第2个回答 2018-12-22
L =lim(x->+∞) [( 2/π)arctanx ]^x
lnL
=lim(x->+∞) ln[( 2/π)arctanx ] / (1/x) (0/0 分子分母分别求导)
=lim(x->+∞) {1/[arctanx .(1+x^2)] } / (-1/x^2)
=lim(x->+∞) [1/arctanx ]. lim(x->+∞) [-x^2/(1+x^2)]
=(2/π) (-1)
=-2/π
L = e^(-2/π)
lim(x->+∞) [( 2/π)arctanx ]^x = e^(-2/π)本回答被网友采纳