9 problems.
- Composition of injective maps is injective
- \(\lim_{x\to 2}(x+1/x)=5/2\)
- \(n\)th derivative of \(xe^{2x}\)
- Basis for \(\operatorname{span}\{(1,1,1,1),(3,4,6,7),(5,6,8,9)\}\)
- A \(3\times 3\) matrix with eigenvalues \(-1,0,1\) satisfies \(A^3=A\)
- Maclaurin series of \(\arctan x\) accurate to \(10^{-5}\) for \(|x|\le 10^{-2}\)
- Uniformly convergent sequences of bounded functions are uniformly bounded
- Directional derivatives exist and equal \(\nabla f\cdot\mathbf{u}\) when the first partials are continuous
- \(\mathbb{F}_8\cong\mathbb{F}_2[t]/\langle t^3+t+1\rangle\)