lean_workbook_plus_3068

(x_1 - x_2)^2 \geq 0 \Rightarrow x_1 \cdot x_2 \leq (x_1^2 + x_2^2)/2 . Then, $f \leq \sqrt{x_1^2 + x_2^2}/2$ which can be made arbitrarily small as $(x_1,x_2) \rightarrow 0$ .