen en muchos cam-:@0.404236:0.147774:0.891817:0.147774:0.891817:0.131276:0.404236:0.131276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pos de la ciencia, la industria y el comercio son la exponencial y la :@0.404236:0.165124:0.895905:0.165124:0.895905:0.148627:0.404236:0.148627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logarítmica, una inversa de la otra, que nos proponemos estudiar a :@0.404236:0.182475:0.895859:0.182475:0.895859:0.165978:0.404236:0.165978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
continuación.:@0.404236:0.199826:0.501449:0.199826:0.501449:0.183328:0.404236:0.183328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición  :@0.404236:0.234990:0.491700:0.234990:0.491700:0.218044:0.404236:0.218044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.484322:0.234744:0.487674:0.234744:0.487674:0.218030:0.484322:0.218030:0.000000
Sea   > 0 con   ≠ 1 fijo. La función  :                   se llama :@0.491700:0.234527:0.892605:0.234527:0.892605:0.218030:0.491700:0.218030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.519963:0.234643:0.528940:0.234643:0.528940:0.218174:0.519963:0.218174:0.000000
a:@0.591762:0.234643:0.600740:0.234643:0.600740:0.218174:0.591762:0.218174:0.000000
u:@0.741085:0.234643:0.750294:0.234643:0.750294:0.218174:0.741085:0.218174:0.000000
función exponencial de base   y de variable entera.    :@0.404236:0.260785:0.802930:0.258622:0.802930:0.242125:0.404236:0.244287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.611835:0.260901:0.620812:0.260901:0.620812:0.244432:0.611835:0.244432:0.000000
Propiedades:@0.404236:0.295949:0.499482:0.295949:0.499482:0.279003:0.404236:0.279003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404236:0.313054:0.414774:0.313054:0.414774:0.296340:0.404236:0.296340:0.000000:0.000000
  (0) =   = 1, a > 0:@0.414774:0.312837:0.560525:0.312841:0.560525:0.296343:0.414774:0.296340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.427971:0.312953:0.437180:0.312953:0.437180:0.296484:0.427971:0.296484:0.000000
a:@0.476674:0.312953:0.485651:0.312953:0.485651:0.296484:0.476674:0.296484:0.000000
0:@0.485660:0.306488:0.490613:0.306488:0.490613:0.296870:0.485660:0.296870:0.000000
ii):@0.404245:0.335758:0.419041:0.335758:0.419041:0.319044:0.404245:0.319044:0.000000:0.000000:0.000000
  Para todo      ,  ( ) =   > 0. :@0.419041:0.335542:0.651490:0.335538:0.651490:0.319040:0.419041:0.319044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.501728:0.335657:0.511091:0.335657:0.511091:0.319188:0.501728:0.319188:0.000000
:@0.515174:0.335019:0.529826:0.335019:0.529826:0.321646:0.515174:0.321646:0.000000
Z:@0.533967:0.334451:0.546258:0.334451:0.546258:0.321589:0.533967:0.321589:0.000000
u n:@0.553155:0.335653:0.577680:0.335653:0.577680:0.319185:0.553155:0.319185:0.000000:0.000000:0.000000
a:@0.602724:0.335653:0.611702:0.335653:0.611702:0.319185:0.602724:0.319185:0.000000
n:@0.611547:0.329252:0.617006:0.329252:0.617006:0.319651:0.611547:0.319651:0.000000
iii):@0.404240:0.358455:0.423293:0.358455:0.423293:0.341741:0.404240:0.341741:0.000000:0.000000:0.000000:0.000000
 Para todo  ,      ,  (  +  ) = :@0.423293:0.358238:0.658363:0.358235:0.658363:0.341737:0.423293:0.341741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.501722:0.358354:0.532777:0.358354:0.532777:0.341885:0.501722:0.341885:0.000000:0.000000:0.000000
:@0.536924:0.357716:0.551576:0.357716:0.551576:0.344343:0.536924:0.344343:0.000000
Z:@0.555718:0.357148:0.568009:0.357148:0.568009:0.344285:0.555718:0.344285:0.000000
u m n:@0.574906:0.358350:0.633319:0.358350:0.633319:0.341882:0.574906:0.341882:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.658363:0.358350:0.667341:0.358350:0.667341:0.341882:0.658363:0.341882:0.000000
m+n:@0.667183:0.351949:0.687614:0.351949:0.687614:0.342348:0.667183:0.342348:0.000000:0.000000:0.000000
 = :@0.687615:0.358235:0.706707:0.358235:0.706707:0.341737:0.687615:0.341737:0.000000:0.000000:0.000000
a a:@0.706707:0.358350:0.733109:0.358350:0.733109:0.341882:0.706707:0.341882:0.000000:0.000000:0.000000
m n:@0.715529:0.351949:0.738414:0.351949:0.738414:0.342348:0.715529:0.342348:0.000000:0.000000:0.000000
 =  ( ) ( ).:@0.738415:0.358235:0.826650:0.358235:0.826650:0.341737:0.738415:0.341737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u m u n:@0.757507:0.358350:0.817942:0.358350:0.817942:0.341882:0.757507:0.341882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iv):@0.404240:0.381152:0.423042:0.381152:0.423042:0.364437:0.404240:0.364437:0.000000:0.000000:0.000000
