104:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Límites y continuidad de funciones:@0.073089:0.043661:0.383513:0.043661:0.383513:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Límites de funciones exponenciales::@0.073089:0.136836:0.376370:0.136836:0.376370:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función exponencial más común es :@0.073081:0.167776:0.356038:0.167776:0.356038:0.152063:0.073081:0.152063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.355706:0.167776:0.373819:0.167776:0.373819:0.151370:0.355706:0.151370:0.000000:0.000000:0.000000
( )=:@0.360327:0.168359:0.395116:0.168359:0.395116:0.150704:0.360327:0.150704:0.000000:0.000000:0.000000:0.000000
e:@0.395024:0.167776:0.402811:0.167776:0.402811:0.151370:0.395024:0.151370:0.000000
x:@0.402772:0.161710:0.407118:0.161710:0.407118:0.152145:0.402772:0.152145:0.000000
, donde e es la base del logaritmo natural.:@0.407081:0.167774:0.708579:0.167774:0.708579:0.152061:0.407081:0.152061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.198710:0.081593:0.198710:0.081593:0.182997:0.073089:0.182997:0.000000:0.000000
Límite de una función exponencial cuando :@0.103290:0.198710:0.418931:0.198710:0.418931:0.182997:0.103290:0.182997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.418570:0.198710:0.426025:0.198710:0.426025:0.182304:0.418570:0.182304:0.000000
∞:@0.454844:0.199292:0.467122:0.199292:0.467122:0.181638:0.454844:0.181638:0.000000
::@0.468134:0.198710:0.471337:0.198710:0.471337:0.182997:0.468134:0.182997:0.000000
x:@0.475335:0.238310:0.480756:0.238310:0.480756:0.226378:0.475335:0.226378:0.000000
∞:@0.491506:0.238733:0.500435:0.238733:0.500435:0.225894:0.491506:0.225894:0.000000
lim :@0.475335:0.229384:0.505283:0.229384:0.505283:0.213671:0.475335:0.213671:0.000000:0.000000:0.000000:0.000000
e:@0.506277:0.229384:0.514064:0.229384:0.514064:0.212978:0.506277:0.212978:0.000000
x:@0.515109:0.223320:0.519456:0.223320:0.519456:0.213755:0.515109:0.213755:0.000000
=∞:@0.520061:0.229966:0.548684:0.229966:0.548684:0.212312:0.520061:0.212312:0.000000:0.000000
Esto significa que, a medida que   crece indefinidamente,   también crece sin límites.:@0.073096:0.265899:0.691037:0.265892:0.691037:0.250180:0.073096:0.250186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.309924:0.265899:0.317379:0.265899:0.317379:0.249493:0.309924:0.249493:0.000000
e:@0.491769:0.265899:0.499555:0.265899:0.499555:0.249493:0.491769:0.249493:0.000000
x:@0.499495:0.259829:0.503841:0.259829:0.503841:0.250264:0.499495:0.250264:0.000000
• :@0.073089:0.296830:0.081593:0.296830:0.081593:0.281117:0.073089:0.281117:0.000000:0.000000
Límite de una función exponencial cuando :@0.103290:0.296830:0.418931:0.296830:0.418931:0.281117:0.103290:0.281117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.418570:0.296830:0.426025:0.296830:0.426025:0.280424:0.418570:0.280424:0.000000
–:@0.454844:0.296308:0.461538:0.296308:0.461538:0.283468:0.454844:0.283468:0.000000
∞:@0.462274:0.297412:0.474552:0.297412:0.474552:0.279758:0.462274:0.279758:0.000000
::@0.475564:0.296830:0.478767:0.296830:0.478767:0.281117:0.475564:0.281117:0.000000
x:@0.473556:0.336430:0.478978:0.336430:0.478978:0.324498:0.473556:0.324498:0.000000
