105:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos combinados de exponenciales y logarítmicas::@0.073089:0.136836:0.490849:0.136836:0.490849:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.174335:0.081593:0.174335:0.081593:0.158622:0.073089:0.158622:0.000000:0.000000
Límite cuando :@0.103290:0.174335:0.211923:0.174335:0.211923:0.158622:0.103290:0.158622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.211764:0.174335:0.219219:0.174335:0.219219:0.157928:0.211764:0.157928:0.000000
∞:@0.248301:0.174917:0.260579:0.174917:0.260579:0.157263:0.248301:0.157263:0.000000
 para :@0.261591:0.174335:0.301590:0.174335:0.301590:0.158622:0.261591:0.158622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In x:@0.308980:0.167510:0.338984:0.167510:0.338984:0.151104:0.308980:0.151104:0.000000:0.000000:0.000000:0.000000
( ):@0.324387:0.168093:0.346144:0.168093:0.346144:0.150438:0.324387:0.150438:0.000000:0.000000:0.000000
x:@0.323835:0.183278:0.331290:0.183278:0.331290:0.166872:0.323835:0.166872:0.000000
::@0.354704:0.174347:0.357906:0.174347:0.357906:0.158635:0.354704:0.158635:0.000000
In x:@0.480320:0.205008:0.510324:0.205008:0.510324:0.188602:0.480320:0.188602:0.000000:0.000000:0.000000:0.000000
( ):@0.495727:0.205591:0.517484:0.205591:0.517484:0.187937:0.495727:0.187937:0.000000:0.000000:0.000000
x:@0.495174:0.220777:0.502629:0.220777:0.502629:0.204371:0.495174:0.204371:0.000000
x:@0.444116:0.220720:0.449538:0.220720:0.449538:0.208788:0.444116:0.208788:0.000000
∞:@0.460289:0.221144:0.469218:0.221144:0.469218:0.208304:0.460289:0.208304:0.000000
lim :@0.444116:0.211262:0.474065:0.211262:0.474065:0.195549:0.444116:0.195549:0.000000:0.000000:0.000000:0.000000
     0 .:@0.504363:0.211262:0.555890:0.211428:0.555890:0.195716:0.504363:0.195549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.524579:0.211844:0.539912:0.211844:0.539912:0.194190:0.524579:0.194190:0.000000
Aunque el logaritmo crece indefinidamente, lo hace mucho más lentamente que  , por lo que este cociente tiende a :@0.073104:0.247638:0.930820:0.247638:0.930820:0.231925:0.073104:0.231925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.670585:0.247638:0.678040:0.247638:0.678040:0.231232:0.670585:0.231232:0.000000
cero.:@0.073104:0.264280:0.107826:0.264280:0.107826:0.248567:0.073104:0.248567:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.073089:0.289135:0.081593:0.289135:0.081593:0.273423:0.073089:0.273423:0.000000:0.000000
Límite cuando :@0.103290:0.289135:0.211923:0.289135:0.211923:0.273423:0.103290:0.273423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.211764:0.289135:0.219219:0.289135:0.219219:0.272729:0.211764:0.272729:0.000000
∞:@0.248301:0.289718:0.260579:0.289718:0.260579:0.272064:0.248301:0.272064:0.000000
 para :@0.261591:0.289135:0.301590:0.289135:0.301590:0.273423:0.261591:0.273423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xe:@0.301480:0.289135:0.316353:0.289135:0.316353:0.272729:0.301480:0.272729:0.000000:0.000000
–:@0.316289:0.283411:0.321655:0.283411:0.321655:0.273119:0.316289:0.273119:0.000000
x:@0.321601:0.283072:0.325948:0.283072:0.325948:0.273507:0.321601:0.273507:0.000000
::@0.325910:0.289135:0.329112:0.289135:0.329112:0.273423:0.325910:0.273423:0.000000
