f(x)在x=0的领域内有二阶导数,又x→0时lim(（sinx+xf（x））\x3)=0,求f(0),f'(0),f''(0)

f(x)在x=0的领域内有二阶导数,又x→0时lim(（sinx+xf（x））\x3)=0,求f(0),f'(0),f''(0)
f(x)在x=0的领域内有二阶导数,又x→0时lim(（sinx+xf（x））\x3)=0,求f(0),f'(0),f''(0)

f(x)在x=0的领域内有二阶导数,又x→0时lim(（sinx+xf（x））\x3)=0,求f(0),f'(0),f''(0)
sinx=x+(1/3!)x³+0(x³)
f(x)=f(0)+f′（0）x+f″(0)x²+0(x³)
xf(x)=f(0)x+f′（0）x²+f″(0)x³+0(x³)
sinx+xf(x)=(1+f(0))x+f′（0）x²+[(1/3!)+f″(0)]x³+0(x³)
lim(（sinx+xf（x））\x3)=0,
1+f(0)=0 f′（0）=0 (1/3!)+f″(0)=0
f(0)=-1 f′（0）=0 f″(0)=-(1/3!)