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 November 1st, 2018, 05:26 PM #1 Newbie   Joined: Oct 2018 From: Indonesia Posts: 4 Thanks: 0 Math Focus: Nonlinear Waves and Differential Equations Uniformly Continuous Function Hello again! How do I solve this problem : Show that $$f\left(t\right)=\frac{\sin{t}}{t}$$ is an uniformly continuous function on $\mathbb{R}$ using $\delta-\varepsilon$ definition! Thank you.
 November 1st, 2018, 07:48 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 645 Thanks: 407 Math Focus: Dynamical systems, analytic function theory, numerics Break the domain into 2 pieces. Use Heine-Cantor theorem for the interval $[-1,1]$. Use the mean value inequality for the unbounded remaining portion. Thanks from Maschke

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