Let $\mathrm{F}: \mathbb{R} \rightarrow \mathbb{R}$ be a 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 ?
Select ALL correct options:
A
$\mathrm{f}(\mathrm{x})=\mathrm{x}|\mathrm{x}|$ has PROPERTY 2
B
$\mathrm{f}(\mathrm{x})=\mathrm{x}^{2 / 3}$ has PROPERTY 1
C
$f(x)=\sin x$ has PROPERTY 2
D
$\mathrm{f}(\mathrm{x})=|\mathrm{x}|$ has PROPERTY 1
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