# Average Value of Continuous Functions and Limits

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.

https://brainmass.com/math/real-analysis/average-value-continuous-functions-limits-37285

#### 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.