136:@0.032380:0.974518:0.061577:0.974518:0.061577:0.956590:0.032380:0.956590:0.000000:0.000000:0.000000
Funciones:@0.073089:0.043661:0.163813:0.043661:0.163813:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las propiedades i) a vii) :@0.082576:0.293715:0.239049:0.293715:0.239049:0.278775:0.082576:0.278775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función exponencial :@0.082576:0.308843:0.256658:0.308843:0.256658:0.293904:0.082576:0.293904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de base   y de variable :@0.082576:0.323972:0.236655:0.323972:0.236655:0.309033:0.082576:0.309033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.137731:0.323972:0.146148:0.323972:0.146148:0.309058:0.137731:0.309058:0.000000
entera también se :@0.082576:0.339101:0.205948:0.339101:0.205948:0.324161:0.082576:0.324161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
verifican para la función  :@0.082576:0.354230:0.246742:0.354230:0.246742:0.339290:0.082576:0.339290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponencial de base   y :@0.082576:0.369359:0.245078:0.369359:0.245078:0.354419:0.082576:0.354419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.222103:0.369359:0.230520:0.369359:0.230520:0.354445:0.222103:0.354445:0.000000
de variable racional.:@0.082559:0.384488:0.213205:0.384488:0.213205:0.369548:0.082559:0.369548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota que: :@0.082559:0.399617:0.150632:0.399617:0.150632:0.384677:0.082559:0.384677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.082559:0.414746:0.087362:0.414746:0.087362:0.399831:0.082559:0.399831:0.000000
       :@0.087295:0.414746:0.145954:0.414746:0.145954:0.399806:0.087295:0.399806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℚ:@0.090893:0.415276:0.122285:0.415276:0.122285:0.399226:0.090893:0.399226:0.000000:0.000000:0.000000
⇔:@0.125803:0.414229:0.142368:0.414229:0.142368:0.399557:0.125803:0.399557:0.000000
∃:@0.145880:0.415091:0.156483:0.415091:0.156483:0.399845:0.145880:0.399845:0.000000
m n :@0.156404:0.414746:0.187629:0.414746:0.187629:0.399831:0.156404:0.399831:0.000000:0.000000:0.000000:0.000000
, :@0.169624:0.414746:0.176133:0.414746:0.176133:0.399806:0.169624:0.399806:0.000000:0.000000
∈ ℤ:@0.187579:0.415276:0.216780:0.415276:0.216780:0.399226:0.187579:0.399226:0.000000:0.000000:0.000000
 :@0.216696:0.414746:0.220361:0.414746:0.220361:0.399806:0.216696:0.399806:0.000000
con   ≠ 0, tal que   =   ,:@0.082574:0.435132:0.242245:0.435139:0.242245:0.420199:0.082574:0.420192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.111273:0.435132:0.119907:0.435132:0.119907:0.420218:0.111273:0.420218:0.000000
r:@0.200581:0.435132:0.205384:0.435132:0.205384:0.420218:0.200581:0.420218:0.000000
m:@0.222555:0.427353:0.236506:0.427353:0.236506:0.411693:0.222555:0.411693:0.000000
n:@0.224997:0.443742:0.234063:0.443742:0.234063:0.428082:0.224997:0.428082:0.000000
v r:@0.082571:0.450268:0.098702:0.450268:0.098702:0.435353:0.082571:0.435353:0.000000:0.000000:0.000000
( ) =   = :@0.089532:0.450268:0.149553:0.450268:0.149553:0.435328:0.089532:0.435328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.120071:0.450268:0.128488:0.450268:0.128488:0.435353:0.120071:0.435353:0.000000
r:@0.129619:0.444755:0.132419:0.444755:0.132419:0.436060:0.129619:0.436060:0.000000
a:@0.149469:0.450268:0.157886:0.450268:0.157886:0.435353:0.149469:0.435353:0.000000
        = (:@0.082584:0.465396:0.127959:0.465396:0.127959:0.450457:0.082584:0.450457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a   :@0.127832:0.465396:0.146256:0.465396:0.146256:0.450482:0.127832:0.450482:0.000000:0.000000:0.000000:0.000000
)  = (:@0.146223:0.465396:0.179811:0.465396:0.179811:0.450457:0.146223:0.450457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.150565:0.459884:0.158312:0.459884:0.158312:0.451189:0.150565:0.451189:0.000000
a:@0.179711:0.465396:0.188128:0.465396:0.188128:0.450482:0.179711:0.450482:0.000000
m:@0.189247:0.459884:0.196994:0.459884:0.196994:0.451189:0.189247:0.451189:0.000000
)  .:@0.196958:0.465396:0.211433:0.465396:0.211433:0.450457:0.196958:0.450457:0.000000:0.000000:0.000000:0.000000
