Let \( f: R \rightarrow R \) be a function we say that \( f \) has ...

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Let \( f: R \rightarrow R \) be a function we say that \( f \) has
PROPERTY 1 if \( \lim _{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}} \) exist and is finite and
\( \mathrm{P} \) PROPERTY 2 if \( \lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h^{2}} \) exist and is finite.
- Then which of the following options is/are correct?
(A) \( f(x)=x^{2 / 3} \) has property 1
(B) \( f(x)=\sin x \) has property 2
(C) \( f(x)=|x| \) has property 1
(D) \( f(x)=x|x| \) has property 2
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