5 problems.
- Pointwise but not uniform convergence of \(1/(1+n^2x^2)\) and \(nx(1-x)^n\), and equicontinuity
- Boundedness and closedness of the self-maps of \([0,1]\) in \(C_b([0,1])\)
- \(|f'|\le k|f|\) and \(f(0)=0\) imply \(f\equiv 0\) on \([0,1]\)
- Riemann-Stieltjes integrability of \(e^{2x}\) against a broken-step integrator on \([0,4]\)
- A positive continuous function on \([a,b]\) is bounded away from zero, via Heine-Borel