当x→0时 fx=x-(ax+bsinx)*cosx与x3次方是等价无穷小求a,b

2025-04-27 14:13:11
推荐回答(2个)
回答1:

简单计算一下即可,答案如图所示

回答2:

f(x) = x-(ax+bsinx)cosx =x-[(a+b)x-bx^3/6+o(x^3)][1-x^2/2+o(x^3)]
= x-(a+b)x-bx^3/6+(a+b)x^3/2 + o(x^3)
= (1-a-b)x + (3a+2b)x^3/6 + o(x^3) ~ x^3
1-a-b = 0, 3a+2b = 1, a = -1, b = 2