How to show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous?
Thank you. Also, how do I become good at writing these proofs?
2026-04-02 16:53:00.1775148780
How can I prove that this function is uniformly continuous?
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You can show that it is differentiable, and has bounded derivative. Then use Lagrange's mean value theorem.