来自候宏的问题
设f(x)在x处可导,则limh→0f(x+h)−f(x−h)2h等于()。A.2f′(x)B.12f′(x)C.f′(x)D.4f′(x)
设f(x)在x处可导,则limh→0f(x+h)−f(x−h)2h等于( )。A.2f′(x)B.12f′(x)C.f′(x)D.4f′(x)
1回答
2019-06-23 08:52
设f(x)在x处可导,则limh→0f(x+h)−f(x−h)2h等于()。A.2f′(x)B.12f′(x)C.f′(x)D.4f′(x)
设f(x)在x处可导,则limh→0f(x+h)−f(x−h)2h等于( )。A.2f′(x)B.12f′(x)C.f′(x)D.4f′(x)
本题主要考查变化率。因为f(x)在x处可导,所以limh→0f(x+h)−f(x−h)2h=limh→0f(x+h)−f(x)2h+limh→0f(x)−f(x−h)2h=12[limh→0f(x+h)−f(x)h+limh→0f(x)−f(x−h)h]=12[f′(x)+limh→0f(x−h)−f(x)−h]=12[f′(x)+f′(x)]=f′(x)。故本题正确答