8 problems.
- Continuity of \(1/x\) at \(x=1\)
- A matrix \(P\) diagonalizing \(\begin{pmatrix} 1 & 2 \\ 1/2 & 1 \end{pmatrix}\)
- \(x^2\sin(1/x)\) is differentiable everywhere but \(f'\) is discontinuous at \(0\)
- Nullspace of \(M\) is the orthogonal complement of the column space of \(M^t\)
- The sum of cubes of three consecutive positive integers is divisible by \(9\)
- Convergence of series, and the alternating series test
- Line integral of \(2xy\,dx+(x^2+y^2)\,dy\) from \((1,0)\) to \((0,1)\)
- Eigenvectors for distinct eigenvalues are linearly independent