This is one of the practice questions I'm working on:
Use the Sequential Criterion to prove that $f(x) = \sin(x^2)$ is not uniformly continuous on $\Bbb R$.
I need some help to get started, for instance, what sequences should I be choosing?
2026-03-28 18:12:58.1774721578
sequential criterion
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Consider the sequence $x_n = \sqrt{\pi(2n+1/2)}$ and $y_n = \sqrt{\pi(2n-1/2)}$.
What happens to the function along these sequences?
What can you say about $\lim_{n \to \infty} (x_n-y_n)$?