Question

求n→∞时,(3n+2)^(1/n)的极限

Answer 1

当n->∞时,lim(3n+2)^(1/n) = e^lim[(1/n)ln(3n+2)]

根据洛比达法则：n->∞时,lim[(1/n)ln(3n+2)] = 3/(3n+2) = 0

故：当n->∞时,lim(3n+2)^(1/n) = e^lim[(1/n)ln(3n+2)] = e^0 = 1