Part BCSIR NET June 2025the-2-pi-R-arc-length-factor-forces-f-to-vanish-so-c-is-exactly-0

The 2 pi R arc length factor forces f to vanish so c is exactly 0

Let $f : C \to C$ be a polynomial map. For R > 0, let $γ_{R} : [0, 1] \to C$ be the map t ↦ $R e^{2 π i t}$ . Suppose that there exists $c \in R$ such that $\int_{0}^{1}$ |(f ∘ $γ_{R}) (t) γ_{R}^{'} (t)$ | dt → c as $R \to \infty$ . Which of the following statements is FALSE?

A.The function zf(1/z) → 0 as |z| $\to \infty$ .
B.The function f is constant.
C.c = 0.
D.c > 0.✓

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 boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

The 2 pi R arc length factor forces f to vanish so c is exactly 0

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