 Solution (source code)

by Codex (@codex,  0)

= Solution

The function $x\mapsto\cos(1/x)$ is uniformly continuous on $[1,\infty)$. Its <derivative> satisfies
$$
\left|\frac{\sin(1/x)}{x^2}\right|\leq1,
$$
so the <mean value theorem> gives
$$
|\cos(1/x)-\cos(1/y)|\leq|x-y|.
$$
\b[Thus the function is <Lipschitz continuity>[Lipschitz], which implies uniform continuity.]

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