9 problems.
- \(\sum_{k=0}^{n-1}a^k=(a^n-1)/(a-1)\)
- Contrapositive and converse of: a local minimum at \(a\) implies \(f'(a)=0\) or nondifferentiability at \(a\)
- Cube and square roots of \(-2+2\sqrt{3}i\)
- No \(n\) makes both \((21n-3)/4\) and \((15n+2)/4\) integers
- An injective linear map sends independent sets to independent sets
- Real \(x\) for which \(\sum_{n=1}^\infty \frac{x^n}{\sqrt{n^2+1}}\) converges
- \(\varepsilon\)-\(\delta\) continuity, and the sum of functions continuous at \(3\)
- Line integral of \(y^2\,dx+(2x-3y)\,dy\) on \(x^2+y^2=9\)
- \(f:\mathbb{R}\to\mathbb{R}^2\) and \(g:\mathbb{R}^2\to\mathbb{R}\) cannot compose to a diffeomorphism