Trace the matrix \[ \begin{bmatrix} 3 & 2 & 1 & 4 \\ 5 & 7 & 8 & 1 \\ 2 & 4 & 6 & 7 \\ 9 & 6 & 4 & 2 \end{bmatrix} \] (answer in integer).
Find the sum of eigenvalues of the matrix: \( \begin{bmatrix} 4 & 1 \\ 3 & 6 \end{bmatrix} \)
If x is an integer with \(x > 1\), the solution of \(\lim_{x \to \infty} \left(\dfrac{1}{x^2} + \dfrac{2}{x^2} + \dfrac{3}{x^2} + \cdots + \dfrac{x-1}{x^2} + \dfrac{1}{x}\right)\) is