 Si   > 1 y  ,      , tal que   <  , entonces :@0.423042:0.380935:0.751014:0.380931:0.751014:0.364434:0.423042:0.364437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443926:0.381051:0.452904:0.381051:0.452904:0.364582:0.443926:0.364582:0.000000
n n:@0.496597:0.381051:0.527177:0.381047:0.527177:0.364578:0.496597:0.364582:0.000000:0.000000:0.000000
1:@0.505963:0.384208:0.510917:0.384208:0.510917:0.374590:0.505963:0.374590:0.000000
2:@0.527177:0.384208:0.532130:0.384208:0.532130:0.374590:0.527177:0.374590:0.000000
:@0.536272:0.380413:0.550924:0.380413:0.550924:0.367039:0.536272:0.367039:0.000000
Z:@0.555066:0.379844:0.567358:0.379844:0.567358:0.366982:0.555066:0.366982:0.000000
n:@0.627541:0.381047:0.636904:0.381047:0.636904:0.364578:0.627541:0.364578:0.000000
1:@0.636904:0.384208:0.641857:0.384208:0.641857:0.374590:0.636904:0.374590:0.000000
n:@0.660947:0.381047:0.670310:0.381047:0.670310:0.364578:0.660947:0.364578:0.000000
2:@0.670311:0.384208:0.675264:0.384208:0.675264:0.374590:0.670311:0.374590:0.000000
u n:@0.427974:0.398398:0.452499:0.398398:0.452499:0.381929:0.427974:0.381929:0.000000:0.000000:0.000000
( ) =   <   =  ( ), es decir que la función   es creciente.:@0.437183:0.398282:0.865163:0.398282:0.865163:0.381784:0.437183:0.381784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.452503:0.401559:0.457456:0.401559:0.457456:0.391941:0.452503:0.391941:0.000000
a:@0.482502:0.398398:0.491479:0.398398:0.491479:0.381929:0.482502:0.381929:0.000000
n:@0.491325:0.391997:0.496784:0.391997:0.496784:0.382395:0.491325:0.382395:0.000000
1:@0.496784:0.394441:0.501737:0.394441:0.501737:0.384823:0.496784:0.384823:0.000000
a:@0.520829:0.398398:0.529806:0.398398:0.529806:0.381929:0.520829:0.381929:0.000000
n:@0.529651:0.391997:0.535110:0.391997:0.535110:0.382395:0.529651:0.382395:0.000000
2:@0.535110:0.394441:0.540063:0.394441:0.540063:0.384823:0.535110:0.384823:0.000000
u n:@0.559155:0.398398:0.583679:0.398398:0.583679:0.381929:0.559155:0.381929:0.000000:0.000000:0.000000
2:@0.583678:0.401559:0.588631:0.401559:0.588631:0.391941:0.583678:0.391941:0.000000
u:@0.765639:0.398398:0.774848:0.398398:0.774848:0.381929:0.765639:0.381929:0.000000
v):@0.404244:0.421200:0.418866:0.421200:0.418866:0.404485:0.404244:0.404485:0.000000:0.000000
  Si 0 <   < 1 y  ,      , tal que   <  , se tiene :@0.418866:0.420983:0.768160:0.420979:0.768160:0.404481:0.418866:0.404485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.471518:0.421098:0.480496:0.421098:0.480496:0.404630:0.471518:0.404630:0.000000
n n:@0.524189:0.421098:0.554763:0.421095:0.554763:0.404626:0.524189:0.404630:0.000000:0.000000:0.000000
1:@0.533551:0.424256:0.538504:0.424256:0.538504:0.414637:0.533551:0.414637:0.000000
2:@0.554763:0.424256:0.559716:0.424256:0.559716:0.414637:0.554763:0.414637:0.000000
:@0.563858:0.420460:0.578511:0.420460:0.578511:0.407087:0.563858:0.407087:0.000000
Z:@0.582653:0.419892:0.594944:0.419892:0.594944:0.407030:0.582653:0.407030:0.000000
n:@0.655128:0.421095:0.664491:0.421095:0.664491:0.404626:0.655128:0.404626:0.000000
1:@0.664490:0.424256:0.669443:0.424256:0.669443:0.414637:0.664490:0.414637:0.000000
n:@0.688535:0.421095:0.697898:0.421095:0.697898:0.404626:0.688535:0.404626:0.000000
2:@0.697897:0.424256:0.702851:0.424256:0.702851:0.414637:0.697897:0.414637:0.000000
u n:@0.427974:0.438445:0.452499:0.438445:0.452499:0.421977:0.427974:0.421977:0.000000:0.000000:0.000000
( ) =   >   =  ( ), esto es, la función   es decreciente.:@0.437183:0.438330:0.849306:0.438330:0.849306:0.421832:0.437183:0.421832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.452503:0.441606:0.457456:0.441606:0.457456:0.431988:0.452503:0.431988:0.000000
a:@0.482502:0.438445:0.491479:0.438445:0.491479:0.421977:0.482502:0.421977:0.000000
n:@0.491325:0.432044:0.496784:0.432044:0.496784:0.422443:0.491325:0.422443:0.000000
1:@0.496784:0.434489:0.501737:0.434489:0.501737:0.424871:0.496784:0.424871:0.000000
a:@0.520829:0.438445:0.529806:0.438445:0.529806:0.421977:0.520829:0.421977:0.000000
n:@0.529651:0.432044:0.535110:0.432044:0.535110:0.422443:0.529651:0.422443:0.000000
2:@0.535110:0.434489:0.540063:0.434489:0.540063:0.424871:0.535110:0.424871:0.000000
