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Difficult Question in Calculus — limits and integrals

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    file.php?id=21.png
    (hebrew) : f(x) a continuous function. proof the following

    2. Relevant equations
    I guess rules of limits and integrals

    3. The attempt at a solution
    I've tried several approaches:
    taking ln() of both sides and using L'Hospitale Rule.
    Thought about using integral reduction formula.
    But really nothing even got me close.
    Looking forward to any advice
     
  2. jcsd
  3. Mar 25, 2015 #2

    Mark44

    Staff: Mentor

    Please show us at least some of what you've tried. Per forum rules, you must show an attempt.
     
  4. Mar 25, 2015 #3
  5. Mar 25, 2015 #4

    Dick

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    Science Advisor
    Homework Helper

  6. Mar 25, 2015 #5

    Ray Vickson

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    If I were doing it would let
    [tex] M = \max_{x \in [a,b]} |f(x)|, \; L_t = \left( \int_a^b |f(x)|^t \, dx \right)^{1/t}, [/tex]
    then I would show that: (1) ## \lim_{t \to \infty} L_t \leq M##; and (2) ##\lim_{t \to \infty} L_t \geq M##.

    (1) is quite easy; (2) is a bit trickier and needs some properties of continuous functions on finite, closed intervals.
     
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