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
2f″(0)=1.
所以
lim
x→0
f(x)−x
x2=1.
故答案为: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
2f″(0)=1.
所以
lim
x→0
f(x)−x
x2=1.
故答案为:1.