u n:@0.559155:0.438445:0.583679:0.438445:0.583679:0.421977:0.559155:0.421977:0.000000:0.000000:0.000000
2:@0.583678:0.441606:0.588631:0.441606:0.588631:0.431988:0.583678:0.431988:0.000000
u:@0.731768:0.438445:0.740977:0.438445:0.740977:0.421977:0.731768:0.421977:0.000000
vi):@0.404244:0.461247:0.423104:0.461247:0.423104:0.444533:0.404244:0.444533:0.000000:0.000000:0.000000
 Para   > 1 y      , el número real  ( ) =   es tan grande como :@0.423104:0.461030:0.895898:0.461026:0.895898:0.444529:0.423104:0.444533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.462637:0.461146:0.471614:0.461146:0.471614:0.444677:0.462637:0.444677:0.000000
n:@0.516001:0.461146:0.525364:0.461146:0.525364:0.444677:0.516001:0.444677:0.000000
:@0.529702:0.460508:0.544354:0.460508:0.544354:0.447135:0.529702:0.447135:0.000000
Z:@0.548674:0.459940:0.560965:0.459940:0.560965:0.447077:0.548674:0.447077:0.000000
+:@0.560965:0.453416:0.567266:0.453416:0.567266:0.443798:0.560965:0.443798:0.000000
u n:@0.681006:0.461142:0.705530:0.461142:0.705530:0.444673:0.681006:0.444673:0.000000:0.000000:0.000000
a:@0.730922:0.461142:0.739899:0.461142:0.739899:0.444673:0.730922:0.444673:0.000000
n:@0.739768:0.454741:0.745227:0.454741:0.745227:0.445140:0.739768:0.445140:0.000000
se quiera según   lo sea, y  (– ) = :@0.427985:0.478377:0.679503:0.478377:0.679503:0.461880:0.427985:0.461880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.543365:0.478493:0.552728:0.478493:0.552728:0.462024:0.543365:0.462024:0.000000
u n:@0.618769:0.478493:0.653793:0.478493:0.653793:0.462024:0.618769:0.462024:0.000000:0.000000:0.000000
a:@0.680167:0.478493:0.689145:0.478493:0.689145:0.462024:0.680167:0.462024:0.000000
–:@0.689148:0.472024:0.695269:0.472024:0.695269:0.462406:0.689148:0.462406:0.000000
n:@0.695269:0.472092:0.700727:0.472092:0.700727:0.462490:0.695269:0.462490:0.000000
 es positivo y tan pequeño :@0.700727:0.478377:0.895911:0.478377:0.895911:0.461880:0.700727:0.461880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como se quiera para   suficientemente grande.:@0.427989:0.495728:0.760463:0.495728:0.760463:0.479230:0.427989:0.479230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.576464:0.495844:0.585827:0.495844:0.585827:0.479375:0.576464:0.479375:0.000000
vii):@0.404254:0.518645:0.426216:0.518645:0.426216:0.501931:0.404254:0.501931:0.000000:0.000000:0.000000:0.000000
 Para 0 <   < 1 y      , el número real  ( ) =   es tan pequeño :@0.425831:0.518429:0.895937:0.518425:0.895937:0.501927:0.425831:0.501931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.491150:0.518544:0.500127:0.518544:0.500127:0.502075:0.491150:0.502075:0.000000
n:@0.545237:0.518544:0.554600:0.518544:0.554600:0.502075:0.545237:0.502075:0.000000
:@0.559089:0.517906:0.573741:0.517906:0.573741:0.504533:0.559089:0.504533:0.000000
Z:@0.578242:0.517338:0.590533:0.517338:0.590533:0.504476:0.578242:0.504476:0.000000
+:@0.590533:0.510814:0.596834:0.510814:0.596834:0.501196:0.590533:0.501196:0.000000
u n:@0.711336:0.518540:0.735861:0.518540:0.735861:0.502072:0.711336:0.502072:0.000000:0.000000:0.000000
a:@0.761638:0.518540:0.770616:0.518540:0.770616:0.502072:0.761638:0.502072:0.000000
n:@0.770420:0.512139:0.775879:0.512139:0.775879:0.502538:0.770420:0.502538:0.000000
como se quiera para   suficientemente grande, y  (– ) = :@0.427986:0.535776:0.849814:0.535776:0.849814:0.519278:0.427986:0.519278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.582320:0.535891:0.591683:0.535891:0.591683:0.519422:0.582320:0.519422:0.000000
u n:@0.788281:0.535891:0.823305:0.535891:0.823305:0.519422:0.788281:0.519422:0.000000:0.000000:0.000000
a:@0.851278:0.535891:0.860256:0.535891:0.860256:0.519422:0.851278:0.519422:0.000000
–:@0.860216:0.529423:0.866338:0.529423:0.866338:0.519804:0.860216:0.519804:0.000000
n:@0.866338:0.529490:0.871796:0.529490:0.871796:0.519889:0.866338:0.519889:0.000000
 es :@0.871796:0.535776:0.895916:0.535776:0.895916:0.519278:0.871796:0.519278:0.000000:0.000000:0.000000:0.000000
tan grande según   también lo sea.:@0.427982:0.553126:0.676386:0.553126:0.676386:0.536629:0.427982:0.536629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.555595:0.553242:0.564958:0.553242:0.564958:0.536773:0.555595:0.536773:0.000000
El gráfico de   es el conjunto discreto  ( ) = {( ,  ) |      }.:@0.404247:0.587828:0.839121:0.587828:0.839121:0.571330:0.404247:0.571330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.494811:0.587943:0.504020:0.587943:0.504020:0.571475:0.494811:0.571475:0.000000
