lim((1+tanx)/(1+sinx))^1/x x趋近于0
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lim((1+tanx)/(1+sinx))^1/x x趋近于0
lim((1+tanx)/(1+sinx))^1/x x趋近于0
lim((1+tanx)/(1+sinx))^1/x x趋近于0
(1+tanx)/(1+sinx)
=(1+sinx-sinx+tanx)/(1+sinx)
=1+(tanx-sinx)/(1+sinx)
=1+(sinx/cosx-sinx)/(1+sinx)
=1+sinx(1-cosx)/(1+sinx)
sinx~x,1-cosx~x²/2
lim(1+tanx)/(1+sinx)^1/x³
=lim(1+x³/2)^1/x³
=lim(1+x³/2)^2/x³*1/2
=e^1/2
后面是1/x³吧
(1+tanx/(1+sinx)^(1/x)=[1-sinx(1-1/cosx)/(1+sinx)]^(1/x)=e^[-2sinx(1-1/cosx)/x]=e^2(-1+1/cosx)]=1