f(x)在点x=o的某一邻域内具有连续的二阶导数lim(x->0)f(x)/x=0f(x)在点x=o的某一邻域内具有连续的二阶导数lim(x->0)f(x)/x=0,则：f(0)=f'(0)=0则：lim(x->0)f(x)/x^2=lim(x->0)f'(x)/2x=0问题是：为什么lim(x->0)f

Question

f(x)在点x=o的某一邻域内具有连续的二阶导数 lim(x->0)f(x)/x=0
f(x)在点x=o的某一邻域内具有连续的二阶导数
lim(x->0)f(x)/x=0,则：
f(0)=f'(0)=0
则：lim(x->0)f(x)/x^2=lim(x->0)f'(x)/2x=0


问题是：为什么lim(x->0)f'(x)/2x=0 ?

Answer 1

lim(x->0)f'(x)/2x
=(1/2)lim(x->0) [f'(x)-f'(0)]/x
=(1/2)f''(0)
除非题目中有条件,f''(0)=0,否则此处推不出这个极限为0.