The Logarithm log(x)

  • Kenneth Eriksson
  • Donald Estep
  • Claes Johnson
Chapter

Abstract

We return to the question of the existence of a primitive function of f (x) = 1/x for x > 0 posed above. Since the function f(x) = 1/x is Lipschitz continuous on any given interval [a, b] with 0 < a < b, we know by the Fundamental Theorem that there is a unique function u(x) which satisfies u′(x) = 1/x for a ≤ x ≤ b and takes on a specific value at some point in [a, b], for example u(1) = 0. Since a > 0 may be chosen as small as we please and b as large as we please, we may consider the function u(x) to be defined for x > 0.

Keywords

Expense 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kenneth Eriksson
    • 1
  • Donald Estep
    • 2
  • Claes Johnson
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.Department of MathematicsColorado State UniversityFort CollinsUSA

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