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Forum Studenti •Limite all'infinito ESERCIZIARIO
Pagina 1 di 1

Limite all'infinito ESERCIZIARIO

Inviato: sabato 11 aprile 2020, 18:53
da EstOmBIFy
A pag. 72 dell'eserciziario c'è questo limite:



Ho idea che nel dominio tenda a ZERO; ma ogni stima che riesco a fare si conclude con , .

Qualcuno ha idee per lo svolgimento? :|

Re: Limite all'infinito ESERCIZIARIO

Inviato: lunedì 13 aprile 2020, 8:03
da Massimo Gobbino
Beh, iniziamo a capire come funziona.

Brutalmente, chi comanda al numeratore? Chi comanda al denominatore? Quali sono gli "ordini" in gioco?

Re: Limite all'infinito ESERCIZIARIO

Inviato: martedì 14 aprile 2020, 11:09
da EstOmBIFy
Buongiorno professore, scusi per il ritardo, ma non avevo visto che avesse risposto... :?

Comunque, continuando a pensarci, forse ho trovato una soluzione, gliela mostro:

.

Adesso, è definitivamente , quindi abbiamo:

.

Il secondo limite, tende a zero: infatti : somma di termini positivi di cui almeno uno è illimitato.
Invece per il primo limite: inizialmente pensavo ad una cosa del tipo: ; ma poi ho pensato anche: in , e da cui , ma abbiamo anche da cui abbiamo la catena di disuguaglianze: . Infine otteniamo:



e quest'ultimo tende a zero; infatti poiché alla peggio e l'altra resta .

Potrebbe andare bene come svolgimento?

Re: Limite all'infinito ESERCIZIARIO

Inviato: mercoledì 15 aprile 2020, 15:54
da ghisi