G u:@0.672685:0.587943:0.699291:0.587943:0.699291:0.571475:0.672685:0.571475:0.000000:0.000000:0.000000
n a:@0.736145:0.587943:0.761383:0.587943:0.761383:0.571475:0.736145:0.571475:0.000000:0.000000:0.000000
n:@0.761215:0.581542:0.766673:0.581542:0.766673:0.571941:0.761215:0.571941:0.000000
n:@0.785919:0.587943:0.795282:0.587943:0.795282:0.571475:0.785919:0.571475:0.000000
:@0.799424:0.587309:0.814076:0.587309:0.814076:0.573936:0.799424:0.573936:0.000000
Z:@0.818218:0.586741:0.830509:0.586741:0.830509:0.573879:0.818218:0.573879:0.000000
Ejercicio resuelto:@0.404227:0.622905:0.522205:0.622905:0.522205:0.606118:0.404227:0.606118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos la función definida como  ( ) = 5 ;      . Tenemos :@0.404227:0.639880:0.895916:0.639880:0.895916:0.623382:0.404227:0.623382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.698712:0.639996:0.723236:0.639996:0.723236:0.623527:0.698712:0.623527:0.000000:0.000000:0.000000
n:@0.758943:0.633595:0.764402:0.633595:0.764402:0.623993:0.758943:0.623993:0.000000
n:@0.772396:0.639996:0.781759:0.639996:0.781759:0.623527:0.772396:0.623527:0.000000
:@0.786930:0.639361:0.801582:0.639361:0.801582:0.625988:0.786930:0.625988:0.000000
Z:@0.806816:0.638793:0.819108:0.638793:0.819108:0.625931:0.806816:0.625931:0.000000
u:@0.404230:0.657347:0.413439:0.657347:0.413439:0.640878:0.404230:0.640878:0.000000
(0) = 5  = 1,  ( ) > 0,    :@0.413439:0.657231:0.578259:0.657231:0.578259:0.640733:0.413439:0.640733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.461434:0.650878:0.466387:0.650878:0.466387:0.641260:0.461434:0.641260:0.000000
u n:@0.500871:0.657347:0.525395:0.657347:0.525395:0.640878:0.500871:0.640878:0.000000:0.000000:0.000000
∀:@0.578258:0.664817:0.589831:0.664817:0.589831:0.645818:0.578258:0.645818:0.000000
n:@0.589838:0.657347:0.599201:0.657347:0.599201:0.640878:0.589838:0.640878:0.000000
    , más aún,  ( ) = 5  ≥ 5,    :@0.599201:0.657231:0.818569:0.657231:0.818569:0.640733:0.599201:0.640733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.603343:0.656712:0.617996:0.656712:0.617996:0.643339:0.603343:0.643339:0.000000
Z:@0.622136:0.656144:0.634428:0.656144:0.634428:0.643282:0.622136:0.643282:0.000000
u n:@0.708136:0.657347:0.732661:0.657347:0.732661:0.640878:0.708136:0.640878:0.000000:0.000000:0.000000
n:@0.766200:0.650945:0.771659:0.650945:0.771659:0.641344:0.766200:0.641344:0.000000
∀:@0.818568:0.664817:0.830141:0.664817:0.830141:0.645818:0.818568:0.645818:0.000000
n:@0.830149:0.657347:0.839512:0.657347:0.839512:0.640878:0.830149:0.640878:0.000000
    ,:@0.839512:0.657231:0.883794:0.657231:0.883794:0.640733:0.839512:0.640733:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.843653:0.656712:0.858306:0.656712:0.858306:0.643339:0.843653:0.643339:0.000000
Z:@0.862448:0.656144:0.874739:0.656144:0.874739:0.643282:0.862448:0.643282:0.000000
+:@0.874739:0.649621:0.881040:0.649621:0.881040:0.640002:0.874739:0.640002:0.000000
0 <  (– ) = 5  =       < 1,    :@0.518159:0.681710:0.712613:0.681709:0.712613:0.665212:0.518159:0.665212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.545747:0.681826:0.580771:0.681826:0.580771:0.665357:0.545747:0.665357:0.000000:0.000000:0.000000
–:@0.614320:0.675356:0.620441:0.675356:0.620441:0.665738:0.614320:0.665738:0.000000
n:@0.620441:0.675424:0.625899:0.675424:0.625899:0.665822:0.620441:0.665822:0.000000
∀:@0.712611:0.689296:0.724184:0.689296:0.724184:0.670297:0.712611:0.670297:0.000000
n:@0.724192:0.681825:0.733555:0.681825:0.733555:0.665356:0.724192:0.665356:0.000000
    .:@0.733555:0.681709:0.777837:0.681709:0.777837:0.665212:0.733555:0.665212:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.737696:0.681191:0.752348:0.681191:0.752348:0.667817:0.737696:0.667817:0.000000
Z:@0.756491:0.680622:0.768782:0.680622:0.768782:0.667760:0.756491:0.667760:0.000000
+:@0.768782:0.674099:0.775083:0.674099:0.775083:0.664481:0.768782:0.664481:0.000000
 :@0.404226:0.699060:0.408368:0.699060:0.408368:0.682562:0.404226:0.682562:0.000000
Verifiquemos que   es estrictamente creciente. Para  ,      , tal que   :@0.404226:0.716411:0.895912:0.716411:0.895912:0.699913:0.404226:0.699913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.532513:0.716526:0.541722:0.716526:0.541722:0.700058:0.532513:0.700058:0.000000
