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This question already has an answer here:

prove the function f(x)= Seq(Abs(x)) is uniformly continuous on its domain prove the function f(x)= Seq(Abs(x)) is uniformly continuous on its domain would someone please check my work. Thank you in advance .

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marked as duplicate by user147263, callculus, J. W. Perry, Milo Brandt, Adam Hughes Nov 25 '15 at 6:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ People would be more willing to check your work if it was more readable: see MathJax tutorial. $\endgroup$ – user147263 Nov 24 '15 at 23:56
  • $\begingroup$ I have posted a picture for what I have done . $\endgroup$ – Ahmad Talafha Nov 25 '15 at 2:45
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Inside $[-1,1]$, it is u.c., since it's continuous on a compact set; outside, $f'(x)$ is bounded, so it is also u.c.

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