x:@0.456815:0.322660:0.462237:0.322660:0.462237:0.310728:0.456815:0.310728:0.000000
∞:@0.472987:0.323084:0.481916:0.323084:0.481916:0.310244:0.472987:0.310244:0.000000
lim :@0.456815:0.313734:0.486764:0.313734:0.486764:0.298021:0.456815:0.298021:0.000000:0.000000:0.000000:0.000000
xe:@0.487758:0.313734:0.502631:0.313734:0.502631:0.297328:0.487758:0.297328:0.000000:0.000000
–:@0.502581:0.308010:0.507946:0.308010:0.507946:0.297717:0.502581:0.297717:0.000000
x:@0.507893:0.307670:0.512239:0.307670:0.512239:0.298105:0.507893:0.298105:0.000000
=:@0.512201:0.314316:0.527534:0.314316:0.527534:0.296662:0.512201:0.296662:0.000000
0.:@0.528547:0.313734:0.543180:0.314261:0.543180:0.298548:0.528547:0.298021:0.000000:0.000000
Aquí, aunque   crece,   decrece mucho más rápido, por lo que el producto tiende a cero.:@0.073078:0.344161:0.724444:0.344167:0.724444:0.328454:0.073078:0.328448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.174152:0.344161:0.181607:0.344161:0.181607:0.327755:0.174152:0.327755:0.000000
e:@0.231472:0.344161:0.239258:0.344161:0.239258:0.327755:0.231472:0.327755:0.000000
–:@0.239211:0.338443:0.244577:0.338443:0.244577:0.328150:0.239211:0.328150:0.000000
x:@0.244523:0.338103:0.248870:0.338103:0.248870:0.328538:0.244523:0.328538:0.000000
Estos límites son clave para entender el comportamiento de funciones en contextos más avanzados como derivadas y :@0.073096:0.369033:0.931579:0.369033:0.931579:0.353320:0.073096:0.353320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cálculo integral.:@0.073096:0.385675:0.186849:0.385675:0.186849:0.369962:0.073096:0.369962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Revisemos algunos ejercicios resueltos sobre funciones exponenciales y logarítmicas.:@0.073096:0.410540:0.688589:0.410540:0.688589:0.394828:0.073096:0.394828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.191383:0.449498:0.196805:0.449498:0.196805:0.437567:0.191383:0.437567:0.000000
–∞:@0.207531:0.449922:0.223877:0.449922:0.223877:0.437083:0.207531:0.437083:0.000000:0.000000
lim :@0.194465:0.440229:0.224414:0.440229:0.224414:0.424517:0.194465:0.424517:0.000000:0.000000:0.000000:0.000000
e:@0.225408:0.440229:0.233194:0.440229:0.233194:0.423823:0.225408:0.423823:0.000000
x:@0.233137:0.434166:0.237483:0.434166:0.237483:0.424601:0.233137:0.424601:0.000000
Solución: :@0.081097:0.466358:0.160761:0.466358:0.160761:0.449689:0.081097:0.449689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función exponencial :@0.164666:0.466358:0.354592:0.466358:0.354592:0.450646:0.164666:0.450646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiende a cero cuanto :@0.081097:0.483000:0.235095:0.483000:0.235095:0.467288:0.081097:0.467288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.234889:0.483000:0.242344:0.483000:0.242344:0.466594:0.234889:0.466594:0.000000
–∞:@0.271433:0.483583:0.293926:0.483583:0.293926:0.465928:0.271433:0.465928:0.000000:0.000000
x:@0.172468:0.511880:0.177890:0.511880:0.177890:0.499948:0.172468:0.499948:0.000000
–∞:@0.188640:0.512304:0.204999:0.512304:0.204999:0.499464:0.188640:0.499464:0.000000:0.000000
lim :@0.175907:0.502953:0.205856:0.502953:0.205856:0.487240:0.175907:0.487240:0.000000:0.000000:0.000000:0.000000
