Develop an elegant approach to the exponential and logarithm functions. Define a function G for x >

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Develop an elegant approach to the exponential and logarithm functions. Define a function G for x > 0:

G(x) = S JI 1 - dt

This exercise proceeds as if we didn’t know that G(x) = ln x and shows directly that G has all the basic properties of the logarithm. Prove the following statements.

ab 1   4 + d^ = 5  /  dt (b) G(ab) = G(a) + G(b). Break up the integral from 1 to ab into two integrals and

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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