Question

qual o limite quando n tende para infinto de raiz de indice n de logaritmo de n?

Answer 1

Resposta:

Lim  [ log n ]^(1/n)

n-->∞

y= [ log n ]^(1/n)

log y = log [ log n ]^(1/n)

log y = (1/n) * log (log n)

y= 10^[(1/n) * log (log n)]

Lim 10^[(1/n) * log (log n)]

n-->∞

=

10^[ Lim (1/n) * log (log n)]

        n-->∞

Usando L'Hôpital

d log (log n)/dn = (1/n)/log  n =1/(n*log n)

d n/dn=1

10^[ Lim 1/(n*log n)]

        n-->∞

=10⁰ = 1