e:@0.206850:0.502953:0.214636:0.502953:0.214636:0.486547:0.206850:0.486547:0.000000
x:@0.214578:0.496889:0.218924:0.496889:0.218924:0.487324:0.214578:0.487324:0.000000
=:@0.218887:0.503535:0.234220:0.503535:0.234220:0.485881:0.218887:0.485881:0.000000
0:@0.235232:0.502953:0.244215:0.502953:0.244215:0.487240:0.235232:0.487240:0.000000
x:@0.466384:0.451725:0.471806:0.451725:0.471806:0.439793:0.466384:0.439793:0.000000
1:@0.482555:0.451725:0.489088:0.451725:0.489088:0.440298:0.482555:0.440298:0.000000
lim :@0.466384:0.443433:0.496332:0.443433:0.496332:0.427720:0.466384:0.427720:0.000000:0.000000:0.000000:0.000000
In x:@0.497290:0.443433:0.527293:0.443433:0.527293:0.427027:0.497290:0.427027:0.000000:0.000000:0.000000:0.000000
( ):@0.512696:0.444015:0.534454:0.444015:0.534454:0.426361:0.512696:0.426361:0.000000:0.000000:0.000000
Solución: :@0.365696:0.474581:0.439395:0.474581:0.439395:0.457911:0.365696:0.457911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sabemos que :@0.439288:0.474581:0.541264:0.474581:0.541264:0.458868:0.439288:0.458868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In:@0.541099:0.474581:0.554352:0.474581:0.554352:0.458175:0.541099:0.458175:0.000000:0.000000
( )=:@0.554297:0.475163:0.590614:0.475163:0.590614:0.457509:0.554297:0.457509:0.000000:0.000000:0.000000:0.000000
1:@0.560334:0.474581:0.569317:0.474581:0.569317:0.458868:0.560334:0.458868:0.000000
0:@0.590522:0.474581:0.599505:0.474581:0.599505:0.458868:0.590522:0.458868:0.000000
x:@0.449544:0.502825:0.454966:0.502825:0.454966:0.490894:0.449544:0.490894:0.000000
1:@0.465716:0.502825:0.472249:0.502825:0.472249:0.491398:0.465716:0.491398:0.000000
lim :@0.449544:0.494534:0.479493:0.494534:0.479493:0.478821:0.449544:0.478821:0.000000:0.000000:0.000000:0.000000
In x:@0.480487:0.494534:0.510491:0.494534:0.510491:0.478127:0.480487:0.478127:0.000000:0.000000:0.000000:0.000000
( )=:@0.495894:0.495116:0.533997:0.495116:0.533997:0.477462:0.495894:0.477462:0.000000:0.000000:0.000000:0.000000
0:@0.535009:0.494534:0.543992:0.494534:0.543992:0.478821:0.535009:0.478821:0.000000
In x:@0.779843:0.443433:0.809846:0.443433:0.809846:0.427027:0.779843:0.427027:0.000000:0.000000:0.000000:0.000000
( ):@0.795249:0.444015:0.817007:0.444015:0.817007:0.426361:0.795249:0.426361:0.000000:0.000000:0.000000
x:@0.794697:0.459201:0.802152:0.459201:0.802152:0.442795:0.794697:0.442795:0.000000
x:@0.743639:0.460931:0.749061:0.460931:0.749061:0.448999:0.743639:0.448999:0.000000
∞:@0.759810:0.461355:0.768740:0.461355:0.768740:0.448515:0.759810:0.448515:0.000000
lim:@0.743639:0.450951:0.768525:0.450951:0.768525:0.435238:0.743639:0.435238:0.000000:0.000000:0.000000
Solución: :@0.650314:0.482626:0.736609:0.482626:0.736609:0.465956:0.650314:0.465956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aunque :@0.744983:0.482626:0.813916:0.482626:0.813916:0.466913:0.744983:0.466913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In x:@0.822551:0.482626:0.853272:0.482626:0.853272:0.466220:0.822551:0.466220:0.000000:0.000000:0.000000:0.000000
( ):@0.838123:0.483208:0.860525:0.483208:0.860525:0.465554:0.838123:0.465554:0.000000:0.000000:0.000000
