证明:lim(1-e^1/x)/(1+e^1/x)当x趋向于0时,不存在
原式=lim(x->0){[2-1-e^(1/x)]/[1+e^(1/x)]}=lim(x->0){2/[1+e^(1/x)]-1}∵右极限=lim(x->0+){2/[1+e^(1/x)]-1}=-1左极限=lim(x->0-){2/[1+e^(1/x)]-1}=1∴右极限≠左极限故lim(x->0)(1-e^1/x)/(1+e^1/x)=不存在.
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