n n:@0.768937:0.716526:0.798753:0.716526:0.798753:0.700058:0.768937:0.700058:0.000000:0.000000:0.000000
1:@0.778349:0.719687:0.783302:0.719687:0.783302:0.710069:0.778349:0.710069:0.000000
2:@0.798758:0.719687:0.803712:0.719687:0.803712:0.710069:0.798758:0.710069:0.000000
:@0.807051:0.715892:0.821703:0.715892:0.821703:0.702519:0.807051:0.702519:0.000000
Z:@0.825043:0.715324:0.837334:0.715324:0.837334:0.702462:0.825043:0.702462:0.000000
n:@0.404232:0.733877:0.413595:0.733877:0.413595:0.717408:0.404232:0.717408:0.000000
1:@0.413599:0.737038:0.418552:0.737038:0.418552:0.727420:0.413599:0.727420:0.000000
 <  , existe      , tal que   =   +  . Luego,:@0.418551:0.733761:0.742681:0.733761:0.742681:0.717264:0.418551:0.717264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.437643:0.733877:0.447006:0.733877:0.447006:0.717408:0.437643:0.717408:0.000000
2:@0.447007:0.737038:0.451960:0.737038:0.451960:0.727420:0.447007:0.727420:0.000000
p:@0.502761:0.733877:0.512028:0.733877:0.512028:0.717408:0.502761:0.717408:0.000000
:@0.516169:0.733243:0.530821:0.733243:0.530821:0.719870:0.516169:0.719870:0.000000
Z:@0.534964:0.732675:0.547255:0.732675:0.547255:0.719812:0.534964:0.719812:0.000000
+:@0.547255:0.726151:0.553556:0.726151:0.553556:0.716533:0.547255:0.716533:0.000000
n:@0.613740:0.733877:0.623103:0.733877:0.623103:0.717408:0.613740:0.717408:0.000000
2:@0.623101:0.737038:0.628054:0.737038:0.628054:0.727420:0.623101:0.727420:0.000000
p n:@0.647147:0.733877:0.684868:0.733877:0.684868:0.717408:0.647147:0.717408:0.000000:0.000000:0.000000
1:@0.684867:0.737038:0.689820:0.737038:0.689820:0.727420:0.684867:0.727420:0.000000
u n:@0.550840:0.764053:0.575364:0.764053:0.575364:0.747584:0.550840:0.747584:0.000000:0.000000:0.000000
( ) = 5  = 5:@0.560049:0.763937:0.651862:0.763937:0.651862:0.747439:0.560049:0.747440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.575369:0.767213:0.580322:0.767213:0.580322:0.757595:0.575369:0.757595:0.000000
n:@0.613862:0.757651:0.619321:0.757651:0.619321:0.748050:0.613862:0.748050:0.000000
2:@0.619321:0.760096:0.624274:0.760096:0.624274:0.750478:0.619321:0.750478:0.000000
p+n:@0.651862:0.757651:0.669069:0.757651:0.669069:0.748050:0.651862:0.748050:0.000000:0.000000:0.000000
1:@0.669069:0.760096:0.674022:0.760096:0.674022:0.750478:0.669069:0.750478:0.000000
 = 5 ( ).:@0.674020:0.763937:0.745163:0.763937:0.745163:0.747439:0.674020:0.747439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.701608:0.757651:0.707010:0.757651:0.707010:0.748050:0.701608:0.748050:0.000000
u n:@0.706977:0.764052:0.731502:0.764052:0.731502:0.747584:0.706977:0.747584:0.000000:0.000000:0.000000
1:@0.731501:0.767213:0.736454:0.767213:0.736454:0.757595:0.731501:0.757595:0.000000
 :@0.404245:0.781287:0.408387:0.781287:0.408387:0.764790:0.404245:0.764790:0.000000
Como 5  > 1, se sigue que  ( ) <  ( ). Así,   <      ( ) <  ( ).:@0.404245:0.798638:0.883645:0.798638:0.883645:0.782141:0.404245:0.782141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.461876:0.792353:0.467279:0.792353:0.467279:0.782751:0.461876:0.782751:0.000000
u n:@0.591615:0.798754:0.616140:0.798754:0.616140:0.782285:0.591615:0.782285:0.000000:0.000000:0.000000
1:@0.616139:0.801915:0.621092:0.801915:0.621092:0.792297:0.616139:0.792297:0.000000
u n:@0.646137:0.798754:0.670662:0.798754:0.670662:0.782285:0.646137:0.782285:0.000000:0.000000:0.000000
2:@0.670661:0.801915:0.675614:0.801915:0.675614:0.792297:0.670661:0.792297:0.000000
n:@0.717573:0.798754:0.726936:0.798754:0.726936:0.782285:0.717573:0.782285:0.000000
1:@0.726936:0.801915:0.731889:0.801915:0.731889:0.792297:0.726936:0.792297:0.000000
n:@0.750980:0.798754:0.760343:0.798754:0.760343:0.782285:0.750980:0.782285:0.000000
2:@0.760342:0.801915:0.765295:0.801915:0.765295:0.792297:0.760342:0.792297:0.000000
⇒:@0.769437:0.797856:0.786798:0.797856:0.786798:0.781684:0.769437:0.781684:0.000000
u n:@0.790938:0.798754:0.815462:0.798754:0.815462:0.782285:0.790938:0.782285:0.000000:0.000000:0.000000
1:@0.815462:0.801915:0.820415:0.801915:0.820415:0.792297:0.815462:0.792297:0.000000
u n:@0.845459:0.798754:0.869984:0.798754:0.869984:0.782285:0.845459:0.782285:0.000000:0.000000:0.000000
2:@0.869983:0.801915:0.874936:0.801915:0.874936:0.792297:0.869983:0.792297:0.000000
