Let $\mathbb{R}\rightarrow\mathbb{R}$ be any function defined
as $f(x)=\begin{cases}{{x}^{\alpha}\sin \frac{1}{{x}^{\beta}}} & {,x\ne0} \\ {0} &
{,x=0}\end{cases}$, $\alpha , \beta \in \mathbb{R}$. Which of the following is true?
($\mathbb{R}$ denotes the set of all real numbers)