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
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
\(\begin{pmatrix} \frac{∂^2f}{∂x^2} & \frac{∂^2f}{∂x∂y} \\ \frac{∂^2f}{∂y∂x} & \frac{∂^2f}{∂y^2} \end{pmatrix}\)
evaluated at the point (cos(n),sin(n)). Then the limit \(\lim\limits_{n \rightarrow \infin}\) an is
Updated On: Oct 1, 2024
- non-existent
- 0
- 6e2
- 12e2
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The Correct Option is D
Solution and Explanation
The correct option is (D) : 12e2.
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