Question

已知lim(x→0)(sinx+xf(x))/x^3=1/3,求f(0),f'(0),f"(0)

Answer 1

简单计算一下即可，答案如图所示

Answer 2

根据条件
sin x+xf(x) =x^3/3 + o(x^3),
而sinx=x-x^3/6 +o(x^3),
因此xf(x)=-x+x^3/2 +o(x^3),
得到f(x)=-1+x^2/2+o(x^2)
f(0)=-1,f′(0)=0,f′′(0)=1