Functions defines on the plane $\mathbb{R}^2$ or open subsets , using $X=(x_1,x_2)\in\mathbb{R}^2$ asthe coordinates
Find all $\alpha \in \mathbb{R}$ such that $(\ln x_1)(x_2^2+x_2)=O(||X||^{\alpha})$ as $||X||\to 0$.
and $|X|| \to \infty$ (note that $x_1>0)$

It might help to be clear on notation. For instance I assume $||X||^\alpha = (x_1^2 + x_2^2)^{\alpha/2}$. In any case this is interesting, anyone got any ideas?