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

A double pole extracts the derivative

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

A.f(1)
B.f(2)
C.f′(1)
D.f′(2)✓

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.

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A double pole extracts the derivative

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