Skip to content
Start free
Part CCSIR NET December 2024the-resolvent-exponentials-cancel-at-this-lambda

The resolvent exponentials cancel at this lambda

Let R(x, t) and u(x) denote the resolvent kernel and the solution, respectively, of the Volterra integral equation u(x) = eˣ dt. Then which of the following statements are true?

  1. A.R(x, t) = 1✓
  2. B.R(x, t) = e^(t−x)
  3. C.u(ln 8) = 10
  4. D.u(ln 7) = 9✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: Volterra equations have eigenvalues just like Fredholm equations

More on this topic

The chapter behind this: Separable kernels and resolvent kernels — free to read

From Linear Integral Equations › Separable kernels and resolvent kernels

ShareWhatsAppTelegram