El grafo de   es el :@0.082582:0.480525:0.199385:0.480525:0.199385:0.465586:0.082582:0.465586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.155743:0.480525:0.162771:0.480525:0.162771:0.465611:0.155743:0.465611:0.000000
conjunto:@0.082566:0.495654:0.142834:0.495654:0.142834:0.480715:0.082566:0.480715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G v:@0.082566:0.510783:0.103801:0.510783:0.103801:0.495869:0.082566:0.495869:0.000000:0.000000:0.000000
( ) = {( ,  ) |      }.:@0.092405:0.510783:0.218142:0.510783:0.218142:0.495843:0.092405:0.495843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r a:@0.133905:0.510783:0.153484:0.510783:0.153484:0.495869:0.133905:0.495869:0.000000:0.000000:0.000000
r:@0.153445:0.505271:0.156245:0.505271:0.156245:0.496575:0.153445:0.496575:0.000000
r:@0.171220:0.510783:0.176023:0.510783:0.176023:0.495869:0.171220:0.495869:0.000000
∈ ℚ:@0.179554:0.511313:0.210946:0.511313:0.210946:0.495264:0.179554:0.495264:0.000000:0.000000:0.000000
Escribe  las propiedades :@0.082581:0.525912:0.244386:0.525912:0.244386:0.510972:0.082581:0.510972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de   con       y   > 0, :@0.082581:0.541041:0.240902:0.541041:0.240902:0.526101:0.082581:0.526101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.103247:0.541041:0.111664:0.541041:0.111664:0.526127:0.103247:0.526127:0.000000
r:@0.111596:0.535529:0.114396:0.535529:0.114396:0.526833:0.111596:0.526833:0.000000
r:@0.146657:0.541041:0.151460:0.541041:0.151460:0.526127:0.146657:0.526127:0.000000
∈ ℚ:@0.154990:0.541571:0.186383:0.541571:0.186383:0.525521:0.154990:0.525521:0.000000:0.000000:0.000000
a:@0.200774:0.541041:0.209191:0.541041:0.209191:0.526127:0.200774:0.526127:0.000000
a:@0.082583:0.556170:0.091000:0.556170:0.091000:0.541255:0.082583:0.541255:0.000000
 ≠ 1.:@0.090933:0.556170:0.119046:0.556170:0.119046:0.541230:0.090933:0.541230:0.000000:0.000000:0.000000:0.000000:0.000000
7.1 Función exponencial. Propiedades :@0.293662:0.244049:0.597764:0.244049:0.597764:0.227102:0.293662:0.227102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dos funciones muy importantes que intervienen en muchos campos de la ciencia, la :@0.293662:0.271411:0.930985:0.271411:0.930985:0.254977:0.293662:0.254977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
industria y el comercio son la exponencial y la logarítmica, una inversa de la otra, que nos :@0.293662:0.288052:0.930752:0.288052:0.930752:0.271619:0.293662:0.271619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proponemos estudiar a continuación.:@0.293662:0.304694:0.566487:0.304694:0.566487:0.288261:0.293662:0.288261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición  :@0.293662:0.337451:0.375666:0.337451:0.375666:0.321017:0.293662:0.321017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.367898:0.337451:0.371709:0.337451:0.371709:0.320781:0.367898:0.320781:0.000000
Sea   > 0 con   ≠ 1 fijo. La función  : :@0.375592:0.337451:0.643639:0.337451:0.643639:0.321017:0.375592:0.321017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.405210:0.337451:0.414469:0.337451:0.414469:0.321045:0.405210:0.321045:0.000000
a:@0.477624:0.337451:0.486883:0.337451:0.486883:0.321045:0.477624:0.321045:0.000000
u:@0.627238:0.337451:0.636552:0.337451:0.636552:0.321045:0.627238:0.321045:0.000000
ℤ:@0.652362:0.331691:0.663524:0.331691:0.663524:0.315641:0.652362:0.315641:0.000000
   :@0.663524:0.331476:0.686498:0.331476:0.686498:0.315043:0.663524:0.315043:0.000000:0.000000:0.000000
:@0.667555:0.330669:0.682465:0.330669:0.682465:0.316310:0.667555:0.316310:0.000000
ℝ:@0.686498:0.331691:0.698580:0.331691:0.698580:0.315641:0.686498:0.315641:0.000000
n:@0.652362:0.348118:0.661860:0.348118:0.661860:0.331712:0.652362:0.331712:0.000000
   :@0.661860:0.348118:0.684834:0.348118:0.684834:0.331684:0.661860:0.331684:0.000000:0.000000:0.000000
:@0.665892:0.347311:0.680801:0.347311:0.680801:0.332951:0.665892:0.332951:0.000000
a:@0.684834:0.348118:0.694093:0.348118:0.694093:0.331712:0.684834:0.331712:0.000000
n:@0.694093:0.342054:0.699631:0.342054:0.699631:0.332490:0.694093:0.332490:0.000000
