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Forum Studenti •Analisi 1 -- 2016/2017 -- Compitini - Pagina 2
Pagina 2 di 2

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: domenica 9 aprile 2017, 21:09
da GIMUSI
per la domanda bonus 6(c) mi chiedo se, una volta determinata l'espressione generale di , sia possibile concludere direttamente dal teorema di esistenza e unicità che l'equazione differenziale ammette soluzioni limitate :?: :roll:

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 9:17
da Massimo Gobbino

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 16:10
da GIMUSI

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 16:12
da GIMUSI

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 16:21
da Federico.M
Ciao GIMUSI... si, le soluzioni degli esercizi che ho risolto coincidono con le tue.. :D ... Quello che mi chiedo è come facciate ad avere le idee giuste per risolvere le bonus questions ... :o ... forse io sono un po' pigro... :roll: .. oppure avete una marcia in più... :) ..

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 16:38
da GIMUSI

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 16:55
da Federico.M
Per quanto riguarda il teorema di esistenza ed unicità non so darti una risposta.. L'ho riguardato e fa accenno a lipschitzianità ed uniforme continuità... forse è lì che bisognerebbe indagare meglio..
Per quanto riguarda le condizioni in cui vengono svolti gli esercizi, hai perfettamente ragione e mi accodo ai tuoi complimenti ai ragazzi ed alle ragazze che li hanno risolti durante la prova d'esame... :D

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 20:38
da Massimo Gobbino
Per la (6c) davvero mi sfugge dove sta il problema. Una volta che abbiamo l'espressione di u'(t), e ce l'abbiamo praticamente fatta al punto (6a), basta vedere che quella non ha primitive limitate.

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 22:34
da GIMUSI

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: lunedì 10 aprile 2017, 23:00
da Federico.M
Non so se sia un ragionamento rigoroso, ma, guardando la cosa da un punto di vista geometrico, se la derivata di una funzione tende all'infinito, allora la funzione avrà tangente con una pendenza molto vicina alla verticale e, quindi, intuitivamente non sarà limitata...
Oppure si può ragionare anche in questo modo (vedi allegato), cioè usando De l'Hopital..

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: martedì 11 aprile 2017, 8:07
da GIMUSI

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: martedì 11 aprile 2017, 8:19
da Federico.M
Per quanto riguarda il mio post precedente, credo che il ragionamento con De l'Hopital sia più corretto delle considerazioni geometriche che ho fatto. Infatti, esistono innumerevoli controesempi in cui la derivata di una funzione è illimitata in un punto, ma la funzione no... Basta pensare, ad esempio, alla funzione radice di x, per x che tende a zero..

Re: Analisi 1 -- 2016/2017 -- Compitini

Inviato: sabato 20 maggio 2017, 19:52
da Massimo Gobbino
Ho aggiunto il terzo compitino (18 maggio 2017).