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Uniform Convergence of nx/nx+1

  1. Oct 24, 2011 #1
    I am given [tex]f_n(x)=\frac{nx}{nx+1}[/tex] defined on [tex] [0,\infty) [/tex] and I have that the function converges pointwise to [tex] 0 \ \mbox{if x=0 and} 1\ \mbox{otherwise}[/tex]

    Is the function uniform convergent on [tex] [0,1] [/tex]?

    No. If we take x=1/n then [tex]Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5[/tex]

    which implies that [tex]Limit_{n\rightarrow\infty} sup |f_n(x)-1|[/tex] is not 0.

    I am then asked if it converges uniformly on the interval [tex](0,1][/tex] which I think it does but how do I show that [tex]Limit_{n\rightarrow\infty} sup |f_n(x)-1|[/tex]=0?

    thanks for any help
     
    Last edited by a moderator: Oct 26, 2011
  2. jcsd
  3. Oct 24, 2011 #2

    mathman

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    Your latex is screwed up.
     
  4. Oct 26, 2011 #3
    Yeah do you know why that is?

    thanks for any help
     
  5. Oct 26, 2011 #4
    don't put TEX in capitals.
     
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