Given any function $f: \mathbb{R^n} \to \mathbb{R^m}$ , if $$\lim_{x\rightarrow a}\|f(x)\| = 0$$ then does $$\lim_{x\rightarrow a}\frac{\|f(x)\|}{\|x-a\|} = 0 $$
as well? Is the converse true?
Given any function $f: \mathbb{R^n} \to \mathbb{R^m}$ , if $$\lim_{x\rightarrow a}\|f(x)\| = 0$$ then does $$\lim_{x\rightarrow a}\frac{\|f(x)\|}{\|x-a\|} = 0 $$
as well? Is the converse true?