6 problems.
- Consider the function \(f(x) = \frac{x}{1-x^2}\),
- \(\limsup a_k=\inf\{s:\text{only finitely many }a_k\ge s\}\)
- A compact metric space is complete and separable, and sequences with summable consecutive distances converge
- \(f(0)=f(2)=0\) and \(f(c)=1\) imply \(|f'|>1\) somewhere on \((0,2)\)
- Pointwise convergence of \(n^\beta x(1-x^2)^n\) on \([0,1]\), uniform if and only if \(\beta<\frac12\)
- Riemann–Stieltjes integral against a jump, and vanishing of \(g\) against \(x^{3k+2}\)