 se llama :@0.707576:0.337452:0.774468:0.337452:0.774468:0.321018:0.707576:0.321018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función exponencial de base   y de variable entera.:@0.293662:0.364815:0.665216:0.364815:0.665216:0.348382:0.293662:0.348382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.506707:0.364815:0.515966:0.364815:0.515966:0.348409:0.506707:0.348409:0.000000
Propiedades:@0.293643:0.392177:0.388487:0.392177:0.388487:0.375508:0.293643:0.375508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i. :@0.293662:0.419542:0.304596:0.419542:0.304596:0.403108:0.293662:0.403108:0.000000:0.000000:0.000000
u:@0.323863:0.419542:0.333177:0.419542:0.333177:0.403136:0.323863:0.403136:0.000000
(0) =   = 1, a > 0.:@0.333104:0.419542:0.458797:0.419542:0.458797:0.403108:0.333104:0.403108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.370397:0.419542:0.379655:0.419542:0.379655:0.403136:0.370397:0.403136:0.000000
0:@0.379592:0.413478:0.384829:0.413478:0.384829:0.403897:0.379592:0.403897:0.000000
ii.  Para todo      ,  ( ) =   > 0. :@0.293662:0.439758:0.545617:0.439758:0.545617:0.423324:0.293662:0.423324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.397124:0.439758:0.406622:0.439758:0.406622:0.423352:0.397124:0.423352:0.000000
∈ ℤ:@0.410451:0.440340:0.441927:0.440340:0.441927:0.422686:0.410451:0.422686:0.000000:0.000000:0.000000
u n:@0.448904:0.439758:0.472446:0.439758:0.472446:0.423352:0.448904:0.423352:0.000000:0.000000:0.000000
a:@0.495952:0.439758:0.505211:0.439758:0.505211:0.423352:0.495952:0.423352:0.000000
n:@0.505163:0.433694:0.510700:0.433694:0.510700:0.424129:0.505163:0.424129:0.000000
iii.  Para todo  ,      ,  (  +  ) = :@0.293662:0.459973:0.551064:0.459973:0.551064:0.443539:0.293662:0.443539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.397124:0.459973:0.428232:0.459973:0.428232:0.443567:0.397124:0.443567:0.000000:0.000000:0.000000
∈ ℤ:@0.432116:0.460555:0.463593:0.460555:0.463593:0.442901:0.432116:0.442901:0.000000:0.000000:0.000000
u m:@0.470569:0.459973:0.499229:0.459973:0.499229:0.443567:0.470569:0.443567:0.000000:0.000000:0.000000
n:@0.517949:0.459973:0.527447:0.459973:0.527447:0.443567:0.517949:0.443567:0.000000
a:@0.550953:0.459973:0.560212:0.459973:0.560212:0.443567:0.550953:0.443567:0.000000
m+n:@0.560180:0.453909:0.580549:0.453909:0.580549:0.444344:0.560180:0.444344:0.000000:0.000000:0.000000
 = :@0.580519:0.459973:0.599405:0.459973:0.599405:0.443539:0.580519:0.443539:0.000000:0.000000:0.000000
a a:@0.599313:0.459973:0.626244:0.459973:0.626244:0.443567:0.599313:0.443567:0.000000:0.000000:0.000000
m n:@0.608503:0.453909:0.631715:0.453909:0.631715:0.444344:0.608503:0.444344:0.000000:0.000000:0.000000
 =  ( ) ( ).:@0.631676:0.459973:0.715337:0.459973:0.715337:0.443539:0.631676:0.443539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u m u n:@0.650470:0.459973:0.707403:0.459973:0.707403:0.443567:0.650470:0.443567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iv.  Si   > 1 y  ,      , tal que   <  , entonces  ( ) = :@0.293662:0.480189:0.704786:0.480189:0.704786:0.463755:0.293662:0.463755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.340061:0.480189:0.349320:0.480189:0.349320:0.463783:0.340061:0.463783:0.000000
n n:@0.392964:0.480189:0.424191:0.480189:0.424191:0.463783:0.392964:0.463783:0.000000:0.000000:0.000000
1:@0.402397:0.483361:0.407634:0.483361:0.407634:0.473780:0.402397:0.473780:0.000000
2:@0.424116:0.483361:0.429353:0.483361:0.429353:0.473780:0.424116:0.473780:0.000000
∈ ℤ:@0.433282:0.480771:0.464777:0.480771:0.464777:0.463117:0.433282:0.463117:0.000000:0.000000:0.000000
n:@0.525871:0.480189:0.535369:0.480189:0.535369:0.463783:0.525871:0.463783:0.000000
1:@0.535301:0.483361:0.540537:0.483361:0.540537:0.473780:0.535301:0.473780:0.000000
n:@0.559322:0.480189:0.568820:0.480189:0.568820:0.463783:0.559322:0.463783:0.000000
2:@0.568762:0.483361:0.573998:0.483361:0.573998:0.473780:0.568762:0.473780:0.000000
u n:@0.652404:0.480189:0.675947:0.480189:0.675947:0.463783:0.652404:0.463783:0.000000:0.000000:0.000000