 crece :@0.862090:0.482626:0.923772:0.482626:0.923772:0.466913:0.862090:0.466913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
indefinidamente, lo hace más :@0.650314:0.499268:0.923669:0.499268:0.923669:0.483555:0.650314:0.483555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lentamente que  , por lo que el :@0.650314:0.515909:0.923735:0.515909:0.923735:0.500197:0.650314:0.500197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.788773:0.515909:0.796228:0.515909:0.796228:0.499503:0.788773:0.499503:0.000000
cociente tiende a 0.:@0.650314:0.532551:0.792171:0.532551:0.792171:0.516839:0.650314:0.516839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
In x:@0.767746:0.552500:0.797749:0.552500:0.797749:0.536094:0.767746:0.536094:0.000000:0.000000:0.000000:0.000000
( ):@0.783153:0.553083:0.804910:0.553083:0.804910:0.535428:0.783153:0.535428:0.000000:0.000000:0.000000
x:@0.782600:0.568268:0.790055:0.568268:0.790055:0.551862:0.782600:0.551862:0.000000
x:@0.731544:0.569998:0.736965:0.569998:0.736965:0.558066:0.731544:0.558066:0.000000
∞:@0.747715:0.570422:0.756644:0.570422:0.756644:0.557582:0.747715:0.557582:0.000000
lim :@0.731544:0.560541:0.761492:0.560541:0.761492:0.544828:0.731544:0.544828:0.000000:0.000000:0.000000:0.000000
     0:@0.791791:0.560541:0.837333:0.560541:0.837333:0.544828:0.791791:0.544828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.812005:0.561124:0.827338:0.561124:0.827338:0.543469:0.812005:0.543469:0.000000
x:@0.184375:0.604941:0.189796:0.604941:0.189796:0.593009:0.184375:0.593009:0.000000
∞:@0.200546:0.605364:0.209475:0.605364:0.209475:0.592525:0.200546:0.592525:0.000000
lim :@0.185086:0.596514:0.215034:0.596514:0.215034:0.580801:0.185086:0.580801:0.000000:0.000000:0.000000:0.000000
xe:@0.216028:0.596514:0.230901:0.596514:0.230901:0.580108:0.216028:0.580108:0.000000:0.000000
–:@0.230851:0.590790:0.236217:0.590790:0.236217:0.580497:0.230851:0.580497:0.000000
x:@0.236163:0.590450:0.240767:0.590450:0.240767:0.581290:0.236163:0.581290:0.000000
Solución: :@0.081097:0.621801:0.159438:0.621801:0.159438:0.605131:0.081097:0.605131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.162475:0.621801:0.170261:0.621801:0.170261:0.605395:0.162475:0.605395:0.000000
–:@0.170634:0.616076:0.176000:0.616076:0.176000:0.605784:0.170634:0.605784:0.000000
x:@0.176301:0.615737:0.180904:0.615737:0.180904:0.606576:0.176301:0.606576:0.000000
  decrece mucho  más :@0.181172:0.621801:0.354616:0.621801:0.354616:0.606088:0.181172:0.606088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rápido que   crece, por lo que el :@0.081091:0.638443:0.354647:0.638443:0.354647:0.622730:0.081091:0.622730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.176147:0.638443:0.183601:0.638443:0.183601:0.622036:0.176147:0.622036:0.000000
producto tiende a 0.:@0.081091:0.655084:0.228327:0.655084:0.228327:0.639372:0.081091:0.639372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.173610:0.683462:0.179031:0.683462:0.179031:0.671531:0.173610:0.671531:0.000000
∞:@0.189781:0.683886:0.198710:0.683886:0.198710:0.671047:0.189781:0.671047:0.000000
lim :@0.174321:0.675037:0.204269:0.675037:0.204269:0.659324:0.174321:0.659324:0.000000:0.000000:0.000000:0.000000
xe:@0.205263:0.675037:0.220137:0.675037:0.220137:0.658631:0.205263:0.658631:0.000000:0.000000
