Explore BrainMass

Explore BrainMass

    Average Value of Continuous Functions and Limits

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    The definition of average value of a continuous function can be extended to an infinite interval by defining the average value of f on the interval [a, ∞) to be

    Lim as t approaches ∞ 1/(t-a)integrand from a to t f(x)dx

    1. Find the average value of {see attachment} on [0, ∞).
    2. Find the lim as x goes to infinity {see attachment}
    3. If f(x) ≥ 0, and integrand from a to infinity f(x)dx, if this limit exists.
    4. Explain what number 3 has to do with the original problem.

    © BrainMass Inc. brainmass.com November 30, 2021, 12:21 am ad1c9bdddf
    https://brainmass.com/math/real-analysis/average-value-continuous-functions-limits-37285

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    The definition of average value of a continuous function can be extended to an infinite interval by defining the average value of f on the interval ...

    Solution Summary

    Average Value of Continuous Functions and Limits are investigated. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT