求极限lim(x→0)(x^2⼀2+cosx-1)⼀{x^3[(1+x)^봀-(1-x)^봀]}

2025-02-26 20:23:44
推荐回答(1个)
回答1:

泰勒公式
cosx=1-x^2/2!+x^4/4!+o(x^4)
(1+x)^1/2=1+x/2+o(x)
(1-x)^1/2=1-x/2+o(x)

带入极限
lim(x→0)(x^2/2+cosx-1)/{x^3[(1+x)^½-(1-x)^½]}

=lim(x→0)(x^4/4!)/(x^3*x)
=1/4!
=1/24