I've seen this question in the Brazil Undergrad Olympiad this year. There is also a solution provided in the official webpage , but I didn't get it. Please, I'd appreciate it if someone could give a solution.
Let $A: \mathbb R^3 \to \mathbb R^2 $ given by $A(x,y,z) = (x+y+z,x+y)$. Prove that there exists an only s $\ge0$ such that the limit $c=\lim\limits_{\epsilon \to 0} \cfrac {vol(\{ v\; \in\;\mathbb R^3 ; \;|v|\; \le\; 1 \; \text{and } |Av| \;\lt \; \epsilon\}) }{\epsilon^s}$ exists, is positive, and compute s and c.
Thanks in advance.