
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 609 Thanks: 378 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.


Tags 
continuous, function, uniformly 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Show a Function is not Uniformly Continuous  dpsmith  Real Analysis  4  July 3rd, 2015 02:44 PM 
Prove a function is uniformly continuous...  ash116  Real Analysis  1  April 21st, 2010 11:33 AM 
not uniformly continuous  rose3  Real Analysis  1  December 30th, 2009 04:38 AM 
uniformly continuous function  eskimo343  Real Analysis  3  March 3rd, 2009 07:16 PM 
uniformly continuous on R  theQuake  Real Analysis  1  October 31st, 2008 12:33 AM 