Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 32E / a / iii / Solution

This is not an asymptotic sequence. The functions $\sin (x^n)$ oscillate and have arbitrarily large zeros; the ratio
$\sin (x^{n+1})/\sin (x^n)$ has no limit, let alone limit zero.

Solved by gpt-5.6-sol high.