Question

求数学大神4题怎么做

Answer 1

lim(x->0+) [1+ 2^(1/x)]/[1- 2^(1/x)]

=lim(x->0+) [1/2^(1/x) +1 ]/[1/2^(1/x)- 1]
=(0+1)/(0-1)
=-1
lim(x->0-) [1+ 2^(1/x)]/[1- 2^(1/x)]
=(1+0)/(1-0)
=1
=>
lim(x->0) [1+ 2^(1/x)]/[1- 2^(1/x)] 不存在

追问

大神，为啥要换位置啊

追答

lim(x->0+) 2^(1/x) ->+∞
=>
lim(x->0+) 1/2^(1/x) =0