 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[Uniformly continuous.] For $x\geq1$, the <derivative> satisfies
$$
\left|\frac{d}{dx}\frac{\sin x}{x}\right|=\left|\frac{\cos x}{x}-\frac{\sin x}{x^2}\right|\leq2.
$$
The <mean value theorem> therefore gives a <Lipschitz condition> with constant two, hence <uniform continuity>.

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