lim (e^1/x-e^-1/x)/(e^1/x+e^-1/x) x趋向0+
=lim (e^1/x-e^-1/x)*e^(1/x)/[(e^1/x+e^-1/x)*e^(1/x)] x趋向0+
=lim (e^2/x-1)/(e^2/x+1) x趋向0+
=lim (e^2/x+1-2)/(e^2/x+1) x趋向0+
=1-lim 2/(e^2/x+1) x趋向0+
=1-0
=1
lim (e^1/x-e^-1/x)/(e^1/x+e^-1/x) x趋向0+
=lim (e^1/x-e^-1/x)*e^(1/x)/[(e^1/x+e^-1/x)*e^(1/x)] x趋向0+
=lim (e^2/x-1)/(e^2/x+1) x趋向0+
=lim (e^2/x+1-2)/(e^2/x+1) x趋向0+
=1-lim 2/(e^2/x+1) x趋向0+
=1-0
=1