Question

lim[tan(兀/4+2/n)]^n n趋于无穷大时为什么不是1

Answer 1

洛必达法则解决.

lim(n->∞) [tan(π/4 + 2/n)]^n

= e^lim(n->∞) n ln[tan(π/4 + 2/n)]

令t = 1/n,t->0,则

= e^lim(t->0) ln[tan(π/4 + 2t)]/t

= e^lim(t->0) [1/tan(π/4 + 2t)] * sec²(π/4 + 2t) * 2