Skip to content
Part BCSIR NET December 2024a-double-pole-extracts-the-derivative

A double pole extracts the derivative

Let γ\gamma be the circle {z∈Cz \in \mathbb{C} : |z| = 3} oriented counterclockwise. Let f be an entire function. What is the value of A for which ∫γ(A/(z−1)−f(z)/(z−2)2)\int_\gamma (A/(z - 1) - f(z)/(z - 2)^{2})dz = 0 holds?

  1. A.f(1)
  2. B.f(2)
  3. C.f′(1)
  4. D.f′(2)✓ Correct

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, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Cauchy's theorem applies to any domain without singularities of f

More on this topic

The chapter behind this: Cauchy's theorem and integral formula — the toolkit — free to read

From Cauchy Theory › Cauchy's theorem and integral formula

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram