A question about limit of a continuous function

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  • #1
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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?
 

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  • #2
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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?
 
  • #3
Ray Vickson
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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?

Show your work. Where are you stuck?

RGV
 
  • #4
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Show your work. Where are you stuck?

RGV

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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