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Forum Studenti •Scritto 10.01.09
Pagina 1 di 1

Scritto 10.01.09

Inviato: mercoledì 27 gennaio 2010, 9:34
da selly
Buongiorno ho provato a risolvere il limite di questo compito con Taylor e con N=3...infatti era la strada giusta, ma il risultato è diverso...nel libro segna 3 e il mio è 2/3....non ho lo scanner per farvi cercare il mio errore quindi vi scrivo il limite dato:
lim x->0 [2log(1+sinx)-arctan(2x)+x^2]/[|sin(x^2)|*sinhx]


Nel secondo esercizio nel p.to a) si deve dim che per ogni lamda>=0 l'eq. ha sol.unica.
xarctan(e^x)=lamda
io ho posto f(x)=xarctan(e^x)
ho fatto i lim a +oo e-oo, ho studiato il segno di f(x), e ho trovato che f(0)=0....Cos'altro devo fare per dimostrare che la soluzione esiste , ma +ke altro che è UNICA?????

Profff mi risponda!!!!!!! :roll:

Re: Scritto 10.01.09

Inviato: mercoledì 27 gennaio 2010, 11:16
da selly

Re: Scritto 10.01.09

Inviato: mercoledì 27 gennaio 2010, 11:32
da Tavaguet

Re: Scritto 10.01.09

Inviato: mercoledì 27 gennaio 2010, 11:44
da selly

Re: Scritto 10.01.09

Inviato: venerdì 18 gennaio 2013, 21:52
da ilaria11
I messaggi sono datati ma provo comunque a scrivere nella speranza che qualcuno risponda.

La derivata non è arctan(e^x)+ x*e^x /(e^(2x)+1) ? E comunque anche io ho problemi a studiarla.

Re: Scritto 10.01.09

Inviato: sabato 19 gennaio 2013, 9:52
da Massimo Gobbino

Re: Scritto 10.01.09

Inviato: domenica 20 gennaio 2013, 12:13
da ilaria11
Cerco i valori per cui si annulla, così da verificare o meno che si annulla sporadicamente e che quindi è strettamente crescente....mi sbaglio? Non devo usare monotonia 3?

Re: Scritto 10.01.09

Inviato: domenica 20 gennaio 2013, 18:44
da Massimo Gobbino
Visto che l'equazione è richiesta solo per [tex]\lambda >0[/tex], in quel caso basta verificare che la funzione è iniettiva e surgettiva come [tex]f:[0,+\infty)\to[0,+\infty)[/tex]. Perché basta questa restrizione? Cosa succede alla funzione quando x è negativo?

Re: Scritto 10.01.09

Inviato: domenica 20 gennaio 2013, 21:04
da ilaria11
Per valori di x negativi la funzione è negativa, dunque basta dimostrare che f'(x)>0 per valori di x positivi, e da questo segue che la funzione è strettamente crescente nell'intervallo [0,+oo] (monotonia 2). Giusto?