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A question about limit of a continuous function

  1. May 21, 2012 #1
    I am trying to solve a question and I need to justify a line in which |lim(x-->0)(f(x))|≤lim(x-->0)|f(x)| where f is a continuous function.

    Any help?
     
  2. jcsd
  3. May 21, 2012 #2

    micromass

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    The absolute value is a continuous function. That is:

    [tex]|\ |:\mathbb{R}\rightarrow \mathbb{R}:x\rightarrow |x|[/tex]

    is continuous. Does that help?? What do you know about continuity and limits?
     
  4. May 21, 2012 #3

    Ray Vickson

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    Show your work. Where are you stuck?

    RGV
     
  5. May 21, 2012 #4
    actually I figured this out. Since || is a continuous, |lim(x-->0)(f(x))|= lim(x-->0)|f(x)| which is obvious from one of the theorems in my book.

    Thanks though!
     
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