76:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 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 Figura 1.2:@0.573325:0.136836:0.647278:0.136836:0.647278:0.120167:0.573325:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.567712:0.306736:0.570857:0.306736:0.570857:0.301235:0.567712:0.301235:0.000000 2:@0.592144:0.306736:0.595289:0.306736:0.595289:0.301235:0.592144:0.301235:0.000000 4:@0.613327:0.306736:0.616472:0.306736:0.616472:0.301235:0.613327:0.301235:0.000000 -10:@0.464329:0.306736:0.472539:0.306736:0.472539:0.301235:0.464329:0.301235:0.000000:0.000000:0.000000 -8:@0.487871:0.306736:0.492936:0.306736:0.492936:0.301235:0.487871:0.301235:0.000000:0.000000 -6:@0.509080:0.306736:0.514145:0.306736:0.514145:0.301235:0.509080:0.301235:0.000000:0.000000 -4:@0.529225:0.306736:0.534291:0.306736:0.534291:0.301235:0.529225:0.301235:0.000000:0.000000 -0.2:@0.562144:0.312903:0.571476:0.312903:0.571476:0.307402:0.562144:0.307402:0.000000:0.000000:0.000000:0.000000 0.2:@0.563105:0.289864:0.570516:0.289864:0.570516:0.284363:0.563105:0.284363:0.000000:0.000000:0.000000 0.4:@0.563105:0.278464:0.570516:0.278464:0.570516:0.272963:0.563105:0.272963:0.000000:0.000000:0.000000 0.6:@0.563105:0.266971:0.570516:0.266971:0.570516:0.261470:0.563105:0.261470:0.000000:0.000000:0.000000 0.8:@0.563105:0.254813:0.570516:0.254813:0.570516:0.249312:0.563105:0.249312:0.000000:0.000000:0.000000 1:@0.565238:0.243510:0.568383:0.243510:0.568383:0.238009:0.565238:0.238009:0.000000 1.2:@0.563105:0.232109:0.570516:0.232109:0.570516:0.226608:0.563105:0.226608:0.000000:0.000000:0.000000 1.4:@0.563105:0.220617:0.570516:0.220617:0.570516:0.215116:0.563105:0.215116:0.000000:0.000000:0.000000 1.6:@0.563105:0.208454:0.570516:0.208454:0.570516:0.202953:0.563105:0.202953:0.000000:0.000000:0.000000 1.8:@0.563105:0.198233:0.570516:0.198233:0.570516:0.192732:0.563105:0.192732:0.000000:0.000000:0.000000 2:@0.565238:0.186833:0.568383:0.186833:0.568383:0.181332:0.565238:0.181332:0.000000 2.2:@0.563105:0.175340:0.570516:0.175340:0.570516:0.169839:0.563105:0.169839:0.000000:0.000000:0.000000 2.4:@0.563099:0.163179:0.570510:0.163179:0.570510:0.157678:0.563099:0.157678:0.000000:0.000000:0.000000 -0.4:@0.562140:0.325032:0.571472:0.325032:0.571472:0.319531:0.562140:0.319531:0.000000:0.000000:0.000000:0.000000 -0.6:@0.562140:0.336243:0.571472:0.336243:0.571472:0.330742:0.562140:0.330742:0.000000:0.000000:0.000000:0.000000 -2:@0.549779:0.306737:0.554845:0.306737:0.554845:0.301236:0.549779:0.301236:0.000000:0.000000 -20:@0.360683:0.306736:0.368893:0.306736:0.368893:0.301235:0.360683:0.301235:0.000000:0.000000:0.000000 -18:@0.382649:0.306736:0.390859:0.306736:0.390859:0.301235:0.382649:0.301235:0.000000:0.000000:0.000000 -16:@0.403858:0.306736:0.412068:0.306736:0.412068:0.301235:0.403858:0.301235:0.000000:0.000000:0.000000 -14:@0.424004:0.306736:0.432214:0.306736:0.432214:0.301235:0.424004:0.301235:0.000000:0.000000:0.000000 -12:@0.444555:0.306736:0.452766:0.306736:0.452766:0.301235:0.444555:0.301235:0.000000:0.000000:0.000000 f x:@0.365959:0.247085:0.378277:0.247085:0.378277:0.236578:0.365959:0.236578:0.000000:0.000000:0.000000 ( )=:@0.369672:0.247085:0.389841:0.247085:0.389841:0.237022:0.369672:0.237022:0.000000:0.000000:0.000000:0.000000 