–∞:@0.489727:0.336853:0.506087:0.336853:0.506087:0.324014:0.489727:0.324014:0.000000:0.000000
lim :@0.477114:0.327502:0.507062:0.327502:0.507062:0.311790:0.477114:0.311790:0.000000:0.000000:0.000000:0.000000
e:@0.508056:0.327502:0.515842:0.327502:0.515842:0.311096:0.508056:0.311096:0.000000
x:@0.516888:0.321439:0.521235:0.321439:0.521235:0.311874:0.516888:0.311874:0.000000
=:@0.521840:0.328085:0.537173:0.328085:0.537173:0.310431:0.521840:0.310431:0.000000
0:@0.538185:0.327502:0.547168:0.327502:0.547168:0.311790:0.538185:0.311790:0.000000
Aquí, conforme  tiende a menos infinito, el valor de e tiende a cero, pero sin llegar nunca a ser exactamente cero.:@0.073089:0.363116:0.894590:0.363116:0.894590:0.347403:0.073089:0.347403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.185153:0.363116:0.195847:0.363116:0.195847:0.346710:0.185153:0.346710:0.000000:0.000000
• :@0.073089:0.394056:0.081593:0.394056:0.081593:0.378343:0.073089:0.378343:0.000000:0.000000
Otras bases exponenciales: Si :@0.103290:0.394056:0.318648:0.394056:0.318648:0.378343:0.103290:0.378343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.318379:0.394056:0.327638:0.394056:0.327638:0.377650:0.318379:0.377650:0.000000
>:@0.327564:0.394638:0.342898:0.394638:0.342898:0.376984:0.327564:0.376984:0.000000
1, ocurre lo mismo que con  ::@0.342805:0.394056:0.560872:0.394056:0.560872:0.378343:0.342805:0.378343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.545396:0.394056:0.553182:0.394056:0.553182:0.377650:0.545396:0.377650:0.000000
x:@0.553112:0.387992:0.557716:0.387992:0.557716:0.378832:0.553112:0.378832:0.000000
x:@0.406157:0.433656:0.411579:0.433656:0.411579:0.421724:0.406157:0.421724:0.000000
∞:@0.422329:0.434080:0.431258:0.434080:0.431258:0.421240:0.422329:0.421240:0.000000
lim :@0.406157:0.424729:0.436105:0.424729:0.436105:0.409016:0.406157:0.409016:0.000000:0.000000:0.000000:0.000000
a:@0.437099:0.424729:0.446358:0.424729:0.446358:0.408323:0.437099:0.408323:0.000000
x:@0.447404:0.418665:0.451750:0.418665:0.451750:0.409100:0.447404:0.409100:0.000000
=∞:@0.452356:0.425311:0.480979:0.425311:0.480979:0.407657:0.452356:0.407657:0.000000:0.000000
      y      :@0.485526:0.430304:0.541116:0.430304:0.541116:0.414591:0.485526:0.414591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.540955:0.434550:0.546377:0.434550:0.546377:0.422618:0.540955:0.422618:0.000000
–∞:@0.557126:0.434973:0.573486:0.434973:0.573486:0.422134:0.557126:0.422134:0.000000:0.000000
lim :@0.544513:0.425622:0.574461:0.425622:0.574461:0.409910:0.544513:0.409910:0.000000:0.000000:0.000000:0.000000
a:@0.575455:0.425622:0.584714:0.425622:0.584714:0.409216:0.575455:0.409216:0.000000
x:@0.585760:0.419559:0.590106:0.419559:0.590106:0.409994:0.585760:0.409994:0.000000
=:@0.590711:0.426205:0.606045:0.426205:0.606045:0.408551:0.590711:0.408551:0.000000
0:@0.607057:0.425622:0.616040:0.425622:0.616040:0.409910:0.607057:0.409910:0.000000
Si 0:@0.073081:0.461236:0.098262:0.461236:0.098262:0.445523:0.073081:0.445523:0.000000:0.000000:0.000000:0.000000
< <:@0.098152:0.461818:0.137911:0.461818:0.137911:0.444164:0.098152:0.444164:0.000000:0.000000:0.000000
a:@0.113393:0.461236:0.122652:0.461236:0.122652:0.444830:0.113393:0.444830:0.000000
