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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

Unique Function Fundamental Theorem Multilinear Algebra Mechanical Difference Primitive Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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