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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 HeineCantor theorem for the interval $[1,1]$. Use the mean value inequality for the unbounded remaining portion.


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continuous, function, uniformly 
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