速求高数解答,lim(1-x分之3)x+2次方,x趋向无穷大,求极限.
问题描述：
速求高数解答,lim(1-x分之3)x+2次方,x趋向无穷大,求极限.
答
lim[x→∞](1-3/x)^(x+2)
=lim[x→∞](1-3/x)^[-3(-x/3)+2]
=lim[x→∞](1-3/x)^[-3(-x/3)]*(1-3/x)^2
=e^(-3)