lim(x→0) tanx-sinx⼀x3方 用洛必达法则解答 :

2025-03-11 03:52:16
推荐回答(1个)
回答1:

lim(x→0)[(x-tanx)/x^2sinx]
(用等价无穷小代换)
=lim(x→0)(x-tanx)/x^3
(0/0,用洛必达法则)
=lim(x→0)(1-sec^2x)/(3x^2)
=lim(x→0)-tan^2x/(3x^2)
(用等价无穷小代换)
=lim(x→0)-x^2/(3x^2)
=-1/3