Question

大学数学求极限，是高手的就进来看看！！！

求当n趋于无穷时[ntan(1/n)]^(n^2)的极限。

Answer 1

log{[ntan(1/n)]^(n^2)}
=n^2*log[ntan(1/n)]
=n^2*log[n*(1/n+1/n^3/3)] (等价无穷小)
=n^2*log[1+1/n^2/3]
=n^2*1/n^2/3
=1/3
所以lim log...=1/3
lim... = e^(1/3)

Answer 2

零的无穷大次方还是零,所以答案为零