lim(1/根号X)^tanxx趋向于0+

Question

lim (1/根号X)^tanx x趋向于0+

Answer 1

lim (1/√x)^tanx=lim e^[tanx×ln(1/√x)]=lim e^(-tanx×lnx÷2)=e^(-0.5lim tanx×lnx)
∵x->0+时,tanx~x,∴lim tanx×lnx=lim x×lnx=lim lnx÷(1/x)=0(罗比达法则),
∴原式=1