lim tan x - sin x / x³ lim eˆ2x - 1 / x

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/06 08:29:51

lim tan x - sin x / x³ lim eˆ2x - 1 / x
x趋近于0 X趋近于0

原式=lim(x->0) sinx(secx-1)/x^3
=lim(x->0) (secx-1)/x^2
=lim(x->0) (1-cosx)/x^2cosx
=lim(x->0) 2sin^2(x/2)/x^2cosx
=lim(x->0) 2(x^2/4)/x^2cosx
=1/2
原式=lim(x->0) 2x/x
=2

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