x:@0.393177:0.241641:0.397951:0.241641:0.397951:0.231134:0.393177:0.231134:0.000000 2 :@0.398613:0.237727:0.403857:0.237727:0.403857:0.231861:0.398613:0.231861:0.000000:0.000000 :@0.404238:0.241952:0.410132:0.241952:0.410132:0.230646:0.404238:0.230646:0.000000 3:@0.410780:0.241641:0.416532:0.241641:0.416532:0.231579:0.410780:0.231579:0.000000 x:@0.417192:0.242449:0.421966:0.242449:0.421966:0.231943:0.417192:0.231943:0.000000 :@0.422627:0.241952:0.432446:0.241952:0.432446:0.230646:0.422627:0.230646:0.000000 2:@0.433094:0.241641:0.438847:0.241641:0.438847:0.231579:0.433094:0.231579:0.000000 x:@0.404332:0.253560:0.409106:0.253560:0.409106:0.243053:0.404332:0.243053:0.000000 2 :@0.409771:0.249647:0.415015:0.249647:0.415015:0.243781:0.409771:0.243781:0.000000:0.000000 :@0.415394:0.253872:0.421288:0.253872:0.421288:0.242567:0.415394:0.242567:0.000000 4:@0.421936:0.253562:0.427689:0.253562:0.427689:0.243499:0.421936:0.243499:0.000000 :@0.637324:0.193580:0.692803:0.193580:0.692803:0.177867:0.637324:0.177867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.755824:0.284990:0.758965:0.284990:0.758965:0.279496:0.755824:0.279496:0.000000 2:@0.788050:0.284990:0.791190:0.284990:0.791190:0.279496:0.788050:0.279496:0.000000 4:@0.816426:0.284990:0.819567:0.284990:0.819567:0.279496:0.816426:0.279496:0.000000 4:@0.843959:0.284990:0.847100:0.284990:0.847100:0.279496:0.843959:0.279496:0.000000 -6:@0.697270:0.284990:0.702328:0.284990:0.702328:0.279496:0.697270:0.279496:0.000000:0.000000 -4:@0.717389:0.284990:0.722447:0.284990:0.722447:0.279496:0.717389:0.279496:0.000000:0.000000 -0.05:@0.746325:0.298833:0.758785:0.298833:0.758785:0.293339:0.746325:0.293339:0.000000:0.000000:0.000000:0.000000:0.000000 0.05:@0.748243:0.259765:0.758785:0.259765:0.758785:0.254271:0.748243:0.254271:0.000000:0.000000:0.000000:0.000000 0.1:@0.751384:0.241276:0.758785:0.241276:0.758785:0.235782:0.751384:0.235782:0.000000:0.000000:0.000000 0.15:@0.748243:0.221827:0.758785:0.221827:0.758785:0.216333:0.748243:0.216333:0.000000:0.000000:0.000000:0.000000 0.2:@0.751384:0.201845:0.758785:0.201845:0.758785:0.196351:0.751384:0.196351:0.000000:0.000000:0.000000 0.25:@0.748243:0.183472:0.758785:0.183472:0.758785:0.177978:0.748243:0.177978:0.000000:0.000000:0.000000:0.000000 0.3:@0.751378:0.163751:0.758780:0.163751:0.758780:0.158257:0.751378:0.158257:0.000000:0.000000:0.000000 -0.1:@0.749461:0.317776:0.758780:0.317776:0.758780:0.312283:0.749461:0.312283:0.000000:0.000000:0.000000:0.000000 -0.15:@0.746320:0.337512:0.758780:0.337512:0.758780:0.332018:0.746320:0.332018:0.000000:0.000000:0.000000:0.000000:0.000000 -2:@0.737908:0.284993:0.742967:0.284993:0.742967:0.279499:0.737908:0.279499:0.000000:0.000000 f x:@0.774314:0.335275:0.782069:0.335275:0.782069:0.328660:0.774314:0.328660:0.000000:0.000000:0.000000 ( )=:@0.776651:0.335275:0.789349:0.335275:0.789349:0.328940:0.776651:0.328940:0.000000:0.000000:0.000000:0.000000 x:@0.791449:0.331847:0.794454:0.331847:0.794454:0.325233:0.791449:0.325233:0.000000 2 :@0.794871:0.329383:0.798172:0.329383:0.798172:0.325690:0.794871:0.325690:0.000000:0.000000 :@0.798410:0.332042:0.802121:0.332042:0.802121:0.324925:0.798410:0.324925:0.000000 