1:@0.675888:0.483361:0.681125:0.483361:0.681125:0.473780:0.675888:0.473780:0.000000
a:@0.704713:0.480189:0.713971:0.480189:0.713971:0.463783:0.704713:0.463783:0.000000
n:@0.713906:0.474125:0.719443:0.474125:0.719443:0.464560:0.713906:0.464560:0.000000
1:@0.719401:0.476647:0.724638:0.476647:0.724638:0.467067:0.719401:0.467067:0.000000
 < :@0.724596:0.480189:0.743500:0.480189:0.743500:0.463755:0.724596:0.463755:0.000000:0.000000:0.000000
a:@0.743426:0.480189:0.752685:0.480189:0.752685:0.463783:0.743426:0.463783:0.000000
n:@0.752627:0.474125:0.758164:0.474125:0.758164:0.464560:0.752627:0.464560:0.000000
2:@0.758121:0.476647:0.763358:0.476647:0.763358:0.467067:0.758121:0.467067:0.000000
 =  ( ), es decir que la :@0.763316:0.480189:0.931040:0.480189:0.931040:0.463755:0.763316:0.463755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.782147:0.480189:0.805690:0.480189:0.805690:0.463783:0.782147:0.463783:0.000000:0.000000:0.000000
2:@0.805631:0.483361:0.810868:0.483361:0.810868:0.473780:0.805631:0.473780:0.000000
función   es creciente.:@0.323784:0.496831:0.486210:0.496831:0.486210:0.480397:0.323784:0.480397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.383350:0.496831:0.392664:0.496831:0.392664:0.480425:0.383350:0.480425:0.000000
v.  Si 0 <   < 1 y  ,      , tal que   <  , se tiene  ( ) = :@0.293662:0.517045:0.733963:0.517045:0.733963:0.500612:0.293662:0.500612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.369587:0.517045:0.378846:0.517045:0.378846:0.500639:0.369587:0.500639:0.000000
n n:@0.424753:0.517045:0.456648:0.517045:0.456648:0.500639:0.424753:0.500639:0.000000:0.000000:0.000000
1:@0.434253:0.520218:0.439490:0.520218:0.439490:0.510637:0.434253:0.510637:0.000000
2:@0.456658:0.520218:0.461895:0.520218:0.461895:0.510637:0.456658:0.510637:0.000000
∈ ℤ:@0.466352:0.517628:0.498417:0.517628:0.498417:0.499974:0.466352:0.499974:0.000000:0.000000:0.000000
n:@0.561646:0.517045:0.571144:0.517045:0.571144:0.500639:0.561646:0.500639:0.000000
1:@0.571163:0.520218:0.576400:0.520218:0.576400:0.510637:0.571163:0.510637:0.000000
n:@0.596300:0.517045:0.605799:0.517045:0.605799:0.500639:0.596300:0.500639:0.000000
2:@0.605794:0.520218:0.611030:0.520218:0.611030:0.510637:0.605794:0.510637:0.000000
u n:@0.680686:0.517045:0.704376:0.517045:0.704376:0.500639:0.680686:0.500639:0.000000:0.000000:0.000000
1:@0.704390:0.520218:0.709626:0.520218:0.709626:0.510637:0.704390:0.510637:0.000000
a:@0.734405:0.517045:0.743664:0.517045:0.743664:0.500639:0.734405:0.500639:0.000000
n:@0.743662:0.510982:0.749200:0.510982:0.749200:0.501417:0.743662:0.501417:0.000000
1:@0.749200:0.513504:0.754437:0.513504:0.754437:0.503923:0.749200:0.503923:0.000000
 > :@0.754442:0.517045:0.773899:0.517045:0.773899:0.500612:0.754442:0.500612:0.000000:0.000000:0.000000
a:@0.774340:0.517045:0.783599:0.517045:0.783599:0.500639:0.774340:0.500639:0.000000
n:@0.783594:0.510982:0.789132:0.510982:0.789132:0.501417:0.783594:0.501417:0.000000
2:@0.789132:0.513504:0.794369:0.513504:0.794369:0.503923:0.789132:0.503923:0.000000
 =  ( ), esto es, la :@0.794373:0.517045:0.930905:0.517045:0.930905:0.500612:0.794373:0.500612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.814271:0.517045:0.837961:0.517045:0.837961:0.500639:0.814271:0.500639:0.000000:0.000000:0.000000
2:@0.837963:0.520218:0.843199:0.520218:0.843199:0.510637:0.837963:0.510637:0.000000
función   es decreciente.:@0.323786:0.533687:0.505004:0.533687:0.505004:0.517253:0.323786:0.517253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.383352:0.533687:0.392666:0.533687:0.392666:0.517281:0.383352:0.517281:0.000000
vi.  Para   > 1 y     :@0.293662:0.553903:0.445369:0.553903:0.445369:0.537469:0.293662:0.537469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.358598:0.553903:0.367856:0.553903:0.367856:0.537497:0.358598:0.537497:0.000000
n:@0.412457:0.553903:0.421955:0.553903:0.421955:0.537497:0.412457:0.537497:0.000000
∈ ℤ:@0.426097:0.554486:0.457831:0.554486:0.457831:0.536832:0.426097:0.536832:0.000000:0.000000:0.000000
+:@0.457761:0.546579:0.464157:0.546579:0.464157:0.536998:0.457761:0.536998:0.000000