–:@0.220086:0.669313:0.225452:0.669313:0.225452:0.659020:0.220086:0.659020:0.000000
x:@0.225398:0.668973:0.230002:0.668973:0.230002:0.659813:0.225398:0.659813:0.000000
=:@0.229956:0.675619:0.245289:0.675619:0.245289:0.657965:0.229956:0.657965:0.000000
0:@0.246302:0.675037:0.255284:0.675037:0.255284:0.659324:0.246302:0.659324:0.000000
x:@0.457846:0.605972:0.463268:0.605972:0.463268:0.594040:0.457846:0.594040:0.000000
0:@0.474018:0.605972:0.480551:0.605972:0.480551:0.594545:0.474018:0.594545:0.000000
+:@0.481295:0.601809:0.487797:0.601809:0.487797:0.594324:0.481295:0.594324:0.000000
lim :@0.460217:0.596514:0.490166:0.596514:0.490166:0.580801:0.460217:0.580801:0.000000:0.000000:0.000000:0.000000
x In x:@0.491160:0.596514:0.534012:0.596514:0.534012:0.580108:0.491160:0.580108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.519415:0.597096:0.541172:0.597096:0.541172:0.579442:0.519415:0.579442:0.000000:0.000000:0.000000
Solución: :@0.365696:0.627662:0.451658:0.627662:0.451658:0.610992:0.365696:0.610992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como :@0.459776:0.627662:0.511979:0.627662:0.511979:0.611949:0.459776:0.611949:0.000000:0.000000:0.000000:0.000000:0.000000
In x:@0.520391:0.627662:0.551020:0.627662:0.551020:0.611256:0.520391:0.611256:0.000000:0.000000:0.000000:0.000000
( ):@0.535908:0.628244:0.558236:0.628244:0.558236:0.610590:0.535908:0.610590:0.000000:0.000000:0.000000
–∞ :@0.588332:0.628246:0.617470:0.628246:0.617470:0.610591:0.588332:0.610591:0.000000:0.000000:0.000000
y :@0.627042:0.627663:0.639173:0.627663:0.639173:0.611951:0.627042:0.611951:0.000000:0.000000
 :@0.635141:0.627663:0.639173:0.627663:0.639173:0.611951:0.635141:0.611951:0.000000
x:@0.365714:0.644305:0.373169:0.644305:0.373169:0.627899:0.365714:0.627899:0.000000
0 , el producto tiende a 0.:@0.400039:0.644305:0.588790:0.644305:0.588790:0.628592:0.400039:0.628592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.408941:0.638581:0.417881:0.638581:0.417881:0.628288:0.408941:0.628288:0.000000
x:@0.433508:0.673714:0.438930:0.673714:0.438930:0.661783:0.433508:0.661783:0.000000
0:@0.449680:0.673714:0.456213:0.673714:0.456213:0.662287:0.449680:0.662287:0.000000
+:@0.456958:0.669551:0.463459:0.669551:0.463459:0.662066:0.456958:0.662066:0.000000
lim :@0.435880:0.664256:0.465828:0.664256:0.465828:0.648544:0.435880:0.648544:0.000000:0.000000:0.000000:0.000000
x In x:@0.466822:0.664256:0.509674:0.664256:0.509674:0.647850:0.466822:0.647850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )=:@0.495077:0.664839:0.533180:0.664839:0.533180:0.647185:0.495077:0.647185:0.000000:0.000000:0.000000:0.000000
0:@0.534193:0.664256:0.543175:0.664256:0.543175:0.648544:0.534193:0.648544:0.000000
e:@0.791447:0.593310:0.799234:0.593310:0.799234:0.576904:0.791447:0.576904:0.000000
x:@0.800271:0.587246:0.804875:0.587246:0.804875:0.578086:0.800271:0.578086:0.000000
x:@0.794434:0.609072:0.801889:0.609072:0.801889:0.592666:0.794434:0.592666:0.000000
x:@0.759978:0.610439:0.765400:0.610439:0.765400:0.598507:0.759978:0.598507:0.000000
∞:@0.776149:0.610862:0.785079:0.610862:0.785079:0.598023:0.776149:0.598023:0.000000
lim:@0.759978:0.600459:0.784864:0.600459:0.784864:0.584746:0.759978:0.584746:0.000000:0.000000:0.000000
