Question

大一高数求解

Answer 1

如下图：

Answer 2

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

追问

没有看懂……

追答

是这样
令 y=1/x
x->0, y->+∞
lim(x->0) x^α.sin(1/x)

=lim(y->+∞) (siny)/y^α
=0 (α>0)
lim(x->0) x^α.sin(1/x) = 0 ( α>0)
-------
lim(h->0) h^(α-1)sin(1/h) 要存在
=>
α-1>0
α>1
lim(h->0) h^(α-1)sin(1/h) =0 ( α>1)