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Forum Studenti •Limite, limiti notevoli [logaritmo del coseno]
Pagina 1 di 1

Limite, limiti notevoli [logaritmo del coseno]

Inviato: lunedì 11 gennaio 2016, 16:19
da Fortuna
Salve di nuovo , il limite che sto affrontando adesso è nella scheda 6 del libro di esercizi di analisi matematica I parte A

Non riesco ad uscire dalla forma indeterminata

Limite per x che tende a 0
[tex]\begin{array}{clr}
& \left( cos x\right) ^{1/sinx}&
\end{array}[/tex]

Quindi 1all'infinito

Utilizzando e-alla sono arrivata a

[tex]e^{(1/sin x) ln cosx}[/tex]

Se moltiplico e divido per x (nell'esponente)
[tex]\begin{array}{rc}
\frac{x}{sin x} \frac{1}{x} ln cosx&
\end{array}[/tex]

Comunque mi ritrovo con 0/infinito

Posso avere un suggerimento per uscire da questo impasse?

Grazie mille

Re: Limite, limiti notevoli

Inviato: lunedì 11 gennaio 2016, 16:41
da GIMUSI

Re: Limite, limiti notevoli

Inviato: martedì 12 gennaio 2016, 14:46
da Fortuna
Stavo cercando di risolverlo con metodologie 'ante o piccolo' perché ancora non ho digerito bene l'o piccolo, dunque :

[tex]\dfrac{\log\cos x}{\sin x}[/tex]

Sostituendo gli sviluppini mi viene

[tex]\dfrac{\log(1+o(x))}{x + o(x)}[/tex]

E da qui? :?

[EDIT by Massimo Gobbino] Ho risistemato le formule.

Re: Limite, limiti notevoli

Inviato: martedì 12 gennaio 2016, 15:02
da GIMUSI
io così sul momento avrei sviluppato al secondo ordine ma mi pare che vada bene anche così...osservando che ln(1+o(x))=o(x) puoi concludere :)

Re: Limite, limiti notevoli

Inviato: martedì 12 gennaio 2016, 17:06
da Fortuna
Ok ci sono! :D :idea:
mi confondeva avere ln(1+ox) invece del classico ln(1+x) .. non so perché lo vedevo in modo diverso :?


Grazie mille :!:

PS : il fatto che sia stato risolto con uno scontro di ordine 1 significa che è risolvibile con i limiti notevoli? O vale solo il viceversa?

Re: Limite, limiti notevoli

Inviato: martedì 12 gennaio 2016, 20:03
da GIMUSI

Re: Limite, limiti notevoli

Inviato: mercoledì 13 gennaio 2016, 8:39
da Massimo Gobbino
Quei limiti con il logaritmo del coseno sono un grande classico dell'epoca "pre o piccolo". Puoi trovare esempi analoghi alla lezione 21 di AM1_15 oppure alla lezione 19 di AM13.