Solución: :@0.650307:0.632134:0.726285:0.632134:0.726285:0.615464:0.650307:0.615464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función exponencial   :@0.727691:0.632134:0.923771:0.632130:0.923771:0.616417:0.727691:0.616421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.906076:0.632134:0.913862:0.632134:0.913862:0.615728:0.906076:0.615728:0.000000
x:@0.915136:0.626066:0.919740:0.626066:0.919740:0.616906:0.915136:0.616906:0.000000
crece mucho más rápido que  , por lo :@0.650312:0.648772:0.923771:0.648772:0.923771:0.633059:0.650312:0.633059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.863763:0.648772:0.871218:0.648772:0.871218:0.632366:0.863763:0.632366:0.000000
que el cociente tiende a  .:@0.650312:0.665414:0.844343:0.665414:0.844343:0.649701:0.650312:0.649701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∞:@0.828955:0.665996:0.841232:0.665996:0.841232:0.648342:0.828955:0.648342:0.000000
e:@0.775110:0.682163:0.782896:0.682163:0.782896:0.665757:0.775110:0.665757:0.000000
x:@0.783934:0.676099:0.788538:0.676099:0.788538:0.666938:0.783934:0.666938:0.000000
x:@0.778097:0.697924:0.785552:0.697924:0.785552:0.681518:0.778097:0.681518:0.000000
x:@0.743639:0.699290:0.749061:0.699290:0.749061:0.687358:0.743639:0.687358:0.000000
∞:@0.759810:0.699713:0.768740:0.699713:0.768740:0.686874:0.759810:0.686874:0.000000
lim     :@0.743639:0.692513:0.793835:0.692513:0.793835:0.676801:0.743639:0.676801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=∞:@0.794811:0.693096:0.823434:0.693096:0.823434:0.675442:0.794811:0.675442:0.000000:0.000000
x:@0.223294:0.722604:0.230749:0.722604:0.230749:0.706197:0.223294:0.706197:0.000000
2:@0.231788:0.716540:0.237025:0.716540:0.237025:0.707379:0.231788:0.707379:0.000000
e:@0.223446:0.738365:0.231233:0.738365:0.231233:0.721959:0.223446:0.721959:0.000000
x:@0.232270:0.732301:0.236874:0.732301:0.236874:0.723141:0.232270:0.723141:0.000000
x:@0.189604:0.739731:0.195026:0.739731:0.195026:0.727799:0.189604:0.727799:0.000000
∞:@0.205776:0.740154:0.214705:0.740154:0.214705:0.727315:0.205776:0.727315:0.000000
lim:@0.189366:0.729572:0.214253:0.729572:0.214253:0.713859:0.189366:0.713859:0.000000:0.000000:0.000000
Solución: :@0.081095:0.761427:0.158604:0.761427:0.158604:0.744757:0.081095:0.744757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aunque   crece, lo hace :@0.160209:0.761427:0.354564:0.761422:0.354564:0.745709:0.160209:0.745714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.224708:0.761427:0.232163:0.761427:0.232163:0.745021:0.224708:0.745021:0.000000
2:@0.232488:0.755358:0.237725:0.755358:0.237725:0.746198:0.232488:0.746198:0.000000
mucho más lentamente que  , por :@0.081100:0.778064:0.354541:0.778064:0.354541:0.762351:0.081100:0.762351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.303367:0.778064:0.311154:0.778064:0.311154:0.761658:0.303367:0.761658:0.000000
x:@0.311380:0.772000:0.315983:0.772000:0.315983:0.762839:0.311380:0.762839:0.000000
lo que el cociente tiende a 0.:@0.081103:0.794706:0.294327:0.794706:0.294327:0.778993:0.081103:0.778993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.208353:0.811455:0.215807:0.811455:0.215807:0.795048:0.208353:0.795048:0.000000