El grafo de   es el conjunto  ( ) = {( , 5 ) |      }.:@0.404229:0.833340:0.765915:0.833340:0.765915:0.816842:0.404229:0.816842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.482579:0.833455:0.491787:0.833455:0.491787:0.816987:0.482579:0.816987:0.000000
G u:@0.599786:0.833455:0.626392:0.833455:0.626392:0.816987:0.599786:0.816987:0.000000:0.000000:0.000000
n:@0.663246:0.833455:0.672609:0.833455:0.672609:0.816987:0.663246:0.816987:0.000000
n:@0.688008:0.827054:0.693467:0.827054:0.693467:0.817453:0.688008:0.817453:0.000000
n:@0.712712:0.833455:0.722075:0.833455:0.722075:0.816987:0.712712:0.816987:0.000000
:@0.726217:0.832821:0.740870:0.832821:0.740870:0.819448:0.726217:0.819448:0.000000
Z:@0.745012:0.832253:0.757303:0.832253:0.757303:0.819391:0.745012:0.819391:0.000000
 :@0.404236:0.850690:0.408378:0.850690:0.408378:0.834193:0.404236:0.834193:0.000000
Sea   > 0 con   ≠ 1 fijo. La función  : :@0.404236:0.868041:0.668301:0.868041:0.668301:0.851544:0.404236:0.851544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.432498:0.868157:0.441476:0.868157:0.441476:0.851688:0.432498:0.851688:0.000000
a:@0.504298:0.868157:0.513276:0.868157:0.513276:0.851688:0.504298:0.851688:0.000000
v:@0.653621:0.868157:0.661404:0.868157:0.661404:0.851688:0.653621:0.851688:0.000000
se llama función exponencial de base   y de variable racional (variable :@0.404236:0.902743:0.895857:0.902743:0.895857:0.886245:0.404236:0.886245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.668529:0.902858:0.677506:0.902858:0.677506:0.886390:0.668529:0.886390:0.000000
independiente).:@0.404236:0.920093:0.516647:0.920093:0.516647:0.903596:0.404236:0.903596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo se llaman estas :@0.199884:0.144338:0.349837:0.144338:0.349837:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones: :@0.153341:0.160180:0.223259:0.160180:0.223259:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.153341:0.176127:0.169523:0.176127:0.169523:0.161090:0.153341:0.161090:0.000000:0.000000:0.000000
( ) =   +           :@0.157263:0.176022:0.282794:0.176022:0.282794:0.160958:0.157263:0.160958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax b,:@0.192390:0.176127:0.235539:0.176127:0.235539:0.161090:0.192390:0.161090:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.254448:0.176127:0.261273:0.176127:0.261273:0.161090:0.254448:0.161090:0.000000
:@0.265057:0.175673:0.279012:0.175673:0.279012:0.162936:0.265057:0.162936:0.000000
:@0.282793:0.175019:0.294888:0.175019:0.294888:0.163326:0.282793:0.163326:0.000000
,:@0.294888:0.176127:0.297492:0.176127:0.297492:0.161090:0.294888:0.161090:0.000000
f x:@0.153341:0.191969:0.169524:0.191969:0.169524:0.176932:0.153341:0.176932:0.000000:0.000000:0.000000
( ) = :@0.157264:0.191864:0.192391:0.191864:0.192391:0.176800:0.157264:0.176800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.192391:0.191969:0.207431:0.191969:0.207431:0.176932:0.192391:0.176932:0.000000:0.000000
2:@0.207434:0.186063:0.211957:0.186063:0.211957:0.177281:0.207434:0.177281:0.000000
 +   +            ?:@0.211956:0.191864:0.335962:0.191864:0.335962:0.176800:0.211956:0.176800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c,:@0.229387:0.191969:0.271410:0.191969:0.271410:0.176932:0.229387:0.176932:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.290319:0.191969:0.297144:0.191969:0.297144:0.176932:0.290319:0.176932:0.000000
:@0.300924:0.191515:0.314879:0.191515:0.314879:0.178778:0.300924:0.178778:0.000000
:@0.318660:0.190861:0.330755:0.190861:0.330755:0.179168:0.318660:0.179168:0.000000
Desequilibrio cognitivo:@0.199646:0.270576:0.363493:0.270576:0.363493:0.255103:0.199646:0.255103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son las propie-:@0.199884:0.299203:0.346196:0.299203:0.346196:0.284140:0.199884:0.284140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dades de la potenciación cuan-:@0.153341:0.315045:0.355569:0.315045:0.355569:0.299982:0.153341:0.299982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do las bases  ,       no nulas y :@0.153341:0.330887:0.364333:0.330887:0.364333:0.315824:0.153341:0.315824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.233936:0.330993:0.256891:0.330993:0.256891:0.315956:0.233936:0.315956:0.000000:0.000000:0.000000
:@0.260677:0.330538:0.274631:0.330538:0.274631:0.317802:0.260677:0.317802:0.000000
:@0.278414:0.329884:0.290509:0.329884:0.290509:0.318191:0.278414:0.318191:0.000000
