Let \( \mathrm{F}: \mathrm{R} \rightarrow \mathrm{R} \) be a function. We say that \( \mathrm{f}...

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Let \( \mathrm{F}: \mathrm{R} \rightarrow \mathrm{R} \) be a function. We say that \( \mathrm{f} \) has
PROPERTY 1; if \( \lim _{h \rightarrow 0} \frac{\mathrm{f}(\mathrm{h})-\mathrm{f}(0)}{\sqrt{|\mathrm{h}|}} \) exists and is finite,
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PROPERTY 2 ; if \( \lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h^{2}} \) exists and is finite.
[JEE Advanced-2019]
Then which of the following options is/are correct ?
(1) \( f(x)=x|x| \) has PROPERTY 2
(2) \( f(x)=x^{2 / 3} \) has PROPERTY 1
(3) \( f(x)=\sin x \) has PROPERTY 2
(4) \( f(x)=|x| \) has PROPERTY 1
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