2:@0.216847:0.805391:0.222084:0.805391:0.222084:0.796230:0.216847:0.796230:0.000000
e:@0.208503:0.827216:0.216289:0.827216:0.216289:0.810810:0.208503:0.810810:0.000000
x:@0.217329:0.821153:0.221932:0.821153:0.221932:0.811992:0.217329:0.811992:0.000000
x:@0.174661:0.828583:0.180082:0.828583:0.180082:0.816651:0.174661:0.816651:0.000000
∞:@0.190834:0.829007:0.199763:0.829007:0.199763:0.816167:0.190834:0.816167:0.000000
lim       0:@0.174425:0.819661:0.255987:0.819661:0.255987:0.803948:0.174425:0.803948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.230659:0.820243:0.245992:0.820243:0.245992:0.802589:0.230659:0.802589:0.000000
x:@0.469085:0.735264:0.474506:0.735264:0.474506:0.723332:0.469085:0.723332:0.000000
0:@0.485256:0.735264:0.491789:0.735264:0.491789:0.723837:0.485256:0.723837:0.000000
+:@0.492534:0.731101:0.499035:0.731101:0.499035:0.723615:0.492534:0.723615:0.000000
lim :@0.471456:0.725806:0.501404:0.725806:0.501404:0.710093:0.471456:0.710093:0.000000:0.000000:0.000000:0.000000
e:@0.502398:0.725806:0.510185:0.725806:0.510185:0.709400:0.502398:0.709400:0.000000
–:@0.510128:0.720082:0.515493:0.720082:0.515493:0.709789:0.510128:0.709789:0.000000
1/:@0.515440:0.719742:0.524401:0.719742:0.524401:0.710581:0.515440:0.710581:0.000000:0.000000
x:@0.524347:0.719742:0.528693:0.719742:0.528693:0.710177:0.524347:0.710177:0.000000
Solución: :@0.365704:0.756955:0.446199:0.756955:0.446199:0.740286:0.365704:0.740286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a medida que :@0.450672:0.756955:0.572271:0.756955:0.572271:0.741242:0.450672:0.741242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.576946:0.756955:0.584401:0.756955:0.584401:0.740549:0.576946:0.740549:0.000000
0 , :@0.612835:0.756955:0.639164:0.756955:0.639164:0.741242:0.612835:0.741242:0.000000:0.000000:0.000000:0.000000
+:@0.622522:0.751231:0.631462:0.751231:0.631462:0.740938:0.622522:0.740938:0.000000
 :@0.635133:0.756955:0.639164:0.756955:0.639164:0.741242:0.635133:0.741242:0.000000
–:@0.365706:0.774179:0.374910:0.774179:0.374910:0.756525:0.365706:0.756525:0.000000
1/:@0.374818:0.773597:0.390188:0.773597:0.390188:0.757884:0.374818:0.757884:0.000000:0.000000
x:@0.390096:0.773597:0.397551:0.773597:0.397551:0.757191:0.390096:0.757191:0.000000
 –∞:@0.424432:0.774179:0.450423:0.774179:0.450423:0.756525:0.424432:0.756525:0.000000:0.000000:0.000000
, por lo que :@0.450331:0.773597:0.536532:0.773597:0.536532:0.757884:0.450331:0.757884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.536274:0.773597:0.544061:0.773597:0.544061:0.757191:0.536274:0.757191:0.000000
–:@0.543995:0.767873:0.549361:0.767873:0.549361:0.757580:0.543995:0.757580:0.000000
1/:@0.549307:0.767533:0.558268:0.767533:0.558268:0.758373:0.549307:0.758373:0.000000:0.000000
x:@0.558215:0.767533:0.562561:0.767533:0.562561:0.757968:0.558215:0.757968:0.000000
 :@0.589471:0.774179:0.594073:0.774179:0.594073:0.756525:0.589471:0.756525:0.000000
0.:@0.593981:0.773597:0.606093:0.773597:0.606093:0.757884:0.593981:0.757884:0.000000:0.000000
x:@0.456998:0.803006:0.462419:0.803006:0.462419:0.791075:0.456998:0.791075:0.000000
0:@0.473169:0.803006:0.479702:0.803006:0.479702:0.791579:0.473169:0.791579:0.000000
