Prove that $$f:\Bbb R\to \Bbb R\\ x\mapsto \frac{1}{1+x^2}$$ is uniformly continuous.
2026-03-30 17:13:22.1774890802
Bounded derivative function is uniformly continuous
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$f$ is continuous and $\lim_{x\to\pm\infty} \dfrac{1}{1+x^2}=0$, thus $f$ is uniformly continuous.