Multivariable limits

Let's say we have a suspicion that $\lim\limits_{\vec{x} \to \vec{0}} f(\vec{x})=L=0$ for a function $f(\vec{x})$ such that after simplifying $\|f(\vec{x})-L\|<\varepsilon$, we get $\|\vec{x}\|^3+2\|\vec{x}\|^2+\|\vec{x}\|<\varepsilon$.

Can we say this limit exists?