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Continuity and limits

  • M. H. Protter
  • C. B. MorreyJr.
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Most of the functions we study in elementary calculus are described by simple formulas. These functions almost always possess derivatives and, in fact, a portion of any first course in calculus is devoted to the development of routine methods for computing derivatives. However, not all functions possess derivatives everywhere. For example, the functions (1 + x2)/x, cot x, and sin(1/x) do not possess derivatives at x = 0 no matter how they are defined at x = 0.

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • M. H. Protter
    • 1
  • C. B. MorreyJr.
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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