9 problems.
- Smooth negations of a quantified inequality, the extreme value theorem, and a biconditional
- Diagonalize \(\begin{pmatrix}7&-3\\1&3\end{pmatrix}\)
- \(N(A^t A)=N(A)\)
- \(f(xy)=xf(y)+yf(x)\) implies \(f(1)=0\) and \(f(u^n)=n u^{n-1}f(u)\)
- \(\varepsilon\)-\(\delta\) proof that \(\lim_{x\to 2} 1/(x^2+1)=1/5\)
- \(A \subseteq f^{-1}(f(A))\), with equality iff \(f\) is injective
- Path-independence of \(\int_C (x+y^3)\,dx+(e^y+3xy^2)\,dy\)
- Pointwise and uniform convergence of \(nx/(n+x)\) on \([0,\infty)\)
- \(a+I\) is a unit in \(R/I\) whenever \((a)+I=R\)