Alternate definitions of means Consider the function f 1t2
Chapter 5, Problem 64(choose chapter or problem)
Alternate definitions of means Consider the function f 1t2 = 1 b a xt + 1 dx 1 b a xt dx . Show that the following means can be defined in terms of f. a. Arithmetic mean: f 102 = a + b 2 b. Geometric mean: f a - 3 2 b = 1ab c. Harmonic mean: f 1-32 = 2ab a + b d. Logarithmic mean: f 1-12 = b - a ln b - ln a (Source: Mathematics Magazine 78, 5, Dec 2005)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer