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November 1st, 2018, 05:26 PM   #1
Joined: Oct 2018
From: Indonesia

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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.
gusrianputra is offline  
November 1st, 2018, 07:48 PM   #2
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From: USA

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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.
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