, el número real  ( ) =   es tan grande como se quiera según   :@0.464110:0.553903:0.930951:0.553903:0.930951:0.537469:0.464110:0.537469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.581051:0.553903:0.604594:0.553903:0.604594:0.537497:0.581051:0.537497:0.000000:0.000000:0.000000
a:@0.628652:0.553903:0.637911:0.553903:0.637911:0.537497:0.628652:0.537497:0.000000
n:@0.637839:0.547839:0.643376:0.547839:0.643376:0.538275:0.637839:0.538275:0.000000
n:@0.917422:0.553903:0.926920:0.553903:0.926920:0.537497:0.917422:0.537497:0.000000
lo sea, y  (– ) = :@0.323788:0.570545:0.437747:0.570545:0.437747:0.554111:0.323788:0.554111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.382341:0.570545:0.414812:0.570545:0.414812:0.554139:0.382341:0.554139:0.000000:0.000000:0.000000
a:@0.437195:0.570545:0.446454:0.570545:0.446454:0.554139:0.437195:0.554139:0.000000
–:@0.446335:0.564481:0.451701:0.564481:0.451701:0.554900:0.446335:0.554900:0.000000
n:@0.451615:0.564481:0.457152:0.564481:0.457152:0.554917:0.451615:0.554917:0.000000
 es positivo y tan pequeño como se quiera para   suficientemente :@0.457081:0.570545:0.930954:0.570545:0.930954:0.554111:0.457081:0.554111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.797100:0.570545:0.806598:0.570545:0.806598:0.554139:0.797100:0.554139:0.000000
grande.:@0.323776:0.587187:0.378799:0.587187:0.378799:0.570753:0.323776:0.570753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vii.  Para 0 <   < 1 y      , el número real  ( ) =   es tan pequeño como se quiera para :@0.293662:0.607403:0.931033:0.607403:0.931033:0.590969:0.293662:0.590969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.384625:0.607403:0.393884:0.607403:0.393884:0.590997:0.384625:0.590997:0.000000
n:@0.435650:0.607403:0.445148:0.607403:0.445148:0.590997:0.435650:0.590997:0.000000
∈ ℤ:@0.448591:0.607985:0.479625:0.607985:0.479625:0.590331:0.448591:0.590331:0.000000:0.000000:0.000000
+:@0.479506:0.600078:0.485902:0.600078:0.485902:0.590497:0.479506:0.590497:0.000000
u n:@0.599748:0.607403:0.623254:0.607403:0.623254:0.590997:0.599748:0.590997:0.000000:0.000000:0.000000
a:@0.645858:0.607403:0.655117:0.607403:0.655117:0.590997:0.645858:0.590997:0.000000
n:@0.655050:0.601339:0.660587:0.601339:0.660587:0.591774:0.655050:0.591774:0.000000
n:@0.323778:0.624045:0.333276:0.624045:0.333276:0.607639:0.323778:0.607639:0.000000
 suficientemente grande, y  (– ) = :@0.333202:0.624045:0.586044:0.624045:0.586044:0.607611:0.333202:0.607611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.529773:0.624045:0.562428:0.624045:0.562428:0.607639:0.529773:0.607639:0.000000:0.000000:0.000000
a:@0.585934:0.624045:0.595193:0.624045:0.595193:0.607639:0.585934:0.607639:0.000000
–:@0.595158:0.617981:0.600523:0.617981:0.600523:0.608400:0.595158:0.608400:0.000000
n:@0.600480:0.617981:0.606018:0.617981:0.606018:0.608416:0.600480:0.608416:0.000000
 es tan grande según   también lo sea.:@0.605974:0.624045:0.885433:0.624045:0.885433:0.607611:0.605974:0.607611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.762049:0.624045:0.771548:0.624045:0.771548:0.607639:0.762049:0.607639:0.000000
El gráfico de   es el conjunto discreto  ( ) = {( ,  ) |      }.:@0.293658:0.651407:0.726144:0.651408:0.726144:0.634974:0.293658:0.634973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.386321:0.651407:0.395635:0.651407:0.395635:0.635001:0.386321:0.635001:0.000000
G u:@0.567595:0.651407:0.592537:0.651407:0.592537:0.635001:0.567595:0.635001:0.000000:0.000000:0.000000
n a:@0.625652:0.651407:0.651403:0.651407:0.651403:0.635001:0.625652:0.635001:0.000000:0.000000:0.000000
n:@0.651360:0.645344:0.656897:0.645344:0.656897:0.635779:0.651360:0.635779:0.000000
n:@0.673370:0.651408:0.682868:0.651408:0.682868:0.635002:0.673370:0.635002:0.000000
∈ ℤ:@0.686752:0.651991:0.718228:0.651991:0.718228:0.634336:0.686752:0.634336:0.000000:0.000000:0.000000
Ejercicio 1:@0.293665:0.678770:0.370068:0.678770:0.370068:0.662100:0.293665:0.662100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos la función definida como  ( ) = 5 ;      .  :@0.293665:0.702554:0.711853:0.702560:0.711853:0.686126:0.293665:0.686120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.587353:0.702554:0.610896:0.702554:0.610896:0.686148:0.587353:0.686148:0.000000:0.000000:0.000000
