Question

Let f(x, y) = $e^{x^2}+y^2$ for (x, y) ∈ $\R^2$ , and an be the determinant of the matrix
$\begin{pmatrix} \frac{∂^2f}{∂x^2} & \frac{∂^2f}{∂x∂y} \\\ \frac{∂^2f}{∂y∂x} & \frac{∂^2f}{∂y^2} \end{pmatrix}$
evaluated at the point (cos(n),sin(n)). Then the limit $\lim\limits_{n \rightarrow \infin}$ an is

• A. non-existent
• B. 0
• C. 6e2
• D. 12e2

Answer 1

Answer: (D)

12e2

Answer 2

The correct option is (D) : 12e2.