Let $F:R\to R$ be a function. We say that $f$ has:
 PROPERTY $1$  if $\underset{h\to 0}{\lim }\frac{f\left(h\right)-f\left(0\right)}{\sqrt{\left|h\right|}}$ exists and is finite, and 
PROPERTY $2$  if $\underset{h\to 0}{\lim }\frac{f\left(h\right)-f\left(0\right)}{h^2}$ exists and is finite.
Then which of the following options is/are correct?

• A

  $f\left(x\right)=x\left|x\right|$ has PROPERTY $2$
• Correct answer
  B

  $f\left(x\right)=x^{2/3}$ has PROPERTY $1$
• C

  $f\left(x\right)=\sin x$ has PROPERTY $2$
• Correct answer
  D

  $f\left(x\right)=\left|x\right|$ has PROPERTY $1$

Hence, the correct answer is options: 'B', 'D'.