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Understanding the Average Value of a Function: A Comprehensive Guide

This guide explores the average value of functions with examples such as f(x) = x ln x over the interval [1, e], and discusses calculations for air pollution levels from a factory. It provides insights into determining the average value over specified intervals, including methods that require and do not require calculators. Readers will learn how to apply the average value concept in various scenarios, including rates of change and pollution levels, enhancing their understanding of this crucial mathematical concept.

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Understanding the Average Value of a Function: A Comprehensive Guide

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  1. Section 8.4 – Average Value of a Function 7.1

  2. Find the average value of One more formula….. The Average Value of a Function

  3. CALCULATOR REQUIRED • The average value of f(x) = x ln x on the interval [1, e] is: • 0.772 • 1.221 • 1.359 • 1.790 • 2.097

  4. NO CALCULATOR The average value of over the interval is:

  5. NO CALCULATOR • If , then the average rate of change of y with respect • to x on the closed interval [0, 4] is: • 1/16 • 1 • 4/3 • d) • e) 2

  6. CALCULATOR REQUIRED • The level of air pollution at a distance x miles from a tire factory • is given by . The average level of pollution • between 10 and 20 miles from the factory is: • 0.226 • 0.230 • 0.234 • 0.238 • 0.242

  7. Find the average value of Find the average value of a) [-1, 0]b) [0, 1]c) [-1, 1]

  8. NO CALCULATOR • Of the average value of over the interval [1, b] is 13/3, • then the value of b could be: • 7/3 • 3 • 11/3 • 4 • 13/3

  9. CALCULATOR REQUIRED • The functions f and g above are defined on the closed interval • [0, b]. They will have the same average value if b is: • 0.848 • 0.852 • 0.854 • 0.858 • 0.862 Graph and find the zero……. 0.854 – Choice C

  10. CALCULATOR REQUIRED

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