lim(x->无穷）[（5x+1)/(5x-1)]^(4x)=?
问题描述：
lim(x->无穷）[（5x+1)/(5x-1)]^(4x)=?
答
=lim(x趋于无穷)[(5x-1+2)/(5x-1)]^4x
=lim(x趋于无穷)[1+2/(5x)]^[(5x/2)(8/5)] 这个形式知道吧
=e^8/5
答
定义y=5x-1
[（5x+1)/(5x-1)]^(4x)=(1+2/y)^((y+1)/5*4)
=((1+2/y)^(y/2))^{(y+1)/y*8/5}
-->e^(8/5)
答
这属於1^(无穷) 类形,主要都是用自然对数然後用洛必特法设 y= [5x+1)/(5x-1)]^(4x)lny = ln{[5x+1)/(5x-1)]^(4x)}lny = ln{[5x+1)/(5x-1)]^(4x)}= 4x ln{[5x+1)/(5x-1)}= 4 ln{[5x+1)/(5x-1)} / (1/x) 当 lim(x->无...