3:@0.802529:0.331847:0.806151:0.331847:0.806151:0.325512:0.802529:0.325512:0.000000 x:@0.806566:0.332355:0.809572:0.332355:0.809572:0.325741:0.806566:0.325741:0.000000 :@0.809987:0.332042:0.816169:0.332042:0.816169:0.324925:0.809987:0.324925:0.000000 2:@0.816577:0.331847:0.820198:0.331847:0.820198:0.325512:0.816577:0.325512:0.000000 x:@0.798471:0.339352:0.801476:0.339352:0.801476:0.332738:0.798471:0.332738:0.000000 2 :@0.801894:0.336888:0.805196:0.336888:0.805196:0.333195:0.801894:0.333195:0.000000:0.000000 :@0.805434:0.339548:0.809144:0.339548:0.809144:0.332430:0.805434:0.332430:0.000000 4:@0.809552:0.339352:0.813174:0.339352:0.813174:0.333017:0.809552:0.333017:0.000000 Debemos tener muy presente lo que sigue::@0.293660:0.366133:0.607883:0.366133:0.607883:0.350420:0.293660:0.350420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.293660:0.390680:0.303383:0.390680:0.303383:0.375765:0.293660:0.375765:0.000000:0.000000 :@0.320660:0.390049:0.323070:0.390049:0.323070:0.378118:0.320660:0.378118:0.000000 2 significa que toma valores cercanos a 2 por la derecha y por la izquierda.:@0.323958:0.390995:0.858362:0.390995:0.858362:0.375282:0.323958:0.375282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.293660:0.415540:0.303383:0.415540:0.303383:0.400626:0.293660:0.400626:0.000000:0.000000 2 significa que toma valores cercanos a 2 por la derecha.:@0.319691:0.415855:0.739228:0.415855:0.739228:0.400143:0.319691:0.400143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.332543:0.410131:0.341482:0.410131:0.341482:0.399839:0.332543:0.399839:0.000000 x :@0.293660:0.440402:0.303383:0.440402:0.303383:0.425488:0.293660:0.425488:0.000000:0.000000 2 significa que toma valores cercanos a 2 por la izquierda.:@0.319691:0.440717:0.743204:0.440717:0.743204:0.425005:0.319691:0.425005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.332543:0.434993:0.337909:0.434993:0.337909:0.424701:0.332543:0.424701:0.000000 1.1 Definición del límite de una función:@0.293660:0.465583:0.601354:0.465583:0.601354:0.448636:0.293660:0.448636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea :@0.293660:0.491447:0.323380:0.491447:0.323380:0.475735:0.293660:0.475735:0.000000:0.000000:0.000000:0.000000 f x:@0.323277:0.491447:0.342965:0.491450:0.342965:0.475044:0.323277:0.475041:0.000000:0.000000:0.000000 ( ):@0.329017:0.491664:0.349576:0.491664:0.349576:0.475615:0.329017:0.475615:0.000000:0.000000:0.000000 una función, definimos con un número real, si:@0.350497:0.491450:0.698272:0.491450:0.698272:0.475737:0.350497:0.475737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.556701:0.491135:0.565119:0.491135:0.565119:0.476220:0.556701:0.476220:0.000000 lim :@0.293662:0.516315:0.323610:0.516315:0.323610:0.500603:0.293662:0.500603:0.000000:0.000000:0.000000:0.000000 f x:@0.324611:0.515995:0.343085:0.515995:0.343085:0.501081:0.324611:0.501081:0.000000:0.000000:0.000000 ( ):@0.329815:0.516525:0.349595:0.516525:0.349595:0.500475:0.329815:0.500475:0.000000:0.000000:0.000000 =:@0.350528:0.516310:0.361499:0.516310:0.361499:0.500598:0.350528:0.500598:0.000000 L:@0.362523:0.515995:0.369451:0.515995:0.369451:0.501081:0.362523:0.501081:0.000000 y equivalente lim :@0.293660:0.541172:0.437359:0.541172:0.437359:0.525460:0.293660:0.525460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.395096:0.540857:0.403513:0.540857:0.403513:0.525942:0.395096:0.525942:0.000000 f x:@0.438355:0.540857:0.456829:0.540857:0.456829:0.525942:0.438355:0.525942:0.000000:0.000000:0.000000 ( ):@0.443559:0.541387:0.463338:0.541387:0.463338:0.525337:0.443559:0.525337:0.000000:0.000000:0.000000 =:@0.464272:0.541172:0.475243:0.541172:0.475243:0.525460:0.464272:0.525460:0.000000 L:@0.476267:0.540857:0.483195:0.540857:0.483195:0.525942:0.476267:0.525942:0.000000 lim :@0.293660:0.566034:0.323609:0.566034:0.323609:0.550322:0.293660:0.550322:0.000000:0.000000:0.000000:0.000000 f x:@0.324611:0.565719:0.343085:0.565719:0.343085:0.550804:0.324611:0.550804:0.000000:0.000000:0.000000 ( ):@0.329815:0.566248:0.349595:0.566248:0.349595:0.550199:0.329815:0.550199:0.000000:0.000000:0.000000 =:@0.350528:0.566034:0.361499:0.566034:0.361499:0.550322:0.350528:0.550322:0.000000 L:@0.362523:0.565719:0.369451:0.565719:0.369451:0.550804:0.362523:0.550804:0.000000 Es decir que el límite de una función existe y es igual a si y solo si los límites laterales existen :@0.293660:0.590895:0.931220:0.590895:0.931220:0.575182:0.293660:0.575182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.666932:0.590580:0.673860:0.590580:0.673860:0.575665:0.666932:0.575665:0.000000 y ambos son iguales a .:@0.293668:0.607537:0.458599:0.607537:0.458599:0.591824:0.293668:0.591824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.448863:0.607221:0.455791:0.607221:0.455791:0.592307:0.448863:0.592307:0.000000 Analicemos algunos ejemplos en forma intuitiva.:@0.293652:0.632402:0.629811:0.632402:0.629811:0.616690:0.293652:0.616690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Evaluar lim:@0.293660:0.657260:0.378789:0.657260:0.378789:0.641548:0.293660:0.641548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 √:@0.379798:0.657475:0.396532:0.657475:0.396532:0.641425:0.379798:0.641425:0.000000 x:@0.397452:0.656945:0.404229:0.656945:0.404229:0.642031:0.397452:0.642031:0.000000 –:@0.405173:0.657843:0.414377:0.657843:0.414377:0.640189:0.405173:0.640189:0.000000 2.:@0.415389:0.656945:0.427404:0.656945:0.427404:0.642661:0.415389:0.642661:0.000000:0.000000 Elaboraremos una tabla con valores cercanos a 2 por la derecha.:@0.293660:0.682121:0.733916:0.682121:0.733916:0.666408:0.293660:0.666408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Valores de cercanos a 2 por la derecha:@0.467560:0.713556:0.753154:0.713556:0.753154:0.697844:0.467560:0.697844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.545276:0.713556:0.555970:0.713556:0.555970:0.697150:0.545276:0.697150:0.000000:0.000000 x:@0.531857:0.735066:0.539312:0.735066:0.539312:0.718660:0.531857:0.718660:0.000000 √:@0.663117:0.738484:0.679851:0.738484:0.679851:0.722435:0.663117:0.722435:0.000000 x:@0.680771:0.737954:0.687549:0.737954:0.687549:0.723040:0.680771:0.723040:0.000000 –:@0.688492:0.738852:0.697696:0.738852:0.697696:0.721198:0.688492:0.721198:0.000000 2:@0.698708:0.737954:0.706875:0.737954:0.706875:0.723670:0.698708:0.723670:0.000000 3:@0.467560:0.758757:0.476543:0.758757:0.476543:0.743044:0.467560:0.743044:0.000000 