1, el comportamiento es inverso::@0.137819:0.461236:0.374454:0.461236:0.374454:0.445523:0.137819:0.445523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.406157:0.500839:0.411579:0.500839:0.411579:0.488907:0.406157:0.488907:0.000000
∞:@0.422329:0.501262:0.431258:0.501262:0.431258:0.488423:0.422329:0.488423:0.000000
lim :@0.406157:0.491911:0.436105:0.491911:0.436105:0.476199:0.406157:0.476199:0.000000:0.000000:0.000000:0.000000
a:@0.437099:0.491911:0.446358:0.491911:0.446358:0.475505:0.437099:0.475505:0.000000
x:@0.447404:0.485847:0.451750:0.485847:0.451750:0.476283:0.447404:0.476283:0.000000
=:@0.452356:0.492494:0.467689:0.492494:0.467689:0.474839:0.452356:0.474839:0.000000
0:@0.468701:0.491911:0.477684:0.491911:0.477684:0.476199:0.468701:0.476199:0.000000
      y      :@0.485526:0.497486:0.541116:0.497486:0.541116:0.481774:0.485526:0.481774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.540955:0.501732:0.546377:0.501732:0.546377:0.489801:0.540955:0.489801:0.000000
–∞:@0.557126:0.502156:0.573486:0.502156:0.573486:0.489317:0.557126:0.489317:0.000000:0.000000
lim :@0.544513:0.492805:0.574461:0.492805:0.574461:0.477092:0.544513:0.477092:0.000000:0.000000:0.000000:0.000000
a:@0.575455:0.492805:0.584714:0.492805:0.584714:0.476399:0.575455:0.476399:0.000000
x:@0.585760:0.486741:0.590106:0.486741:0.590106:0.477176:0.585760:0.477176:0.000000
=∞:@0.590711:0.493388:0.619335:0.493388:0.619335:0.475733:0.590711:0.475733:0.000000:0.000000
2.  Límites de funciones logarítmicas::@0.073089:0.528421:0.360411:0.528421:0.360411:0.511752:0.073089:0.511752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función logaritmica más común es :@0.073081:0.559361:0.348925:0.559361:0.348925:0.543648:0.073081:0.543648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.348601:0.559361:0.366714:0.559361:0.366714:0.542955:0.348601:0.542955:0.000000:0.000000:0.000000
( )= ( ):@0.353221:0.559944:0.420666:0.559944:0.420666:0.542289:0.353221:0.542289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In x:@0.387919:0.559361:0.414610:0.559361:0.414610:0.542955:0.387919:0.542955:0.000000:0.000000:0.000000:0.000000
, que es el logaritmo natural de   (base  ).:@0.420574:0.559361:0.718753:0.559361:0.718753:0.543648:0.420574:0.543648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.648971:0.559361:0.656426:0.559361:0.656426:0.542955:0.648971:0.542955:0.000000
e:@0.703033:0.559361:0.710819:0.559361:0.710819:0.542955:0.703033:0.542955:0.000000
• :@0.073089:0.590295:0.081593:0.590295:0.081593:0.574582:0.073089:0.574582:0.000000:0.000000
Límite de una función logarítmica cuando :@0.103290:0.590295:0.411818:0.590295:0.411818:0.574582:0.103290:0.574582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.411465:0.590295:0.418919:0.590295:0.418919:0.573889:0.411465:0.573889:0.000000
∞:@0.447739:0.590877:0.460017:0.590877:0.460017:0.573223:0.447739:0.573223:0.000000
::@0.461029:0.590295:0.464232:0.590295:0.464232:0.574582:0.461029:0.574582:0.000000
x:@0.449126:0.629895:0.454548:0.629895:0.454548:0.617963:0.449126:0.617963:0.000000
∞:@0.465298:0.630318:0.474227:0.630318:0.474227:0.617479:0.465298:0.617479:0.000000
lim :@0.449126:0.620967:0.479075:0.620967:0.479075:0.605255:0.449126:0.605255:0.000000:0.000000:0.000000:0.000000
In x:@0.480069:0.620967:0.510073:0.620967:0.510073:0.604561:0.480069:0.604561:0.000000:0.000000:0.000000:0.000000
