8 problems.
- Negation of two quantified statements
- The plane \(3x+4y+5z=0\) as kernel or image of an endomorphism of \(\mathbb{R}^3\)
- \(\int_0^\infty x^n e^{-x}\,dx = n!\)
- When does a matrix with eigenvalues \(\pm 1\) satisfy \(A^2=I\)?
- Uniform convergence to zero implies convergence of the integrals
- \(\lim_{x\to 1}\frac{x^2+1}{x}=2\)
- Gradient is orthogonal to level curves
- A left inverse forces \(f\) injective and \(g\) surjective, but neither need be bijective