Part CCSIR NET December 2024a-fractional-growth-rate-rounds-to-an-integer-both-times

A fractional growth rate rounds to an integer both times

Let $f : \mathbb{C}$ \ {0} $\to \mathbb{C}$ be a non-zero holomorphic function such that |f(z)| ≤ |z|^(5/2) + 1/|z| $^(1/2), z \in \mathbb{C}$ \ {0}. Which of the following statements are true?

A.f has a pole at z = 0.
B.There is an entire function g such that f = g on $\mathbb{C}$ \ {0}.✓ Correct
C.f is a polynomial of degree at most 2.✓ Correct
D.f has an essential singularity at z = 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

A fractional growth rate rounds to an integer both times

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