( )=∞:@0.495476:0.621550:0.546869:0.621550:0.546869:0.603896:0.495476:0.603896:0.000000:0.000000:0.000000:0.000000:0.000000
Esto indica que el logaritmo natural crece indefinidamente a medida que aumenta.:@0.073084:0.657482:0.675248:0.657482:0.675248:0.641770:0.073084:0.641770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.688413:0.081593:0.688413:0.081593:0.672701:0.073089:0.672701:0.000000:0.000000
Límite de una función logarítmica cuando :@0.103290:0.688413:0.411818:0.688413:0.411818:0.672701:0.103290:0.672701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.411465:0.688413:0.418919:0.688413:0.418919:0.672007:0.411465:0.672007:0.000000
∞:@0.447739:0.688996:0.460017:0.688996:0.460017:0.671342:0.447739:0.671342:0.000000
+:@0.461029:0.682689:0.469968:0.682689:0.469968:0.672397:0.461029:0.672397:0.000000
::@0.469915:0.688413:0.473117:0.688413:0.473117:0.672701:0.469915:0.672701:0.000000
x:@0.443137:0.728015:0.448559:0.728015:0.448559:0.716083:0.443137:0.716083:0.000000
∞:@0.459310:0.728438:0.468240:0.728438:0.468240:0.715599:0.459310:0.715599:0.000000
+:@0.468976:0.723852:0.475477:0.723852:0.475477:0.716366:0.468976:0.716366:0.000000
lim :@0.446932:0.719087:0.476881:0.719087:0.476881:0.703375:0.446932:0.703375:0.000000:0.000000:0.000000:0.000000
In x:@0.477875:0.719087:0.507879:0.719087:0.507879:0.702681:0.477875:0.702681:0.000000:0.000000:0.000000:0.000000
( )=–∞:@0.493282:0.719670:0.554891:0.719670:0.554891:0.702016:0.493282:0.702016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aquí, conforme   se aproxima a cero por la derecha (valores positivos cercanos a 0), el valor del logaritmo natural tiende :@0.073081:0.755602:0.931411:0.755602:0.931411:0.739890:0.073081:0.739890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.188034:0.755602:0.195489:0.755602:0.195489:0.739196:0.188034:0.739196:0.000000
a menos infinito.:@0.073081:0.772244:0.193175:0.772244:0.193175:0.756531:0.073081:0.756531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.834111:0.081593:0.834111:0.081593:0.818399:0.073089:0.818399:0.000000:0.000000
Límite de una función logarítmica cuando :@0.103290:0.834111:0.411818:0.834111:0.411818:0.818399:0.103290:0.818399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.411465:0.834111:0.418919:0.834111:0.418919:0.817705:0.411465:0.817705:0.000000
1::@0.447739:0.834111:0.459851:0.834111:0.459851:0.818399:0.447739:0.818399:0.000000:0.000000
x:@0.449126:0.873077:0.454548:0.873077:0.454548:0.861146:0.449126:0.861146:0.000000
1:@0.465298:0.873077:0.471831:0.873077:0.471831:0.861650:0.465298:0.861650:0.000000
lim :@0.449126:0.864785:0.479075:0.864785:0.479075:0.849073:0.449126:0.849073:0.000000:0.000000:0.000000:0.000000
In x:@0.480069:0.864785:0.510073:0.864785:0.510073:0.848379:0.480069:0.848379:0.000000:0.000000:0.000000:0.000000
( )=∞:@0.495476:0.865368:0.546869:0.865368:0.546869:0.847714:0.495476:0.847714:0.000000:0.000000:0.000000:0.000000:0.000000
El logaritmo natural de 1 siempre es cero, y este límite refleja ese comportamiento.:@0.073084:0.901300:0.670310:0.901300:0.670310:0.885588:0.073084:0.885588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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