9 problems.
- Negations of statements about odd integers and a sequential limit
- The binomial theorem, \((x+y)^5\equiv x^5+y^5\pmod{5}\), and \((x+y)^{5^n}\equiv x^{5^n}+y^{5^n}\pmod{5}\)
- Injectivity of \(g\circ f\) versus injectivity of \(f\) and \(g\)
- The \(\varepsilon\)-\(\delta\) definition of \(\lim_{x\to a}f(x)=\ell\), and \(\lim_{x\to 2}\frac{2x+1}{x^2+1}\)
- A counterclockwise line integral \(\int_C (x^3-y^3)\,dx+(x^3+y^3)\,dy\) is nonnegative
- Cube roots of \(-2-2i\)
- Diagonalizability of \(\begin{pmatrix}0&1\\6&-1\end{pmatrix}\) and a closed form for \(A^k\begin{pmatrix}1\\7\end{pmatrix}\)
- Independent images under a linear map imply independent preimages
- \(x-x^3/3 \le \arctan x \le x\) for \(x\ge 0\)