For the Sturm–Liouville eigenvalue problem, verify the following general proper...

For the Sturm–Liouville eigenvalue problem,

verify the following general properties:

(a) There is an infinite number of eigenvalues with a smallest but no largest.

(b) The nth eigenfunction has n − 1 zeros.

(c) The eigenfunctions are complete and orthogonal.

(d) What does the Rayleigh quotient say concerning negative and zero eigenvalues?