9 problems.
- Negation, converse, and contrapositive of “if there exists a purple apple, then all lemons are pink”
- Eigenvalues and eigenvectors of \(\begin{pmatrix}1&-2\\3&-4\end{pmatrix}\)
- Determinant of a \(4\times 4\) integer matrix
- Dimension of \(\operatorname{span}\{x^2+x+1,\,x^2+2x,\,x^2+2,\,x-1\}\) over \(\mathbb{Q}\)
- Inductive formula for the derivatives of \(xe^{2x}\)
- Maclaurin series of \(xe^{2x}\) and a remainder bound on \([0,1/2]\)
- Extrema of \(xy\) on the ellipse \(x^2+4y^2=8\)
- The line integral \(\int_{\partial R} x\,dy+y\,dx\) on the upper region between \(x^2+y^2=4\) and \((x-1)^2+y^2=1\)
- Product of continuous functions is continuous, by \(\varepsilon\)-\(\delta\)