n:@0.643309:0.696496:0.648847:0.696496:0.648847:0.686932:0.643309:0.686932:0.000000
n:@0.655876:0.702560:0.665375:0.702560:0.665375:0.686154:0.655876:0.686154:0.000000
∈ ℤ:@0.669203:0.703143:0.700680:0.703143:0.700680:0.685488:0.669203:0.685488:0.000000:0.000000:0.000000
Tenemos  (0) = 5  = 1,  ( ) > 0,    :@0.293658:0.719202:0.534273:0.719202:0.534273:0.702768:0.293658:0.702768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.363845:0.719202:0.373159:0.719202:0.373159:0.702796:0.363845:0.702796:0.000000
0:@0.419283:0.713138:0.424520:0.713138:0.424520:0.703557:0.419283:0.703557:0.000000
u n:@0.459245:0.719202:0.482788:0.719202:0.482788:0.702796:0.459245:0.702796:0.000000:0.000000:0.000000
∀ ∈ ℤ:@0.534126:0.719785:0.591170:0.719785:0.591170:0.702130:0.534126:0.702130:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.546311:0.719202:0.555810:0.719202:0.555810:0.702796:0.546311:0.702796:0.000000
    , más aún,  ( ) = 5  ≥ 5,    :@0.555736:0.719202:0.775201:0.719202:0.775201:0.702768:0.555736:0.702768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.666989:0.719202:0.690532:0.719202:0.690532:0.702796:0.666989:0.702796:0.000000:0.000000:0.000000
n:@0.722947:0.713138:0.728485:0.713138:0.728485:0.703574:0.722947:0.703574:0.000000
∀ ∈ ℤ:@0.775072:0.719785:0.832116:0.719785:0.832116:0.702130:0.775072:0.702130:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.787257:0.719202:0.796755:0.719202:0.796755:0.702796:0.787257:0.702796:0.000000
   :@0.796682:0.719202:0.819912:0.719202:0.819912:0.702768:0.796682:0.702768:0.000000:0.000000:0.000000
+:@0.832009:0.711878:0.838405:0.711878:0.838405:0.702296:0.832009:0.702296:0.000000
,:@0.838358:0.719202:0.841560:0.719202:0.841560:0.702768:0.838358:0.702768:0.000000
0 <  (– ) = 5  =   < 1,    :@0.484276:0.750572:0.669941:0.750568:0.669941:0.734134:0.484276:0.734138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u n:@0.511960:0.750572:0.544615:0.750572:0.544615:0.734166:0.511960:0.734166:0.000000:0.000000:0.000000
–:@0.577057:0.744504:0.582422:0.744504:0.582422:0.734923:0.577057:0.734923:0.000000
n:@0.582379:0.744504:0.587917:0.744504:0.587917:0.734940:0.582379:0.734940:0.000000
1:@0.610474:0.743098:0.619457:0.743098:0.619457:0.726664:0.610474:0.726664:0.000000
5:@0.607713:0.759490:0.616696:0.759490:0.616696:0.743057:0.607713:0.743057:0.000000
n:@0.616689:0.753424:0.622226:0.753424:0.622226:0.743859:0.616689:0.743859:0.000000
∀ ∈ ℤ:@0.669812:0.751151:0.726856:0.751151:0.726856:0.733496:0.669812:0.733496:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.681998:0.750568:0.691496:0.750568:0.691496:0.734162:0.681998:0.734162:0.000000
   :@0.691422:0.750568:0.714652:0.750568:0.714652:0.734134:0.691422:0.734134:0.000000:0.000000:0.000000
+:@0.726748:0.743243:0.733144:0.743243:0.733144:0.733663:0.726748:0.733663:0.000000
.:@0.733096:0.750568:0.736299:0.750568:0.736299:0.734134:0.733096:0.734134:0.000000
Verifiquemos que   es estrictamente creciente. Para  , :@0.293660:0.777930:0.704622:0.777931:0.704622:0.761498:0.293660:0.761496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.428898:0.777930:0.438212:0.777930:0.438212:0.761524:0.428898:0.761524:0.000000
n n:@0.682532:0.777930:0.714820:0.777931:0.714820:0.761525:0.682532:0.761524:0.000000:0.000000:0.000000
1:@0.692067:0.781104:0.697304:0.781104:0.697304:0.771523:0.692067:0.771523:0.000000
2:@0.714868:0.781104:0.720105:0.781104:0.720105:0.771523:0.714868:0.771523:0.000000
∈ ℤ:@0.720136:0.778514:0.752551:0.778514:0.752551:0.760860:0.720136:0.760860:0.000000:0.000000:0.000000
  , tal que     <  , existe :@0.735525:0.777931:0.930971:0.777931:0.930971:0.761498:0.735525:0.761498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.826493:0.777931:0.835991:0.777931:0.835991:0.761525:0.826493:0.761525:0.000000
1:@0.836040:0.781104:0.841277:0.781104:0.841277:0.771523:0.836040:0.771523:0.000000
n:@0.861812:0.777931:0.871310:0.777931:0.871310:0.761525:0.861812:0.761525:0.000000
2:@0.871352:0.781104:0.876589:0.781104:0.876589:0.771523:0.871352:0.771523:0.000000
