lichengren02
春芽
共回答了11个问题采纳率:72.7% 举报
lim(x->无穷)[(4+x)/(2+x)]^x
=lim(x->无穷)[(2+2+x)/(2+x)]^x
=lim(x->无穷)[1+2/(2+x)]^[(x+2)/2*2x/(x+2)]
=lim(x->无穷){[1+2/(2+x)]^[(x+2)/2]}^(2x/(x+2))
因为:
lim(x->无穷)2x/(x+2)=2
lim(x->无穷)[1+2/(2+x)]^[(x+2)/2]
=e
(利用lim(x->无穷)(1+1/x)^x=e)
注:
这个重要极限只是一个形式:
lim(1+无穷小)^(对应无穷大量)
=e
所以结果是;
=e^2
1年前
6