Question

数学导数问题？

Answer 1

lim(x->0) x^a. sin(1/x) = 0
=> a>0
ie a> 0 , f(x) 在x=0 连续
f'(0)
=lim(h->0) [ h^a. sin(1/h) -f(0) ]/h
=lim(h->0) h^(a-1). sin(1/h)
=0
=>
a-1>0
a>1
ie a> 1 , f(x) 在x=0 可导