$f(x)$ is continuous for $\forall x \geq 0$ and monotonically decrease. $f(0)=0$. $a>0$. Is it true $$ \varlimsup_{x\rightarrow 0^+}\frac{f(x)}{x^a}=\varliminf_{\delta \rightarrow 0^+}\frac{f(x)}{x^a} $$ whenever both are finite or infinite?

$f(x)$ is continuous for $\forall x \geq 0$ and monotonically decrease. $f(0)=0$. $a>0$. Is it true $$ \varlimsup_{x\rightarrow 0^+}\frac{f(x)}{x^a}=\varliminf_{x \rightarrow 0^+}\frac{f(x)}{x^a} $$ whenever both are finite or infinite?