 :@0.926906:0.777931:0.930938:0.777931:0.930938:0.761498:0.926906:0.761498:0.000000
p:@0.293660:0.794573:0.302919:0.794573:0.302919:0.778167:0.293660:0.778167:0.000000
   :@0.302845:0.794573:0.326075:0.794573:0.326075:0.778139:0.302845:0.778139:0.000000:0.000000:0.000000
∈ ℤ:@0.306803:0.795156:0.338279:0.795156:0.338279:0.777501:0.306803:0.777501:0.000000:0.000000:0.000000
+:@0.338182:0.787249:0.344578:0.787249:0.344578:0.777668:0.338182:0.777668:0.000000
, tal que   =   +  . Luego,:@0.344531:0.794573:0.537679:0.794573:0.537679:0.778139:0.344531:0.778139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.405643:0.794573:0.415141:0.794573:0.415141:0.778167:0.405643:0.778167:0.000000
2:@0.415076:0.797746:0.420313:0.797746:0.420313:0.788165:0.415076:0.788165:0.000000
p:@0.439061:0.794573:0.448320:0.794573:0.448320:0.778167:0.439061:0.778167:0.000000
n:@0.467040:0.794573:0.476538:0.794573:0.476538:0.778167:0.467040:0.778167:0.000000
1:@0.476473:0.797746:0.481709:0.797746:0.481709:0.788165:0.476473:0.788165:0.000000
u n:@0.514463:0.814793:0.538006:0.814793:0.538006:0.798387:0.514463:0.798387:0.000000:0.000000:0.000000
( ) = 5  = 5:@0.523704:0.814793:0.614095:0.814788:0.614095:0.798354:0.523704:0.798359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.537933:0.817960:0.543170:0.817960:0.543170:0.808379:0.537933:0.808379:0.000000
n:@0.575612:0.808724:0.581150:0.808724:0.581150:0.799159:0.575612:0.799159:0.000000
2:@0.581107:0.811247:0.586344:0.811247:0.586344:0.801666:0.581107:0.801666:0.000000
p+n:@0.613993:0.808724:0.631239:0.808724:0.631239:0.799159:0.613993:0.799159:0.000000:0.000000:0.000000
1:@0.631206:0.811247:0.636443:0.811247:0.636443:0.801666:0.631206:0.801666:0.000000
 = 5 ( ).:@0.636398:0.814788:0.706125:0.814788:0.706125:0.798354:0.636398:0.798354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.664091:0.808724:0.669489:0.808724:0.669489:0.799159:0.664091:0.799159:0.000000
u n:@0.669451:0.814788:0.692994:0.814788:0.692994:0.798382:0.669451:0.798382:0.000000:0.000000:0.000000
1:@0.692927:0.817960:0.698164:0.817960:0.698164:0.808379:0.692927:0.808379:0.000000
Como 5  > 1, se sigue que  ( ) <  ( ). Así,   <      ( ) <  ( ).:@0.293655:0.842150:0.770200:0.842151:0.770200:0.825717:0.293655:0.825716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.351235:0.836087:0.356633:0.836087:0.356633:0.826523:0.351235:0.826523:0.000000
u n:@0.486310:0.842151:0.509853:0.842151:0.509853:0.825745:0.486310:0.825745:0.000000:0.000000:0.000000
1:@0.509783:0.845324:0.515020:0.845324:0.515020:0.835743:0.509783:0.835743:0.000000
u n:@0.538552:0.842151:0.562095:0.842151:0.562095:0.825745:0.538552:0.825745:0.000000:0.000000:0.000000
2:@0.562038:0.845324:0.567275:0.845324:0.567275:0.835743:0.562038:0.835743:0.000000
n:@0.607265:0.842151:0.616763:0.842151:0.616763:0.825745:0.607265:0.825745:0.000000
1:@0.616696:0.845324:0.621933:0.845324:0.621933:0.835743:0.616696:0.835743:0.000000
n:@0.640679:0.842151:0.650177:0.842151:0.650177:0.825745:0.640679:0.825745:0.000000
2:@0.650108:0.845324:0.655345:0.845324:0.655345:0.835743:0.650108:0.835743:0.000000
⇒:@0.659255:0.841735:0.677423:0.841735:0.677423:0.824747:0.659255:0.824747:0.000000
u n:@0.681288:0.842151:0.704831:0.842151:0.704831:0.825745:0.681288:0.825745:0.000000:0.000000:0.000000
1:@0.704748:0.845324:0.709985:0.845324:0.709985:0.835743:0.704748:0.835743:0.000000
u n:@0.733518:0.842151:0.757061:0.842151:0.757061:0.825745:0.733518:0.825745:0.000000:0.000000:0.000000
2:@0.757004:0.845324:0.762241:0.845324:0.762241:0.835743:0.757004:0.835743:0.000000
El grafo de   es el conjunto  ( ) = {( , 5 ) |      }.:@0.293655:0.869513:0.651915:0.869514:0.651915:0.853081:0.293655:0.853079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.374132:0.869513:0.383446:0.869513:0.383446:0.853107:0.374132:0.853107:0.000000
G u:@0.493650:0.869513:0.518592:0.869513:0.518592:0.853107:0.493650:0.853107:0.000000:0.000000:0.000000
n:@0.551706:0.869513:0.561205:0.869513:0.561205:0.853107:0.551706:0.853107:0.000000
n:@0.577132:0.863451:0.582669:0.863451:0.582669:0.853886:0.577132:0.853886:0.000000
