lim(x/x+1)^x+3求极限.lim(x/x+1)^(x+3)=lim[1-1/(x+1)]^(x+1+2)=lim{1+[-1/(x+1)]}^-[-(x+1)]*lim[1-1/(x+1)]^2=e^-1*1=1/e=lim{1+[-1/(x+1)]}^-[-(x+1)]*lim[1-1/(x+1)]^2这一步骤中为什么是-[-(x+1)]次方而不是-(x+1)呢?

Question

lim(x/x+1)^x+3求极限.
lim(x/x+1)^(x+3)
=lim[1-1/(x+1)]^(x+1+2)
=lim{1+[-1/(x+1)]}^-[-(x+1)]*lim[1-1/(x+1)]^2
=e^-1*1
=1/e
=lim{1+[-1/(x+1)]}^-[-(x+1)]*lim[1-1/(x+1)]^2
这一步骤中为什么是-[-(x+1)]次方而不是-(x+1)呢?

Answer 1

因为你要保证指数是恒等变形啊.如果是-(x+1),指数就不是恒等变形了.