Question

导数定义求极限设f'(x0)存在,求当x→0时f(x)/x的极限,其中f(0)=0,且f(0)存在

Answer 1

f'(0)=[f(0+dx)-f(0)]/dx,dx趋近0

=f(dx)/dx

当x→0时f(x)/x的极限=f'(0)