# Average Value of Continuous Functions and Limits

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

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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 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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