1:@0.616972:0.758757:0.625955:0.758757:0.625955:0.743044:0.616972:0.743044:0.000000 2,5:@0.467560:0.779240:0.488581:0.779240:0.488581:0.763527:0.467560:0.763527:0.000000:0.000000:0.000000 0,707106781:@0.616972:0.779240:0.709266:0.779240:0.709266:0.763527:0.616972:0.763527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,1:@0.467560:0.799723:0.488581:0.799723:0.488581:0.784011:0.467560:0.784011:0.000000:0.000000:0.000000 0,316227766:@0.616972:0.799723:0.709266:0.799723:0.709266:0.784011:0.616972:0.784011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,01:@0.467560:0.820207:0.497490:0.820207:0.497490:0.804494:0.467560:0.804494:0.000000:0.000000:0.000000:0.000000 0,1:@0.616972:0.820207:0.637993:0.820207:0.637993:0.804494:0.616972:0.804494:0.000000:0.000000:0.000000 2,001:@0.467560:0.840690:0.506399:0.840690:0.506399:0.824977:0.467560:0.824977:0.000000:0.000000:0.000000:0.000000:0.000000 0,031622777:@0.616972:0.840690:0.709266:0.840690:0.709266:0.824977:0.616972:0.824977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,0001:@0.467560:0.861173:0.515309:0.861173:0.515309:0.845461:0.467560:0.845461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,01:@0.616972:0.861173:0.646902:0.861173:0.646902:0.845461:0.616972:0.845461:0.000000:0.000000:0.000000:0.000000 2,00001:@0.467560:0.881657:0.524218:0.881657:0.524218:0.865944:0.467560:0.865944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,003162278:@0.616972:0.881657:0.709266:0.881657:0.709266:0.865944:0.616972:0.865944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,000001:@0.467560:0.902140:0.533127:0.902140:0.533127:0.886427:0.467560:0.886427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,001:@0.616972:0.902140:0.655811:0.902140:0.655811:0.886427:0.616972:0.886427:0.000000:0.000000:0.000000:0.000000:0.000000 2,0000001:@0.467560:0.922623:0.542036:0.922623:0.542036:0.906911:0.467560:0.906911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0,000316228:@0.616972:0.922623:0.709266:0.922623:0.709266:0.906911:0.616972:0.906911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,00000001:@0.467560:0.943107:0.550945:0.943107:0.550945:0.927394:0.467560:0.927394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1E-04:@0.616972:0.943107:0.657689:0.943107:0.657689:0.927394:0.616972:0.927394:0.000000:0.000000:0.000000:0.000000:0.000000 x a:@0.291578:0.525576:0.314484:0.525576:0.314484:0.513644:0.291578:0.513644:0.000000:0.000000:0.000000 –:@0.315238:0.521412:0.319141:0.521412:0.319141:0.513927:0.315238:0.513927:0.000000 x a:@0.408787:0.548689:0.431693:0.548689:0.431693:0.536757:0.408787:0.536757:0.000000:0.000000:0.000000 x a:@0.291289:0.573460:0.314194:0.573462:0.314194:0.561531:0.291289:0.561528:0.000000:0.000000:0.000000 +:@0.314949:0.569299:0.321450:0.569299:0.321450:0.561814:0.314949:0.561814:0.000000 x:@0.351767:0.664689:0.357189:0.664689:0.357189:0.652757:0.351767:0.652757:0.000000 2:@0.367938:0.664689:0.374471:0.664689:0.374471:0.653261:0.367938:0.653261:0.000000 +:@0.375216:0.660526:0.381717:0.660526:0.381717:0.653040:0.375216:0.653040:0.000000 La definición del límite :@0.078581:0.422081:0.246669:0.422081:0.246669:0.406368:0.078581:0.406368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de