设f(x)二阶可导,且f(0)=0,f′(0)=1,f″(0)=2,则limx→0f(x)?xx2=______

2024-11-09 10:06:14
推荐回答(1个)
回答(1):

因为f(x)二阶可导,且
f(0)=0,f′(0)=1,f(0)=2,
所以由L’Hospital法则

lim
x→0
f(x)?x
x2
lim
x→0
f′(x)?1
2x
1
2
lim
x→0
f′(x)?f′(0)
x
1
2
f″(0)=1.
所以
lim
x→0
f(x)?x
x2
=1

故答案为:1.