7 problems.
- \(\lim|a_{n+1}/a_n|=L\) implies \(\lim|a_n|^{1/n}=L\), and the ratio test for the radius of convergence
- A power series has an expansion about every point of its disc of convergence
- Convergence of \(\sum nz^n\), \(\sum z^n/n^2\), and \(\sum z^n/n\) on \(S^1\)
- \(\lim_{x\to+\infty}\int_{\gamma_x}f=iAb\) when \(f(x+iy)\to A\) independently of \(y\)
- Fresnel integrals \(\int_0^\infty\sin(x^2)\,dx=\int_0^\infty\cos(x^2)\,dx=\frac{\sqrt{2\pi}}{4}\)
- \(\int_0^\infty\frac{\sin x}{x}\,dx=\frac\pi 2\)
- Continuous functions on \(\overline{\mathbb{D}}\) need not be uniformly approximable by polynomials in \(z\)