lim(x,y)趋向于(无穷,a) (1+1/x)^(x^2/(x+y))
问题描述:
lim(x,y)趋向于(无穷,a) (1+1/x)^(x^2/(x+y))
answer:e
答
lim(x,y)趋向于(无穷,a) (1+1/x)^(x^2/(x+y))
= (1+1/x)^[x*x/(x+y)]
=e^[x/(x+y)]
=e^[1/(1+y/x)]
=e