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.

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