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Math Help - uniform convergence

  1. #1
    xyz
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    uniform convergence



    is this true or false? Explain why. I think it is not true because the interval is unbounded. However, I cannot explain why.
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  2. #2
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    Quote Originally Posted by xyz View Post


    is this true or false? Explain why. I think it is not true because the interval is unbounded. However, I cannot explain why.
    It is true. Here is a hint

    f_n(t)=\frac{1}{t\ln(n)} the largest value of any sequence member is given when t=1 i.e f_n(1)\gef_n(t) for all t \in [1,\infty]
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  3. #3
    xyz
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    uniform convergence

    If thats true, I am not quite sure how this problem is done. The complete problem is



    I appreciate your help a lot. The next thing, is to take limit of n on both sides. Does that mean right hand limit at 0 and left hand limit at 0? Please let me know how the problem ends up with 1 as value of integral when it should be 0?
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  4. #4
    Super Member redsoxfan325's Avatar
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    It's true that uniform convergence allows you to interchange the limit and the integral, but only on a bounded interval [a,b]. (The proof of the theorem uses the value b-a, which makes no sense if b=\infty.)
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