n:@0.599142:0.869514:0.608640:0.869514:0.608640:0.853108:0.599142:0.853108:0.000000
∈ ℤ:@0.612524:0.870097:0.644000:0.870097:0.644000:0.852443:0.612524:0.852443:0.000000:0.000000:0.000000
Sea   > 0 con   ≠ 1 fijo. La función  :  :@0.293655:0.903186:0.564076:0.903186:0.564076:0.886753:0.293655:0.886753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.323272:0.903186:0.332531:0.903186:0.332531:0.886780:0.323272:0.886780:0.000000
a:@0.395687:0.903186:0.404945:0.903186:0.404945:0.886780:0.395687:0.886780:0.000000
v:@0.545301:0.903186:0.553032:0.903186:0.553032:0.886780:0.545301:0.886780:0.000000
ℚ:@0.572783:0.897195:0.588116:0.897195:0.588116:0.879541:0.572783:0.879541:0.000000
   :@0.588116:0.896613:0.612579:0.896613:0.612579:0.880179:0.588116:0.880179:0.000000:0.000000:0.000000
:@0.592147:0.896072:0.608548:0.896072:0.608548:0.880276:0.592147:0.880276:0.000000
ℝ:@0.612579:0.897195:0.625869:0.897195:0.625869:0.879541:0.612579:0.879541:0.000000
r:@0.572783:0.913255:0.578066:0.913255:0.578066:0.896849:0.572783:0.896849:0.000000
    ( )   :@0.578066:0.913255:0.649762:0.913255:0.649762:0.896821:0.578066:0.896821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.582097:0.912714:0.598498:0.912714:0.598498:0.896918:0.582097:0.896918:0.000000
v r:@0.602529:0.913255:0.620421:0.913255:0.620421:0.896849:0.602529:0.896849:0.000000:0.000000:0.000000
:@0.629330:0.912714:0.645731:0.912714:0.645731:0.896918:0.629330:0.896918:0.000000
a:@0.649762:0.913255:0.659021:0.913255:0.659021:0.896849:0.649762:0.896849:0.000000
r:@0.659049:0.907192:0.662129:0.907192:0.662129:0.897627:0.659049:0.897627:0.000000
Se llama función exponencial de base   y de variable racional (variable independiente).:@0.293662:0.937693:0.922406:0.937693:0.922406:0.921259:0.293662:0.921259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.571200:0.937693:0.580459:0.937693:0.580459:0.921287:0.571200:0.921287:0.000000
Tema 7. Función exponencial :@0.073089:0.098522:0.508266:0.098522:0.508266:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son las propiedades de la potenciación cuando las bases  ,       no nulas :@0.309882:0.174382:0.891211:0.174382:0.891211:0.158696:0.309882:0.158696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.765610:0.174382:0.790191:0.174382:0.790191:0.158722:0.765610:0.158722:0.000000:0.000000:0.000000
∈ ℝ:@0.794030:0.174754:0.823898:0.174754:0.823898:0.158705:0.794030:0.158705:0.000000:0.000000:0.000000
y los exponentes  ,      ?:@0.309889:0.190268:0.501976:0.190268:0.501976:0.174581:0.309889:0.174581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.431653:0.190268:0.461575:0.190268:0.461575:0.174608:0.431653:0.174608:0.000000:0.000000:0.000000
∈ ℝ:@0.465413:0.190640:0.495281:0.190640:0.495281:0.174590:0.465413:0.174590:0.000000:0.000000:0.000000
m:@0.160927:0.440935:0.169298:0.440935:0.169298:0.431539:0.160927:0.431539:0.000000
n:@0.162392:0.450769:0.167832:0.450769:0.167832:0.441372:0.162392:0.441372:0.000000
1:@0.138233:0.455218:0.143132:0.455218:0.143132:0.446255:0.138233:0.446255:0.000000
n:@0.138092:0.461270:0.143273:0.461270:0.143273:0.452321:0.138092:0.452321:0.000000
1:@0.202148:0.455230:0.207292:0.455230:0.207292:0.445818:0.202148:0.445818:0.000000
n:@0.202000:0.465063:0.207440:0.465063:0.207440:0.455667:0.202000:0.455667:0.000000
Competencia :@0.078581:0.257474:0.187141:0.257474:0.187141:0.240527:0.078581:0.240527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.274116:0.176057:0.274116:0.176057:0.257169:0.078581:0.257169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 3 (Ev. 1 G. 10) Reconoce la relación funcional entre variables asociadas a problemas. EC. Reconoce una función :@0.257236:0.965315:0.864422:0.965315:0.864422:0.953363:0.257236:0.953363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponencial, construye su gráfica en el plano cartesiano, describe sus características e identifica sus componentes principales.:@0.257236:0.977418:0.917767:0.977418:0.917767:0.965466:0.257236:0.965466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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