Let F: R → R be a function. We say that f has: PROPERTY 1 if _ h →...

\left(A\right)f\left(x\right) = \left|x\right|$<br/>$\lim_{h \to 0} \dfrac{\left|h\right| - 0}{\sqrt{\left|h\right|}} = \lim_{h \to 0} \sqrt{\left|h\right|} = 0$<br/>\left(B\right)f\left(x\right) = {x}^{\dfrac{2}{3}}$
$\lim_{h \to 0} \dfrac{{h}^{\dfrac{2}{3}} - 0}{\sqrt{\left|h\right|}} =\lim_{h \to 0} {\left|h\right|}^{\dfrac{1}{6}} = 0$
\left(C\right)f\left(x\right) = x\left|x\right|$<br/>$\lim_{h \to 0} \dfrac{h\left|h\right| - 0}{{h}^{2}} = \lim_{h \to 0} \dfrac{\left|h\right|}{h} = \left\{$$\begin{array}{ll}1, ifh \to {0}^{+} \\ - 1, if h \to {0}^{-}\end{array}$$\right)
Does not exist
$\left(D\right)f\left(x\right) = sin x$
$\lim_{h \to 0} \dfrac{sin h - 0}{{h}^{2}} = \lim_{h \to 0} \dfrac{1}{h}\dfrac{sin h}{h} ⇒$ does not exist