los exponentes  ,      ?:@0.153341:0.346729:0.321819:0.346729:0.321819:0.331666:0.153341:0.331666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.254640:0.346835:0.282995:0.346835:0.282995:0.331798:0.254640:0.331798:0.000000:0.000000:0.000000
:@0.286782:0.346380:0.300737:0.346380:0.300737:0.333644:0.286782:0.333644:0.000000
:@0.304518:0.345726:0.316613:0.345726:0.316613:0.334033:0.304518:0.334033:0.000000
Recuerda que…:@0.199644:0.468094:0.309404:0.468094:0.309404:0.452621:0.199644:0.452621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las propiedades i) a :@0.199880:0.496721:0.332418:0.496721:0.332418:0.481658:0.199880:0.481658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vii) de la función exponencial :@0.153337:0.512563:0.347635:0.512563:0.347635:0.497500:0.153337:0.497500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de base   y de variable entera :@0.153337:0.528405:0.348022:0.528405:0.348022:0.513342:0.153337:0.513342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.206580:0.528511:0.214777:0.528511:0.214777:0.513474:0.206580:0.513474:0.000000
también se verifican para la :@0.153337:0.544247:0.334319:0.544247:0.334319:0.529184:0.153337:0.529184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función  exponencial de base   :@0.153337:0.560089:0.358644:0.560089:0.358644:0.545026:0.153337:0.545026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.346666:0.560195:0.354863:0.560195:0.354863:0.545158:0.346666:0.545158:0.000000
y de variable racional.:@0.153337:0.575931:0.291735:0.575931:0.291735:0.560868:0.153337:0.560868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota que::@0.153337:0.591773:0.217627:0.591773:0.217627:0.576710:0.153337:0.576710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.189661:0.607721:0.195166:0.607721:0.195166:0.592684:0.189661:0.592684:0.000000
       :@0.195166:0.607615:0.254789:0.607615:0.254789:0.592552:0.195166:0.592552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.198951:0.607266:0.212905:0.607266:0.212905:0.594530:0.198951:0.594530:0.000000
Q:@0.216688:0.606613:0.230643:0.606613:0.230643:0.594920:0.216688:0.594920:0.000000
⇔:@0.234424:0.606877:0.251007:0.606877:0.251007:0.592245:0.234424:0.592245:0.000000
∃:@0.254788:0.613985:0.264130:0.613985:0.264130:0.597577:0.254788:0.597577:0.000000
m n :@0.264129:0.607721:0.296266:0.607721:0.296266:0.592684:0.264129:0.592684:0.000000:0.000000:0.000000:0.000000
, :@0.277638:0.607615:0.283936:0.607615:0.283936:0.592552:0.277638:0.592552:0.000000:0.000000
:@0.296265:0.607266:0.310220:0.607266:0.310220:0.594530:0.296265:0.594530:0.000000
   :@0.310220:0.607615:0.328957:0.607615:0.328957:0.592552:0.310220:0.592552:0.000000:0.000000:0.000000
Z:@0.314003:0.606613:0.325177:0.606613:0.325177:0.594920:0.314003:0.594920:0.000000
con   ≠ 0, tal que   =      ,:@0.153338:0.630586:0.313018:0.630586:0.313018:0.615523:0.153338:0.615523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.181728:0.630692:0.190277:0.630692:0.190277:0.615655:0.181728:0.615655:0.000000
r:@0.270417:0.630692:0.275923:0.630692:0.275923:0.615655:0.270417:0.615655:0.000000
v r:@0.153338:0.657227:0.171385:0.657227:0.171385:0.642190:0.153338:0.642190:0.000000:0.000000:0.000000
( ) =   = :@0.160444:0.657121:0.224326:0.657119:0.224326:0.642056:0.160444:0.642058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.194252:0.657227:0.202449:0.657227:0.202449:0.642190:0.194252:0.642190:0.000000
r:@0.203685:0.651381:0.206895:0.651381:0.206895:0.642615:0.203685:0.642615:0.000000
a:@0.224326:0.657225:0.232523:0.657225:0.232523:0.642188:0.224326:0.642188:0.000000
        = (:@0.153351:0.683654:0.201283:0.683654:0.201283:0.668591:0.153351:0.668591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a   :@0.201283:0.683760:0.222057:0.683760:0.222057:0.668723:0.201283:0.668723:0.000000:0.000000:0.000000:0.000000
)  = ( )  .:@0.222057:0.683654:0.291045:0.683653:0.291045:0.668590:0.222057:0.668591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.227485:0.677915:0.235361:0.677915:0.235361:0.669149:0.227485:0.669149:0.000000
a:@0.258227:0.683759:0.266424:0.683759:0.266424:0.668722:0.258227:0.668722:0.000000
m:@0.267654:0.677915:0.275530:0.677915:0.275530:0.669149:0.267654:0.669149:0.000000