una función se :@0.078581:0.438723:0.212438:0.438723:0.212438:0.423010:0.078581:0.423010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 refiere al valor al que :@0.078581:0.455365:0.232009:0.455365:0.232009:0.439652:0.078581:0.439652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se aproxima la función :@0.078581:0.472007:0.245943:0.472007:0.245943:0.456294:0.078581:0.456294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuando la variable :@0.078581:0.488648:0.215119:0.488648:0.215119:0.472936:0.078581:0.472936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 independiente se acerca :@0.078581:0.505290:0.260890:0.505290:0.260890:0.489578:0.078581:0.489578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a un punto específico. :@0.078581:0.521932:0.242796:0.521932:0.242796:0.506219:0.078581:0.506219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Formalmente, el límite :@0.078581:0.538574:0.245056:0.538574:0.245056:0.522861:0.078581:0.522861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de una funciòn :@0.078581:0.555216:0.192761:0.555216:0.192761:0.539503:0.078581:0.539503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.192581:0.554901:0.209047:0.554901:0.209047:0.539986:0.192581:0.539986:0.000000:0.000000:0.000000 ( ):@0.196781:0.555430:0.214552:0.555430:0.214552:0.539381:0.196781:0.539381:0.000000:0.000000:0.000000 :@0.214566:0.555216:0.218597:0.555216:0.218597:0.539503:0.214566:0.539503:0.000000 cuando tiende a un :@0.078573:0.571858:0.235359:0.571858:0.235359:0.556145:0.078573:0.556145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.138060:0.571542:0.144837:0.571542:0.144837:0.556628:0.138060:0.556628:0.000000 valor , se denota como::@0.078585:0.588499:0.258874:0.588499:0.258874:0.572787:0.078585:0.572787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.117930:0.588184:0.126347:0.588184:0.126347:0.573270:0.117930:0.573270:0.000000 x:@0.125024:0.623451:0.130446:0.623451:0.130446:0.611519:0.125024:0.611519:0.000000 a:@0.140928:0.624081:0.149346:0.624081:0.149346:0.609167:0.140928:0.609167:0.000000 –:@0.149285:0.619288:0.153188:0.619288:0.153188:0.611802:0.149285:0.611802:0.000000 lim :@0.126210:0.614361:0.156159:0.614361:0.156159:0.598648:0.126210:0.598648:0.000000:0.000000:0.000000:0.000000 f x:@0.157153:0.614361:0.176841:0.614361:0.176841:0.597955:0.157153:0.597955:0.000000:0.000000:0.000000 ( )=:@0.162893:0.614575:0.198312:0.614575:0.198312:0.598526:0.162893:0.598526:0.000000:0.000000:0.000000:0.000000 L:@0.199233:0.614046:0.206160:0.614046:0.206160:0.599131:0.199233:0.599131:0.000000 Competencia :@0.078581:0.378854:0.177273:0.378854:0.177273:0.363448:0.078581:0.363448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.393983:0.167196:0.393983:0.167196:0.378577:0.078581:0.378577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Límites laterales:@0.080269:0.804406:0.196377:0.804406:0.196377:0.788999:0.080269:0.788999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t.ly/eGbiq:@0.105028:0.930570:0.176117:0.930570:0.176117:0.914857:0.105028:0.914857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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