Explain why or why not Determine whether the
Chapter 5, Problem 41(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If f is symmetric about the line x = 2, then 1 4 0 f 1x2 dx = 21 2 0 f 1x2 dx. b. If f has the property f 1a + x2 = -f 1a - x2, for all x, where a is a constant, then 1 a + 2 a - 2 f 1x2 dx = 0. c. The average value of a linear function on an interval 3a, b4 is the function value at the midpoint of 3a, b4. d. Consider the function f 1x2 = x1a - x2 on the interval 30, a4, for a 7 0. Its average value on 30, a4 is 12 of its maximum value.
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