El grafo de   es el conjunto:@0.153351:0.706624:0.326820:0.706624:0.326820:0.691561:0.153351:0.691561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.224887:0.706730:0.231994:0.706730:0.231994:0.691693:0.224887:0.691693:0.000000
G v:@0.153351:0.722572:0.176341:0.722572:0.176341:0.707535:0.153351:0.707535:0.000000:0.000000:0.000000
( ) = {( ,  ) |      }.:@0.163799:0.722466:0.299464:0.722465:0.299464:0.707402:0.163799:0.707403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r a:@0.209990:0.722572:0.229990:0.722572:0.229990:0.707535:0.209990:0.707535:0.000000:0.000000:0.000000
r:@0.229840:0.716727:0.233050:0.716727:0.233050:0.707961:0.229840:0.707961:0.000000
r:@0.250623:0.722570:0.256128:0.722570:0.256128:0.707534:0.250623:0.707534:0.000000
:@0.259909:0.722116:0.273864:0.722116:0.273864:0.709379:0.259909:0.709379:0.000000
Q:@0.277647:0.721462:0.291601:0.721462:0.291601:0.709769:0.277647:0.709769:0.000000
Escribe  las propiedades de :@0.153344:0.745436:0.331824:0.745436:0.331824:0.730372:0.153344:0.730372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.153344:0.761383:0.161541:0.761383:0.161541:0.746346:0.153344:0.746346:0.000000
r:@0.161400:0.755539:0.164610:0.755539:0.164610:0.746772:0.161400:0.746772:0.000000
 con       y   > 0,   ≠ 1.:@0.164610:0.761278:0.328049:0.761278:0.328049:0.746214:0.164610:0.746214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.196782:0.761383:0.202288:0.761383:0.202288:0.746346:0.196782:0.746346:0.000000
:@0.206069:0.760929:0.220023:0.760929:0.220023:0.748192:0.206069:0.748192:0.000000
Q:@0.223804:0.760275:0.237759:0.760275:0.237759:0.748582:0.223804:0.748582:0.000000
a:@0.252464:0.761383:0.260661:0.761383:0.260661:0.746346:0.252464:0.746346:0.000000
a:@0.292148:0.761383:0.300345:0.761383:0.300345:0.746346:0.292148:0.746346:0.000000
m:@0.295223:0.623445:0.308732:0.623445:0.308732:0.608408:0.295223:0.608408:0.000000
n:@0.297703:0.639788:0.306252:0.639788:0.306252:0.624752:0.297703:0.624752:0.000000
m:@0.232856:0.642192:0.240961:0.642192:0.240961:0.633169:0.232856:0.633169:0.000000
n:@0.234344:0.651998:0.239473:0.651998:0.239473:0.642976:0.234344:0.642976:0.000000
1:@0.212038:0.668200:0.216692:0.668200:0.216692:0.659162:0.212038:0.659162:0.000000
n:@0.211805:0.678069:0.216935:0.678069:0.216935:0.669047:0.211805:0.669047:0.000000
1:@0.282398:0.668200:0.287052:0.668200:0.287052:0.659162:0.282398:0.659162:0.000000
n:@0.282165:0.678069:0.287295:0.678069:0.287295:0.669047:0.282165:0.669047:0.000000
Z:@0.769139:0.240185:0.781430:0.240185:0.781430:0.227323:0.769139:0.227323:0.000000
   :@0.781430:0.241272:0.805858:0.241272:0.805858:0.224774:0.781430:0.224774:0.000000:0.000000:0.000000
→:@0.785572:0.249371:0.801716:0.249371:0.801716:0.229508:0.785572:0.229508:0.000000
:@0.805856:0.240185:0.819161:0.240185:0.819161:0.227323:0.805856:0.227323:0.000000
n:@0.769139:0.258738:0.778501:0.258738:0.778501:0.242269:0.769139:0.242269:0.000000
→:@0.782644:0.266721:0.798788:0.266721:0.798788:0.246859:0.782644:0.246859:0.000000
a:@0.802930:0.258738:0.811907:0.258738:0.811907:0.242269:0.802930:0.242269:0.000000
n:@0.811752:0.252337:0.817210:0.252337:0.817210:0.242736:0.811752:0.242736:0.000000
1:@0.651245:0.686819:0.659741:0.686819:0.659741:0.670321:0.651245:0.670321:0.000000
5:@0.648510:0.703158:0.657006:0.703158:0.657006:0.686660:0.648510:0.686660:0.000000
n:@0.657109:0.696880:0.662567:0.696880:0.662567:0.687278:0.657109:0.687278:0.000000
Q:@0.681168:0.860788:0.696519:0.860788:0.696519:0.847926:0.681168:0.847926:0.000000
   :@0.696519:0.861875:0.720947:0.861875:0.720947:0.845378:0.696519:0.845378:0.000000:0.000000:0.000000
→:@0.700661:0.869974:0.716805:0.869974:0.716805:0.850112:0.700661:0.850112:0.000000
:@0.720945:0.860788:0.734250:0.860788:0.734250:0.847926:0.720945:0.847926:0.000000
r:@0.681168:0.879342:0.687198:0.879342:0.687198:0.862873:0.681168:0.862873:0.000000
    ( )   :@0.687198:0.879226:0.761774:0.879226:0.761774:0.862729:0.687198:0.862729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.691340:0.887325:0.707485:0.887325:0.707485:0.867462:0.691340:0.867462:0.000000
v r:@0.711627:0.879342:0.731393:0.879342:0.731393:0.862873:0.711627:0.862873:0.000000:0.000000:0.000000
→:@0.741488:0.887325:0.757632:0.887325:0.757632:0.867462:0.741488:0.867462:0.000000
a:@0.761774:0.879342:0.770752:0.879342:0.770752:0.862873:0.761774:0.862873:0.000000
r:@0.770593:0.872942:0.774108:0.872942:0.774108:0.863341:0.770593:0.863341:0.000000