lim(x->0)(e^x+ax^2+bx)^(1⼀x^2)=1,求a,b

2025-04-29 00:17:22
推荐回答(3个)
回答1:

简单计算一下即可,答案如图所示

回答2:

回答3:

x->0
e^x = 1+ x +(1/2)x^2 +(1/6)x^3 +o(x^3)
e^x+ax^2+bx = 1 + (1+b)x + (1/2+a)x^2 +(1/6)x^3 +o(x^3)
lim(x->0) (e^x+ax^2+bx)^(1/x^2) =1

=>
1+b=0 and 1/2+a =0
b=-1 and a=-1/2