Let $$f: R \rightarrow R$$ bea function. We say that f has
PROPERTY 1 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{\sqrt{|h|}}$$ exists and is finite, and
PROPERTY 2 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{h^2}$$ exists and is finite.
Then which of the following options is/are correct?

A

$$f(x) = |x|$$ has PROPERTY 1

B

$$f(x) = x^{\frac{2}{3}}$$ has PROPERTY 1

C

$$f(x) = x|x|$$ has PROPERTY 2

D

$$f(x) = \sin x$$ has PROPERTY 2