讨论分段函数当x不等于0时f(x)=x方×sin1⼀x,当x=0时f(x)=0在x=0处是否可导?

2024-11-06 03:41:27
推荐回答(1个)
回答(1):

f(x)
=x^2 .sin(1/x) ; x≠0
=0 ; x=0

lim(x->0) f(x)
=lim(x->0) x^2.sin(1/x)
=0
=f(0)
x=0 , f(x) 连续

f'(0)
=lim(h->0) [f(h)- f(0)] /h
=lim(h->0) h.sin(1/h)
=0