+:@0.480447:0.798843:0.486948:0.798843:0.486948:0.791358:0.480447:0.791358:0.000000
lim :@0.459369:0.793549:0.489318:0.793549:0.489318:0.777837:0.459369:0.777837:0.000000:0.000000:0.000000:0.000000
e:@0.490312:0.793549:0.498098:0.793549:0.498098:0.777143:0.490312:0.777143:0.000000
–:@0.498041:0.787825:0.503407:0.787825:0.503407:0.777533:0.498041:0.777533:0.000000
1/:@0.503353:0.787486:0.512314:0.787486:0.512314:0.778325:0.503353:0.778325:0.000000:0.000000
x:@0.512260:0.787486:0.516606:0.787486:0.516606:0.777921:0.512260:0.777921:0.000000
=:@0.516570:0.794132:0.531904:0.794132:0.531904:0.776478:0.516570:0.776478:0.000000
0:@0.532916:0.793549:0.541899:0.793549:0.541899:0.777837:0.532916:0.777837:0.000000
x:@0.759429:0.730525:0.764851:0.730525:0.764851:0.718593:0.759429:0.718593:0.000000
0:@0.775601:0.730525:0.782133:0.730525:0.782133:0.719097:0.775601:0.719097:0.000000
lim :@0.759429:0.722604:0.789378:0.722604:0.789378:0.706891:0.759429:0.706891:0.000000:0.000000:0.000000:0.000000
e:@0.790372:0.722604:0.798158:0.722604:0.798158:0.706197:0.790372:0.706197:0.000000
x:@0.799205:0.716540:0.803552:0.716540:0.803552:0.706975:0.799205:0.706975:0.000000
2:@0.804153:0.714017:0.809389:0.714017:0.809389:0.704857:0.804153:0.704857:0.000000
Solución: :@0.650312:0.753381:0.734572:0.753381:0.734572:0.736711:0.650312:0.736711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función :@0.741502:0.753381:0.835388:0.753381:0.835388:0.737668:0.741502:0.737668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.842585:0.753381:0.850372:0.753381:0.850372:0.736975:0.842585:0.736975:0.000000
x:@0.852409:0.747317:0.856755:0.747317:0.856755:0.737752:0.852409:0.737752:0.000000
2:@0.857946:0.744794:0.863183:0.744794:0.863183:0.735634:0.857946:0.735634:0.000000
 crece :@0.864482:0.753381:0.923774:0.753381:0.923774:0.737668:0.864482:0.737668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rápidamente a medida que :@0.650314:0.770023:0.866833:0.770023:0.866833:0.754310:0.650314:0.754310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.868863:0.770023:0.876318:0.770023:0.876318:0.753617:0.868863:0.753617:0.000000
∞:@0.903929:0.770605:0.916207:0.770605:0.916207:0.752951:0.903929:0.752951:0.000000
, :@0.916538:0.770023:0.923772:0.770023:0.923772:0.754310:0.916538:0.754310:0.000000:0.000000
por lo que el límite es  .:@0.650314:0.786665:0.825514:0.786665:0.825514:0.770952:0.650314:0.770952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∞:@0.810126:0.787247:0.822403:0.787247:0.822403:0.769593:0.810126:0.769593:0.000000
x:@0.744462:0.811336:0.749884:0.811336:0.749884:0.799404:0.744462:0.799404:0.000000
0:@0.760634:0.811336:0.767167:0.811336:0.767167:0.799909:0.760634:0.799909:0.000000
lim :@0.744462:0.806617:0.774411:0.806617:0.774411:0.790904:0.744462:0.790904:0.000000:0.000000:0.000000:0.000000
e:@0.775405:0.806617:0.783191:0.806617:0.783191:0.790211:0.775405:0.790211:0.000000
x:@0.784239:0.800553:0.788585:0.800553:0.788585:0.790989:0.784239:0.790989:0.000000
2:@0.789186:0.798031:0.794423:0.798031:0.794423:0.788870:0.789186:0.788870:0.000000
=∞:@0.795024:0.807200:0.823647:0.807200:0.823647:0.789545:0.795024:0.789545:0.000000:0.000000
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