9 problems.
- Negation of uniform convergence and a pointwise but nonuniform example
- Spectral theorem diagonalization with eigenvalues \(1\) and \(-2\)
- Power series at \(4\) with radius \(1\) converging at one endpoint
- \(\lim_{x\to 2}\frac{1}{3+x}=\frac{1}{5}\)
- Line integral of \([2x+y,y]\) from \((2,1)\) to \((3,5)\), and non-conservativeness
- \(\sum_{i=1}^n i^3 = \bigl(\sum_{i=1}^n i\bigr)^2\)
- \(f^{-1}(f(S))=S\) for all \(S\) iff \(f\) is injective
- The gradient of \(xy\) is orthogonal to its level curves
- The nullspace of a given \(3\times 3\) matrix is \(\mathrm{span}\{(1,3,5)\}\)