Let f(x, y) = \(\rm e^{x^2+y^2}\) for (x, y) ∈ ℝ², and a_n be the determinant of the matrix 

\(\left(\begin{array}{cc} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial x \partial y} \\ \frac{\partial^2 f}{\partial y \partial x} & \frac{\partial^2 f}{\partial y^2} \end{array}\right)\)

evaluated at the point (cos(n),sin(n)). Then the limit \(\displaystyle\lim_{n \rightarrow \infty}\) a_n is