lim(x→0)(e^tan x-e^sin x)/x^3,

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/19 17:57:37

lim(x→0)(e^tan x-e^sin x)/x^3,
rt

=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

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