lim{1+x/1-x}^(1/x)要解法 X→0
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lim{1+x/1-x}^(1/x)要解法X→0lim{1+x/1-x}^(1/x)要解法X→0lim{1+x/1-x}^(1/x)要解法X→0lim(x→0)[(1+x)/(1-x)]^(1/x)=
lim{1+x/1-x}^(1/x)要解法 X→0
lim{1+x/1-x}^(1/x)要解法 X→0
lim{1+x/1-x}^(1/x)要解法 X→0
lim(x→0) [(1+x)/(1-x)]^(1/x)
=lim(x→0) [(1-x+2x)/(1-x)]^(1/x)
=lim(x→0) [1+2x/(1-x)]^(1/x)
=lim(x→0) [1+2x/(1-x)]^[(1-x)/2x]*2/(1-x)
∵lim(x→0) [1+2x/(1-x)]^[(1-x)/2x]=e
∵lim(x→0) 2/(1-x)=2/(1-0)=2
∴原式=e²
∵1/x=(1-x+x)/x=[(1-x)/x]+1
原式=lim[1+x/(1-x)]^[(1-x)/x]·lim[1+x/(1-x)]
=e·1
=e
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