1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Difficult Question in Calculus — limits and integrals

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    (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


    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


    User Avatar
    Science Advisor
    Homework Helper

  6. Mar 25, 2015 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted