f(x)
=x^k. sin(1/x) ; x≠0
=0 ; x=0
lim(x->0) f(x)
=lim(x->0) x^k. sin(1/x)
=0 当 k>0
ie
k>0 , x=0 , f(x) 连续
f'(0)
=lim(h->0) [h^k. sin(1/h) -f(0)]/h
=lim(h->0) h^(k-1). sin(1/h)
=0 当 k>1
k>1 , x=0 , f(x) 可导
