lim(x→0)(e^tan x-e^sin x)/x^3,rt
问题描述：
lim(x→0)(e^tan x-e^sin x)/x^3,
rt
答
=lim e^sinx · (e^(tanx-sinx) -1)/x^3=1×lim (e^(tanx-sinx) -1)/x^3=lim (tanx-sinx)/x^3=lim (sinx /x) · lim(1/cosx -1)/x²=lim (1-/cosx)/x² /lim cosx=lim(1/2)x²/x² /1=1/2